Search | arXiv e-print repository

<!DOCTYPE html> <html lang="en"> <head> <meta charset="utf-8"/> <meta name="viewport" content="width=device-width, initial-scale=1"/>  <link rel="apple-touch-icon" sizes="180x180" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/apple-touch-icon.png"> <link rel="icon" type="image/png" sizes="32x32" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/favicon-32x32.png"> <link rel="icon" type="image/png" sizes="16x16" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/favicon-16x16.png"> <link rel="manifest" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/site.webmanifest"> <link rel="mask-icon" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/safari-pinned-tab.svg" color="#b31b1b"> <link rel="shortcut icon" href="https://static.arxiv.org/static/base/1.0.0a5/images/icons/favicon.ico"> <meta name="msapplication-TileColor" content="#b31b1b"> <meta name="msapplication-config" content="images/icons/browserconfig.xml"> <meta name="theme-color" content="#b31b1b">  <title>Search | arXiv e-print repository</title> <script defer src="https://static.arxiv.org/static/base/1.0.0a5/fontawesome-free-5.11.2-web/js/all.js"></script> <link rel="stylesheet" href="https://static.arxiv.org/static/base/1.0.0a5/css/arxivstyle.css" /> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ messageStyle: "none", extensions: ["tex2jax.js"], jax: ["input/TeX", "output/HTML-CSS"], tex2jax: { inlineMath: [ ['$','$'], ["\$","\$"] ], displayMath: [ ['$$','$$'], ["\\[","\\]"] ], processEscapes: true, ignoreClass: '.*', processClass: 'mathjax.*' }, TeX: { extensions: ["AMSmath.js", "AMSsymbols.js", "noErrors.js"], noErrors: { inlineDelimiters: ["$","$"], multiLine: false, style: { "font-size": "normal", "border": "" } } }, "HTML-CSS": { availableFonts: ["TeX"] } }); </script> <script src='//static.arxiv.org/MathJax-2.7.3/MathJax.js'></script> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/notification.js"></script> <link rel="stylesheet" href="https://static.arxiv.org/static/search/0.5.6/css/bulma-tooltip.min.css" /> <link rel="stylesheet" href="https://static.arxiv.org/static/search/0.5.6/css/search.css" /> <script src="https://code.jquery.com/jquery-3.2.1.slim.min.js" integrity="sha256-k2WSCIexGzOj3Euiig+TlR8gA0EmPjuc79OEeY5L45g=" crossorigin="anonymous"></script> <script src="https://static.arxiv.org/static/search/0.5.6/js/fieldset.js"></script> <style> radio#cf-customfield_11400 { display: none; } </style> </head> <body> <header><a href="#main-container" class="is-sr-only">Skip to main content</a>  <div class="attribution level is-marginless" role="banner"> <div class="level-left"> <a class="level-item" href="https://cornell.edu/"><img src="https://static.arxiv.org/static/base/1.0.0a5/images/cornell-reduced-white-SMALL.svg" alt="Cornell University" width="200" aria-label="logo" /></a> </div> <div class="level-right is-marginless"><p class="sponsors level-item is-marginless"><span id="support-ack-url">We gratefully acknowledge support from<br /> the Simons Foundation, <a href="https://info.arxiv.org/about/ourmembers.html">member institutions</a>, and all contributors. <a href="https://info.arxiv.org/about/donate.html">Donate</a></span></p></div> </div>  <div class="identity level is-marginless"> <div class="level-left"> <div class="level-item"> <a class="arxiv" href="https://arxiv.org/" aria-label="arxiv-logo"> <img src="https://static.arxiv.org/static/base/1.0.0a5/images/arxiv-logo-one-color-white.svg" aria-label="logo" alt="arxiv logo" width="85" style="width:85px;"/> </a> </div> </div> <div class="search-block level-right"> <form class="level-item mini-search" method="GET" action="https://arxiv.org/search"> <div class="field has-addons"> <div class="control"> <input class="input is-small" type="text" name="query" placeholder="Search..." aria-label="Search term or terms" /> <p class="help"><a href="https://info.arxiv.org/help">Help</a> | <a href="https://arxiv.org/search/advanced">Advanced Search</a></p> </div> <div class="control"> <div class="select is-small"> <select name="searchtype" aria-label="Field to search"> <option value="all" selected="selected">All fields</option> <option value="title">Title</option> <option value="author">Author</option> <option value="abstract">Abstract</option> <option value="comments">Comments</option> <option value="journal_ref">Journal reference</option> <option value="acm_class">ACM classification</option> <option value="msc_class">MSC classification</option> <option value="report_num">Report number</option> <option value="paper_id">arXiv identifier</option> <option value="doi">DOI</option> <option value="orcid">ORCID</option> <option value="author_id">arXiv author ID</option> <option value="help">Help pages</option> <option value="full_text">Full text</option> </select> </div> </div> <input type="hidden" name="source" value="header"> <button class="button is-small is-cul-darker">Search</button> </div> </form> </div> </div>  <div class="container"> <div class="user-tools is-size-7 has-text-right has-text-weight-bold" role="navigation" aria-label="User menu"> <a href="https://arxiv.org/login">Login</a> </div> </div> </header> <main class="container" id="main-container"> <div class="level is-marginless"> <div class="level-left"> <h1 class="title is-clearfix"> Showing 1–50 of 130 results for author: <span class="mathjax">Christ, N</span> </h1> </div> <div class="level-right is-hidden-mobile">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> <div class="content"> <form method="GET" action="/search/hep-lat" aria-role="search"> Searching in archive <strong>hep-lat</strong>. <a href="/search/?searchtype=author&query=Christ%2C+N">Search in all archives.</a> <div class="field has-addons-tablet"> <div class="control is-expanded"> <label for="query" class="hidden-label">Search term or terms</label> <input class="input is-medium" id="query" name="query" placeholder="Search term..." type="text" value="Christ, N"> </div> <div class="select control is-medium"> <label class="is-hidden" for="searchtype">Field</label> <select class="is-medium" id="searchtype" name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> </div> <div class="control"> <button class="button is-link is-medium">Search</button> </div> </div> <div class="field"> <div class="control is-size-7"> <label class="radio"> <input checked id="abstracts-0" name="abstracts" type="radio" value="show"> Show abstracts </label> <label class="radio"> <input id="abstracts-1" name="abstracts" type="radio" value="hide"> Hide abstracts </label> </div> </div> <div class="is-clearfix" style="height: 2.5em"> <div class="is-pulled-right"> <a href="/search/advanced?terms-0-term=Christ%2C+N&terms-0-field=author&size=50&order=-announced_date_first">Advanced Search</a> </div> </div> <input type="hidden" name="order" value="-announced_date_first"> <input type="hidden" name="size" value="50"> </form> <div class="level breathe-horizontal"> <div class="level-left"> <form method="GET" action="/search/"> <div style="display: none;"> <select id="searchtype" name="searchtype"><option value="all">All fields</option><option value="title">Title</option><option selected value="author">Author(s)</option><option value="abstract">Abstract</option><option value="comments">Comments</option><option value="journal_ref">Journal reference</option><option value="acm_class">ACM classification</option><option value="msc_class">MSC classification</option><option value="report_num">Report number</option><option value="paper_id">arXiv identifier</option><option value="doi">DOI</option><option value="orcid">ORCID</option><option value="license">License (URI)</option><option value="author_id">arXiv author ID</option><option value="help">Help pages</option><option value="full_text">Full text</option></select> <input id="query" name="query" type="text" value="Christ, N"> <ul id="abstracts"><li><input checked id="abstracts-0" name="abstracts" type="radio" value="show"> <label for="abstracts-0">Show abstracts</label></li><li><input id="abstracts-1" name="abstracts" type="radio" value="hide"> <label for="abstracts-1">Hide abstracts</label></li></ul> </div> <div class="box field is-grouped is-grouped-multiline level-item"> <div class="control"> <span class="select is-small"> <select id="size" name="size"><option value="25">25</option><option selected value="50">50</option><option value="100">100</option><option value="200">200</option></select> </span> <label for="size">results per page</label>. </div> <div class="control"> <label for="order">Sort results by</label> <span class="select is-small"> <select id="order" name="order"><option selected value="-announced_date_first">Announcement date (newest first)</option><option value="announced_date_first">Announcement date (oldest first)</option><option value="-submitted_date">Submission date (newest first)</option><option value="submitted_date">Submission date (oldest first)</option><option value="">Relevance</option></select> </span> </div> <div class="control"> <button class="button is-small is-link">Go</button> </div> </div> </form> </div> </div> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Christ%2C+N&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Christ%2C+N&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Christ%2C+N&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> <li> <a href="/search/?searchtype=author&query=Christ%2C+N&start=100" class="pagination-link " aria-label="Page 3" aria-current="page">3 </a> </li> </ul> </nav> <ol class="breathe-horizontal" start="1"> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2409.11379">arXiv:2409.11379</a> <span> [<a href="https://arxiv.org/pdf/2409.11379">pdf</a>, <a href="https://arxiv.org/format/2409.11379">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Bootstrap-determined p-values in Lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Eranki%2C+R">Rajiv Eranki</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">Christopher Kelly</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2409.11379v1-abstract-short" style="display: inline;"> We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p-value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.11379v1-abstract-full').style.display = 'inline'; document.getElementById('2409.11379v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2409.11379v1-abstract-full" style="display: none;"> We present a general method to determine the probability that stochastic Monte Carlo data, in particular those generated in a lattice QCD calculation, would have been obtained were that data drawn from the distribution predicted by a given theoretical hypothesis. Such a probability, or p-value, is often used as an important heuristic measure of the validity of that hypothesis. The proposed method offers the benefit that it remains usable in cases where the standard Hotelling $T^2$ methods based on the conventional $蠂^2$ statistic do not apply, such as for uncorrelated fits. Specifically, we analyze a general alternative to the correlated $蠂^2$ statistic referred to as $q^2$, and show how to use the bootstrap as a data-driven method to determine the expected distribution of $q^2$ for a given hypothesis with minimal assumptions. This distribution can then be used to determine the p-value for a fit to the data. We also describe a bootstrap approach for quantifying the impact upon this p-value of estimating population parameters from a single ensemble of $N$ samples. The overall method is accurate up to a $1/N$ bias which we do not attempt to quantify. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2409.11379v1-abstract-full').style.display = 'none'; document.getElementById('2409.11379v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 September, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">46 pages, 22 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2406.07447">arXiv:2406.07447</a> <span> [<a href="https://arxiv.org/pdf/2406.07447">pdf</a>, <a href="https://arxiv.org/format/2406.07447">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Calculating the two-photon exchange contribution to $K_L\rightarrow渭^+渭^-$ decay </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Chao%2C+E">En-Hung Chao</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2406.07447v1-abstract-short" style="display: inline;"> We present a theoretical framework within which both the real and imaginary parts of the complex, two-photon exchange amplitude contributing to $K_L\rightarrow渭^+渭^-$ decay can be calculated using lattice QCD. The real part of this two-photon amplitude is of approximately the same size as that coming from a second-order weak strangeness-changing neutral-current process. Thus a test of the standard… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.07447v1-abstract-full').style.display = 'inline'; document.getElementById('2406.07447v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2406.07447v1-abstract-full" style="display: none;"> We present a theoretical framework within which both the real and imaginary parts of the complex, two-photon exchange amplitude contributing to $K_L\rightarrow渭^+渭^-$ decay can be calculated using lattice QCD. The real part of this two-photon amplitude is of approximately the same size as that coming from a second-order weak strangeness-changing neutral-current process. Thus a test of the standard model prediction for this second-order weak process depends on an accurate result of this two-photon amplitude. A limiting factor of our proposed method comes from low-energy three-particle $蟺蟺纬$ states. The contribution from these states will be significantly distorted by the finite volume of our calculation -- a distortion for which there is no available correction. However, a simple estimate of the contribution of these three-particle states suggests their contribution to be at most a few percent allowing their neglect in a lattice calculation with a 10% target accuracy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2406.07447v1-abstract-full').style.display = 'none'; document.getElementById('2406.07447v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 June, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">31 pages, 10 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2402.08915">arXiv:2402.08915</a> <span> [<a href="https://arxiv.org/pdf/2402.08915">pdf</a>, <a href="https://arxiv.org/format/2402.08915">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Lattice calculation of electromagnetic corrections to $K\ell3$ decay </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+T">Tianle Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2402.08915v1-abstract-short" style="display: inline;"> We describe a first-principles method to apply lattice QCD to compute the order $伪_{\mathrm{EM}}$ corrections to $K\to蟺\ell谓_\ell$ decay. This method formulates the calculation in infinite volume with the conventional infinite-volume, continuum treatment of QED. Infinite volume reconstruction is used to replace the QCD components of the calculation with finite-volume amplitudes which can be comput… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.08915v1-abstract-full').style.display = 'inline'; document.getElementById('2402.08915v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2402.08915v1-abstract-full" style="display: none;"> We describe a first-principles method to apply lattice QCD to compute the order $伪_{\mathrm{EM}}$ corrections to $K\to蟺\ell谓_\ell$ decay. This method formulates the calculation in infinite volume with the conventional infinite-volume, continuum treatment of QED. Infinite volume reconstruction is used to replace the QCD components of the calculation with finite-volume amplitudes which can be computed in Euclidean space using lattice QCD, introducing finite-volume errors which vanish exponentially as the volume used in the QCD calculation is increased. This approach has also been described in an appendix to the recent paper: arXiv:2304.08026. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2402.08915v1-abstract-full').style.display = 'none'; document.getElementById('2402.08915v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 February, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, 1 figure, presented at the 40th International Symposium on Lattice Field Theory, (LATTICE2023), July 31st - August 4th, 2023, Fermilab, Batavia, Illinois, USA</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2401.13226">arXiv:2401.13226</a> <span> [<a href="https://arxiv.org/pdf/2401.13226">pdf</a>, <a href="https://arxiv.org/format/2401.13226">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Riemannian Manifold HMC with fermions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2401.13226v1-abstract-short" style="display: inline;"> We report on our study of the Riemannian Manifold HMC (RMHMC) algorithm with the mass term for the gauge momenta replaced by rational functions of the gauge covariant Laplace operator. A comparison of HMC and RMHMC on a 2+1+1 flavor dynamical ensemble with lattice spacing a ~0.05fm shows increased rate of change in long distance modes, identified by Wilson flowed energy, per fermion molecular dyna… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.13226v1-abstract-full').style.display = 'inline'; document.getElementById('2401.13226v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2401.13226v1-abstract-full" style="display: none;"> We report on our study of the Riemannian Manifold HMC (RMHMC) algorithm with the mass term for the gauge momenta replaced by rational functions of the gauge covariant Laplace operator. A comparison of HMC and RMHMC on a 2+1+1 flavor dynamical ensemble with lattice spacing a ~0.05fm shows increased rate of change in long distance modes, identified by Wilson flowed energy, per fermion molecular dynamics step. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2401.13226v1-abstract-full').style.display = 'none'; document.getElementById('2401.13226v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 January, 2024; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2024. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermilab, Batavia, Illinois, USA</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2312.01224">arXiv:2312.01224</a> <span> [<a href="https://arxiv.org/pdf/2312.01224">pdf</a>, <a href="https://arxiv.org/format/2312.01224">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> $K_{\rm L}\rightarrow渭^+渭^-$ from lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Chao%2C+E">En-Hung Chao</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2312.01224v2-abstract-short" style="display: inline;"> We propose a lattice-QCD-suitable framework for computing the two-photon long-distance contribution to the complex $K_{\rm L}\rightarrow渭^+渭^-$ decay amplitude, where QED is treated perturbatively in the continuum and infinite-volume. We provide preliminary numerical results on the quark-connected diagrams on one ensemble at physical pion mass from this method, with well-controlled systematic erro… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.01224v2-abstract-full').style.display = 'inline'; document.getElementById('2312.01224v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2312.01224v2-abstract-full" style="display: none;"> We propose a lattice-QCD-suitable framework for computing the two-photon long-distance contribution to the complex $K_{\rm L}\rightarrow渭^+渭^-$ decay amplitude, where QED is treated perturbatively in the continuum and infinite-volume. We provide preliminary numerical results on the quark-connected diagrams on one ensemble at physical pion mass from this method, with well-controlled systematic errors. The successful application of this method will allow the determination of the dispersive part of the aforementioned contribution from first-principles and enable a meaningful comparison between the Standard-Model prediction and experiment. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2312.01224v2-abstract-full').style.display = 'none'; document.getElementById('2312.01224v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 2 December, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">contribution to the 40th International Symposium on Lattice Field Theory, Lattice 2023, Fermi National Accelerator Laboratory; references added</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2311.02923">arXiv:2311.02923</a> <span> [<a href="https://arxiv.org/pdf/2311.02923">pdf</a>, <a href="https://arxiv.org/format/2311.02923">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Workshop summary -- Kaons@CERN 2023 </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Anzivino%2C+G">G. Anzivino</a>, <a href="/search/hep-lat?searchtype=author&query=Cuendis%2C+S+A">S. Arguedas Cuendis</a>, <a href="/search/hep-lat?searchtype=author&query=Bernard%2C+V">V. Bernard</a>, <a href="/search/hep-lat?searchtype=author&query=Bijnens%2C+J">J. Bijnens</a>, <a href="/search/hep-lat?searchtype=author&query=Bloch-Devaux%2C+B">B. Bloch-Devaux</a>, <a href="/search/hep-lat?searchtype=author&query=Bordone%2C+M">M. Bordone</a>, <a href="/search/hep-lat?searchtype=author&query=Brizioli%2C+F">F. Brizioli</a>, <a href="/search/hep-lat?searchtype=author&query=Brod%2C+J">J. Brod</a>, <a href="/search/hep-lat?searchtype=author&query=Camalich%2C+J+M">J. M. Camalich</a>, <a href="/search/hep-lat?searchtype=author&query=Ceccucci%2C+A">A. Ceccucci</a>, <a href="/search/hep-lat?searchtype=author&query=Cenci%2C+P">P. Cenci</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Colangelo%2C+G">G. Colangelo</a>, <a href="/search/hep-lat?searchtype=author&query=Cornella%2C+C">C. Cornella</a>, <a href="/search/hep-lat?searchtype=author&query=Crivellin%2C+A">A. Crivellin</a>, <a href="/search/hep-lat?searchtype=author&query=D%27Ambrosio%2C+G">G. D'Ambrosio</a>, <a href="/search/hep-lat?searchtype=author&query=Deppisch%2C+F+F">F. F. Deppisch</a>, <a href="/search/hep-lat?searchtype=author&query=Dery%2C+A">A. Dery</a>, <a href="/search/hep-lat?searchtype=author&query=Dettori%2C+F">F. Dettori</a>, <a href="/search/hep-lat?searchtype=author&query=Di+Carlo%2C+M">M. Di Carlo</a>, <a href="/search/hep-lat?searchtype=author&query=D%C3%B6brich%2C+B">B. D枚brich</a>, <a href="/search/hep-lat?searchtype=author&query=Engelfried%2C+J">J. Engelfried</a>, <a href="/search/hep-lat?searchtype=author&query=Fantechi%2C+R">R. Fantechi</a>, <a href="/search/hep-lat?searchtype=author&query=Gonz%C3%A1lez-Alonso%2C+M">M. Gonz谩lez-Alonso</a>, <a href="/search/hep-lat?searchtype=author&query=Gorbahn%2C+M">M. Gorbahn</a> , et al. (38 additional authors not shown) </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2311.02923v3-abstract-short" style="display: inline;"> Kaon physics is at a turning point -- while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical develo… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.02923v3-abstract-full').style.display = 'inline'; document.getElementById('2311.02923v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2311.02923v3-abstract-full" style="display: none;"> Kaon physics is at a turning point -- while the rare-kaon experiments NA62 and KOTO are in full swing, the end of their lifetime is approaching and the future experimental landscape needs to be defined. With HIKE, KOTO-II and LHCb-Phase-II on the table and under scrutiny, it is a very good moment in time to take stock and contemplate about the opportunities these experiments and theoretical developments provide for particle physics in the coming decade and beyond. This paper provides a compact summary of talks and discussions from the Kaons@CERN 2023 workshop. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2311.02923v3-abstract-full').style.display = 'none'; document.getElementById('2311.02923v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 May, 2024; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 6 November, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">55 pages, Summary of Kaons@CERN 23 workshop, references updated, typos fixed, version as published in EPJC</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CERN-TH-2023-206 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2309.01193">arXiv:2309.01193</a> <span> [<a href="https://arxiv.org/pdf/2309.01193">pdf</a>, <a href="https://arxiv.org/ps/2309.01193">ps</a>, <a href="https://arxiv.org/format/2309.01193">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Long-distance contribution to $蔚_K$ from lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Bai%2C+Z">Ziyuan Bai</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Karpie%2C+J+M">Joseph M. Karpie</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Soni%2C+A">Amarjit Soni</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+B">Bigeng Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2309.01193v1-abstract-short" style="display: inline;"> A lattice QCD approach to the calculation of the long-distance contributions to $蔚_K$ is presented. This parameter describes indirect CP violation in $K\to蟺蟺$ decay. While the short-distance contribution to $蔚_K$ can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, $B_K$, there is a long-distance part which is estimated to be approximately $5\%$… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.01193v1-abstract-full').style.display = 'inline'; document.getElementById('2309.01193v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2309.01193v1-abstract-full" style="display: none;"> A lattice QCD approach to the calculation of the long-distance contributions to $蔚_K$ is presented. This parameter describes indirect CP violation in $K\to蟺蟺$ decay. While the short-distance contribution to $蔚_K$ can be accurately calculated in terms of standard model parameters and a single hadronic matrix element, $B_K$, there is a long-distance part which is estimated to be approximately $5\%$ of the total and is more difficult to determine. A method for determining this small but phenomenologically important contribution to $蔚_K$ using lattice QCD is proposed and a complete exploratory calculation of the contribution is presented. This exploratory calculation uses an unphysical light quark mass corresponding to a 339 MeV pion mass and an unphysical charm quark mass of 968 MeV, expressed in the $\overline{\mathrm{MS}}$ scheme at 2 GeV. This calculation demonstrates that future work should be able to determine this long-distance contribution from first principles with a controlled error of 10\% or less. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2309.01193v1-abstract-full').style.display = 'none'; document.getElementById('2309.01193v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 September, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2304.08026">arXiv:2304.08026</a> <span> [<a href="https://arxiv.org/pdf/2304.08026">pdf</a>, <a href="https://arxiv.org/ps/2304.08026">ps</a>, <a href="https://arxiv.org/format/2304.08026">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.108.014501">10.1103/PhysRevD.108.014501 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Radiative corrections to leptonic decays using infinite-volume reconstruction </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Lu-Chang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+T">Tianle Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2304.08026v1-abstract-short" style="display: inline;"> Lattice QCD calculations of leptonic decay constants have now reached sub-percent precision so that isospin-breaking corrections, including QED effects, must be included to fully exploit this precision in determining fundamental quantities, in particular the elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, from experimental measurements. A number of collaborations have performed, or are per… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.08026v1-abstract-full').style.display = 'inline'; document.getElementById('2304.08026v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2304.08026v1-abstract-full" style="display: none;"> Lattice QCD calculations of leptonic decay constants have now reached sub-percent precision so that isospin-breaking corrections, including QED effects, must be included to fully exploit this precision in determining fundamental quantities, in particular the elements of the Cabibbo-Kobayashi-Maskawa (CKM) matrix, from experimental measurements. A number of collaborations have performed, or are performing, such computations. In this paper we develop a new theoretical framework, based on Infinite-Volume Reconstruction (IVR), for the computation of electromagnetic corrections to leptonic decay widths. In this method, the hadronic correlation functions are first processed theoretically in infinite volume, in such a way that the required matrix elements can be determined non-perturbatively from lattice QCD computations with finite-volume uncertainties which are exponentially small in the volume. The cancellation of infrared divergences in this framework is performed fully analytically. We also outline how this IVR treatment can be extended to determine the QED effects in semi-leptonic kaon decays with a similar degree of accuracy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.08026v1-abstract-full').style.display = 'none'; document.getElementById('2304.08026v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2023. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2304.04423">arXiv:2304.04423</a> <span> [<a href="https://arxiv.org/pdf/2304.04423">pdf</a>, <a href="https://arxiv.org/format/2304.04423">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Hadronic light-by-light contribution to the muon anomaly from lattice QCD with infinite volume QED at physical pion mass </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Tu%2C+C">Cheng Tu</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2304.04423v1-abstract-short" style="display: inline;"> The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment, $(g-2$)/2, is computed in the infinite volume QED framework with lattice QCD. We report $a_渭^\text{HLbL}=12.47(1.15)(0.99) \times 10^{-10}$ where the first error is statistical and the second systematic. The result is mainly based on the 2+1 flavor M枚bius domain wall fermion ensemble with inverse lattice spa… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.04423v1-abstract-full').style.display = 'inline'; document.getElementById('2304.04423v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2304.04423v1-abstract-full" style="display: none;"> The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment, $(g-2$)/2, is computed in the infinite volume QED framework with lattice QCD. We report $a_渭^\text{HLbL}=12.47(1.15)(0.99) \times 10^{-10}$ where the first error is statistical and the second systematic. The result is mainly based on the 2+1 flavor M枚bius domain wall fermion ensemble with inverse lattice spacing $a^{-1} = 1.73~\mathrm{GeV}$, lattice size $L=5.5~\mathrm{fm}$, and $m_蟺= 139~\mathrm{MeV}$, generated by the RBC-UKQCD collaborations. The leading systematic error of this result comes from the lattice discretization. This result is consistent with previous determinations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2304.04423v1-abstract-full').style.display = 'none'; document.getElementById('2304.04423v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 10 April, 2023; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2023. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">29 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2209.10758">arXiv:2209.10758</a> <span> [<a href="https://arxiv.org/pdf/2209.10758">pdf</a>, <a href="https://arxiv.org/format/2209.10758">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Theory">hep-th</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> </div> <p class="title is-5 mathjax"> Report of the Snowmass 2021 Topical Group on Lattice Gauge Theory </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Davoudi%2C+Z">Zohreh Davoudi</a>, <a href="/search/hep-lat?searchtype=author&query=Neil%2C+E+T">Ethan T. Neil</a>, <a href="/search/hep-lat?searchtype=author&query=Bauer%2C+C+W">Christian W. Bauer</a>, <a href="/search/hep-lat?searchtype=author&query=Bhattacharya%2C+T">Tanmoy Bhattacharya</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P">Peter Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Brower%2C+R+C">Richard C. Brower</a>, <a href="/search/hep-lat?searchtype=author&query=Catterall%2C+S">Simon Catterall</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Cirigliano%2C+V">Vincenzo Cirigliano</a>, <a href="/search/hep-lat?searchtype=author&query=Colangelo%2C+G">Gilberto Colangelo</a>, <a href="/search/hep-lat?searchtype=author&query=DeTar%2C+C">Carleton DeTar</a>, <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">William Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Edwards%2C+R+G">Robert G. Edwards</a>, <a href="/search/hep-lat?searchtype=author&query=El-Khadra%2C+A+X">Aida X. El-Khadra</a>, <a href="/search/hep-lat?searchtype=author&query=Gottlieb%2C+S">Steven Gottlieb</a>, <a href="/search/hep-lat?searchtype=author&query=Gupta%2C+R">Rajan Gupta</a>, <a href="/search/hep-lat?searchtype=author&query=Hackett%2C+D+C">Daniel C. Hackett</a>, <a href="/search/hep-lat?searchtype=author&query=Hasenfratz%2C+A">Anna Hasenfratz</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jay%2C+W+I">William I. Jay</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">Christopher Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Kronfeld%2C+A+S">Andreas S. Kronfeld</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> , et al. (13 additional authors not shown) </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2209.10758v1-abstract-short" style="display: inline;"> Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.10758v1-abstract-full').style.display = 'inline'; document.getElementById('2209.10758v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2209.10758v1-abstract-full" style="display: none;"> Lattice gauge theory continues to be a powerful theoretical and computational approach to simulating strongly interacting quantum field theories, whose applications permeate almost all disciplines of modern-day research in High-Energy Physics. Whether it is to enable precision quark- and lepton-flavor physics, to uncover signals of new physics in nucleons and nuclei, to elucidate hadron structure and spectrum, to serve as a numerical laboratory to reach beyond the Standard Model, or to invent and improve state-of-the-art computational paradigms, the lattice-gauge-theory program is in a prime position to impact the course of developments and enhance discovery potential of a vibrant experimental program in High-Energy Physics over the coming decade. This projection is based on abundant successful results that have emerged using lattice gauge theory over the years: on continued improvement in theoretical frameworks and algorithmic suits; on the forthcoming transition into the exascale era of high-performance computing; and on a skillful, dedicated, and organized community of lattice gauge theorists in the U.S. and worldwide. The prospects of this effort in pushing the frontiers of research in High-Energy Physics have recently been studied within the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021), and the conclusions are summarized in this Topical Report. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2209.10758v1-abstract-full').style.display = 'none'; document.getElementById('2209.10758v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 September, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">57 pages, 1 figure. Submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021). Topical Group Report for TF05 - Lattice Gauge Theory</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> UMD-PP-022-08, LA-UR-22-29361, FERMILAB-CONF-22-703-T </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2208.03834">arXiv:2208.03834</a> <span> [<a href="https://arxiv.org/pdf/2208.03834">pdf</a>, <a href="https://arxiv.org/format/2208.03834">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.130.191901">10.1103/PhysRevLett.130.191901 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Lattice QCD calculation of $蟺^0\rightarrow e^+ e^-$ decay </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Tu%2C+C">Cheng Tu</a>, <a href="/search/hep-lat?searchtype=author&query=Zhao%2C+Y">Yidi Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2208.03834v2-abstract-short" style="display: inline;"> We extend the application of lattice QCD to the two-photon-mediated, order $伪^2$ rare decay $蟺^0\rightarrow e^+ e^-$. By combining Minkowski- and Euclidean-space methods we are able to calculate the complex amplitude describing this decay directly from the underlying theories (QCD and QED) which predict this decay. The leading connected and disconnected diagrams are considered; a continuum limit i… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.03834v2-abstract-full').style.display = 'inline'; document.getElementById('2208.03834v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2208.03834v2-abstract-full" style="display: none;"> We extend the application of lattice QCD to the two-photon-mediated, order $伪^2$ rare decay $蟺^0\rightarrow e^+ e^-$. By combining Minkowski- and Euclidean-space methods we are able to calculate the complex amplitude describing this decay directly from the underlying theories (QCD and QED) which predict this decay. The leading connected and disconnected diagrams are considered; a continuum limit is evaluated and the systematic errors are estimated. We find $\mathrm{Re} \mathcal{A} = 18.60(1.19)(1.04)\,$eV, $\mathrm{Im} \mathcal{A} = 32.59(1.50)(1.65)\,$eV, a more accurate value for the ratio $\frac{\mathrm{Re} \mathcal{A}}{\mathrm{Im} \mathcal{A}}=0.571(10)(4)$ and a result for the partial width $螕(蟺^0\to纬纬) = 6.60(0.61)(0.67)\,$eV. Here the first errors are statistical and the second systematic. This calculation is the first step in determining the more challenging, two-photon-mediated decay amplitude that contributes to the rare decay $K\to渭^+渭^-$. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2208.03834v2-abstract-full').style.display = 'none'; document.getElementById('2208.03834v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 7 August, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2022. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2207.07641">arXiv:2207.07641</a> <span> [<a href="https://arxiv.org/pdf/2207.07641">pdf</a>, <a href="https://arxiv.org/format/2207.07641">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Lattice QCD and Particle Physics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Kronfeld%2C+A+S">Andreas S. Kronfeld</a>, <a href="/search/hep-lat?searchtype=author&query=Bhattacharya%2C+T">Tanmoy Bhattacharya</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=DeTar%2C+C">Carleton DeTar</a>, <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">William Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Edwards%2C+R">Robert Edwards</a>, <a href="/search/hep-lat?searchtype=author&query=Hasenfratz%2C+A">Anna Hasenfratz</a>, <a href="/search/hep-lat?searchtype=author&query=Lin%2C+H">Huey-Wen Lin</a>, <a href="/search/hep-lat?searchtype=author&query=Mukherjee%2C+S">Swagato Mukherjee</a>, <a href="/search/hep-lat?searchtype=author&query=Orginos%2C+K">Konstantinos Orginos</a>, <a href="/search/hep-lat?searchtype=author&query=Brower%2C+R">Richard Brower</a>, <a href="/search/hep-lat?searchtype=author&query=Cirigliano%2C+V">Vincenzo Cirigliano</a>, <a href="/search/hep-lat?searchtype=author&query=Davoudi%2C+Z">Zohreh Davoudi</a>, <a href="/search/hep-lat?searchtype=author&query=J%C3%B3o%2C+B">B谩lint J贸o</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Meinel%2C+S">Stefan Meinel</a>, <a href="/search/hep-lat?searchtype=author&query=Neil%2C+E+T">Ethan T. Neil</a>, <a href="/search/hep-lat?searchtype=author&query=Petreczky%2C+P">Peter Petreczky</a>, <a href="/search/hep-lat?searchtype=author&query=Richards%2C+D+G">David G. Richards</a>, <a href="/search/hep-lat?searchtype=author&query=Bazavov%2C+A">Alexei Bazavov</a>, <a href="/search/hep-lat?searchtype=author&query=Catterall%2C+S">Simon Catterall</a>, <a href="/search/hep-lat?searchtype=author&query=Dudek%2C+J+J">Jozef J. Dudek</a>, <a href="/search/hep-lat?searchtype=author&query=El-Khadra%2C+A+X">Aida X. El-Khadra</a> , et al. (57 additional authors not shown) </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2207.07641v2-abstract-short" style="display: inline;"> Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021). </span> <span class="abstract-full has-text-grey-dark mathjax" id="2207.07641v2-abstract-full" style="display: none;"> Contribution from the USQCD Collaboration to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021). <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2207.07641v2-abstract-full').style.display = 'none'; document.getElementById('2207.07641v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 October, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 15 July, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">27 pp. main text, 4 pp. appendices, 29 pp. references, 1 p. index</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FERMILAB-CONF-22-531-T </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2204.00039">arXiv:2204.00039</a> <span> [<a href="https://arxiv.org/pdf/2204.00039">pdf</a>, <a href="https://arxiv.org/format/2204.00039">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computational Physics">physics.comp-ph</span> </div> </div> <p class="title is-5 mathjax"> Lattice QCD and the Computational Frontier </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P">Peter Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Bollweg%2C+D">Dennis Bollweg</a>, <a href="/search/hep-lat?searchtype=author&query=Brower%2C+R">Richard Brower</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=DeTar%2C+C">Carleton DeTar</a>, <a href="/search/hep-lat?searchtype=author&query=Edwards%2C+R">Robert Edwards</a>, <a href="/search/hep-lat?searchtype=author&query=Gottlieb%2C+S">Steven Gottlieb</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Joo%2C+B">Balint Joo</a>, <a href="/search/hep-lat?searchtype=author&query=Joswig%2C+F">Fabian Joswig</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">Christopher Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Kronfeld%2C+A">Andreas Kronfeld</a>, <a href="/search/hep-lat?searchtype=author&query=Lin%2C+M">Meifeng Lin</a>, <a href="/search/hep-lat?searchtype=author&query=Osborn%2C+J">James Osborn</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">Antonin Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Richings%2C+J">James Richings</a>, <a href="/search/hep-lat?searchtype=author&query=Yamaguchi%2C+A">Azusa Yamaguchi</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2204.00039v1-abstract-short" style="display: inline;"> The search for new physics requires a joint experimental and theoretical effort. Lattice QCD is already an essential tool for obtaining precise model-free theoretical predictions of the hadronic processes underlying many key experimental searches, such as those involving heavy flavor physics, the anomalous magnetic moment of the muon, nucleon-neutrino scattering, and rare, second-order electroweak… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.00039v1-abstract-full').style.display = 'inline'; document.getElementById('2204.00039v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2204.00039v1-abstract-full" style="display: none;"> The search for new physics requires a joint experimental and theoretical effort. Lattice QCD is already an essential tool for obtaining precise model-free theoretical predictions of the hadronic processes underlying many key experimental searches, such as those involving heavy flavor physics, the anomalous magnetic moment of the muon, nucleon-neutrino scattering, and rare, second-order electroweak processes. As experimental measurements become more precise over the next decade, lattice QCD will play an increasing role in providing the needed matching theoretical precision. Achieving the needed precision requires simulations with lattices with substantially increased resolution. As we push to finer lattice spacing we encounter an array of new challenges. They include algorithmic and software-engineering challenges, challenges in computer technology and design, and challenges in maintaining the necessary human resources. In this white paper we describe those challenges and discuss ways they are being dealt with. Overcoming them is key to supporting the community effort required to deliver the needed theoretical support for experiments in the coming decade. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2204.00039v1-abstract-full').style.display = 'none'; document.getElementById('2204.00039v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 31 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Contribution to Snowmass 2021. 22 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.15810">arXiv:2203.15810</a> <span> [<a href="https://arxiv.org/pdf/2203.15810">pdf</a>, <a href="https://arxiv.org/format/2203.15810">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Experiment">nucl-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> </div> <p class="title is-5 mathjax"> Prospects for precise predictions of $a_渭$ in the Standard Model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Colangelo%2C+G">G. Colangelo</a>, <a href="/search/hep-lat?searchtype=author&query=Davier%2C+M">M. Davier</a>, <a href="/search/hep-lat?searchtype=author&query=El-Khadra%2C+A+X">A. X. El-Khadra</a>, <a href="/search/hep-lat?searchtype=author&query=Hoferichter%2C+M">M. Hoferichter</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">C. Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Lellouch%2C+L">L. Lellouch</a>, <a href="/search/hep-lat?searchtype=author&query=Mibe%2C+T">T. Mibe</a>, <a href="/search/hep-lat?searchtype=author&query=Roberts%2C+B+L">B. L. Roberts</a>, <a href="/search/hep-lat?searchtype=author&query=Teubner%2C+T">T. Teubner</a>, <a href="/search/hep-lat?searchtype=author&query=Wittig%2C+H">H. Wittig</a>, <a href="/search/hep-lat?searchtype=author&query=Ananthanarayan%2C+B">B. Ananthanarayan</a>, <a href="/search/hep-lat?searchtype=author&query=Bashir%2C+A">A. Bashir</a>, <a href="/search/hep-lat?searchtype=author&query=Bijnens%2C+J">J. Bijnens</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">T. Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P">P. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Bray-Ali%2C+N">N. Bray-Ali</a>, <a href="/search/hep-lat?searchtype=author&query=Caprini%2C+I">I. Caprini</a>, <a href="/search/hep-lat?searchtype=author&query=Calame%2C+C+M+C">C. M. Carloni Calame</a>, <a href="/search/hep-lat?searchtype=author&query=Cat%C3%A0%2C+O">O. Cat脿</a>, <a href="/search/hep-lat?searchtype=author&query=C%C3%A8%2C+M">M. C猫</a>, <a href="/search/hep-lat?searchtype=author&query=Charles%2C+J">J. Charles</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Curciarello%2C+F">F. Curciarello</a>, <a href="/search/hep-lat?searchtype=author&query=Danilkin%2C+I">I. Danilkin</a>, <a href="/search/hep-lat?searchtype=author&query=Das%2C+D">D. Das</a> , et al. (57 additional authors not shown) </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.15810v1-abstract-short" style="display: inline;"> We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon $g-2$ Theory Initiative to update the Standard Model prediction. </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.15810v1-abstract-full" style="display: none;"> We discuss the prospects for improving the precision on the hadronic corrections to the anomalous magnetic moment of the muon, and the plans of the Muon $g-2$ Theory Initiative to update the Standard Model prediction. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.15810v1-abstract-full').style.display = 'none'; document.getElementById('2203.15810v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Contribution to the US Community Study on the Future of Particle Physics (Snowmass 2021)</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FERMILAB-CONF-22-236-T, LTH 1303, MITP-22-030 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2203.10998">arXiv:2203.10998</a> <span> [<a href="https://arxiv.org/pdf/2203.10998">pdf</a>, <a href="https://arxiv.org/ps/2203.10998">ps</a>, <a href="https://arxiv.org/format/2203.10998">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Discovering new physics in rare kaon decays </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P">Peter Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Bruno%2C+M">Mattia Bruno</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Erben%2C+F">Felix Erben</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Guelpers%2C+V">Vera Guelpers</a>, <a href="/search/hep-lat?searchtype=author&query=Hill%2C+R">Ryan Hill</a>, <a href="/search/hep-lat?searchtype=author&query=Hodgson%2C+R">Raoul Hodgson</a>, <a href="/search/hep-lat?searchtype=author&query=Hoying%2C+D">Danel Hoying</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jang%2C+Y">Yong-Chull Jang</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Karpie%2C+J">Joe Karpie</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">Christopher Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">Antonin Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C">Christopher Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Soni%2C+A">Amarjit Soni</a>, <a href="/search/hep-lat?searchtype=author&query=Tomii%2C+M">Masaaki Tomii</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+B">Bigeng Wang</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+T">Tianle Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2203.10998v1-abstract-short" style="display: inline;"> The decays and mixing of $K$ mesons are remarkably sensitive to the weak interactions of quarks and leptons at high energies. They provide important tests of the standard model at both first and second order in the Fermi constant $G_F$ and offer a window into possible new phenomena at energies as high as 1,000 TeV. These possibilities become even more compelling as the growing capabilities of latt… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.10998v1-abstract-full').style.display = 'inline'; document.getElementById('2203.10998v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2203.10998v1-abstract-full" style="display: none;"> The decays and mixing of $K$ mesons are remarkably sensitive to the weak interactions of quarks and leptons at high energies. They provide important tests of the standard model at both first and second order in the Fermi constant $G_F$ and offer a window into possible new phenomena at energies as high as 1,000 TeV. These possibilities become even more compelling as the growing capabilities of lattice QCD make high-precision standard model predictions possible. Here we discuss and attempt to forecast some of these capabilities. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2203.10998v1-abstract-full').style.display = 'none'; document.getElementById('2203.10998v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 21 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2022. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">submitted to the Rare Processes and Precision, Theory and Computational Frontiers for the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2112.04556">arXiv:2112.04556</a> <span> [<a href="https://arxiv.org/pdf/2112.04556">pdf</a>, <a href="https://arxiv.org/format/2112.04556">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Riemannian manifold hybrid Monte Carlo in lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Nguyen%2C+T">Tuan Nguyen</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P">Peter Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Jang%2C+Y">Yong-Chull Jang</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2112.04556v1-abstract-short" style="display: inline;"> Critical slowing down presents a critical obstacle to lattice QCD calculation at the smaller lattice spacings made possible by Exascale computers. Inspired by the concept of Fourier acceleration, we study a version of the Riemannian Manifold HMC (RMHMC) algorithm in which the canonical mass term of the HMC algorithm is replaced by a rational function of the SU(3) gauge covariant Laplacian. We have… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.04556v1-abstract-full').style.display = 'inline'; document.getElementById('2112.04556v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2112.04556v1-abstract-full" style="display: none;"> Critical slowing down presents a critical obstacle to lattice QCD calculation at the smaller lattice spacings made possible by Exascale computers. Inspired by the concept of Fourier acceleration, we study a version of the Riemannian Manifold HMC (RMHMC) algorithm in which the canonical mass term of the HMC algorithm is replaced by a rational function of the SU(3) gauge covariant Laplacian. We have developed a suite of tools using Chebyshev filters based on the SU(3) gauge covariant Laplacian that provides the power spectra of both the gauge and fermion forces and determines the spectral dependence of the resulting RMHMC evolution of long- and short-distance QCD observables. These tools can be used to optimize the RMHMC mass term and to monitor the resulting acceleration mode-wise. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.04556v1-abstract-full').style.display = 'none'; document.getElementById('2112.04556v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 4 figures, 2021 Lattice Proceedings</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2112.00153">arXiv:2112.00153</a> <span> [<a href="https://arxiv.org/pdf/2112.00153">pdf</a>, <a href="https://arxiv.org/format/2112.00153">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Coulomb corrections to pi-pi scattering </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Karpie%2C+J">Joseph Karpie</a>, <a href="/search/hep-lat?searchtype=author&query=Nguyen%2C+T">Tuan Nguyen</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2112.00153v2-abstract-short" style="display: inline;"> The relationship between finite volume multi-hadron energy levels and matrix elements and two particle scattering phase shifts and decays is well known, but the inclusion of long range interactions such as QED is non-trivial. Inclusion of QED is an important systematic error correction to $K\to蟺蟺$ decays. In this talk, we present a method of including a truncated, finite-range Coulomb interaction… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.00153v2-abstract-full').style.display = 'inline'; document.getElementById('2112.00153v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2112.00153v2-abstract-full" style="display: none;"> The relationship between finite volume multi-hadron energy levels and matrix elements and two particle scattering phase shifts and decays is well known, but the inclusion of long range interactions such as QED is non-trivial. Inclusion of QED is an important systematic error correction to $K\to蟺蟺$ decays. In this talk, we present a method of including a truncated, finite-range Coulomb interaction in a finite-volume lattice QCD calculation. We show how the omission caused by the truncation can be restored by an infinite-volume analytic calculation so that the final result contains no power-law finite-volume errors beyond those usually present in Luscher's finite-volume phase shift determination. This approach allows us to calculate the QED corrected infinite-volume phase shift for $蟺蟺$ scattering in Coulomb gauge, a necessary ingredient to $K\to蟺蟺$, while neglecting the transverse radiation for now. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2112.00153v2-abstract-full').style.display = 'none'; document.getElementById('2112.00153v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 December, 2021; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 30 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, 3 figures, Proceedings of the 38th International Symposium on Lattice Field Theory, 26-30 July 2021, Zoom/Gather @ MIT, USA</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2111.04668">arXiv:2111.04668</a> <span> [<a href="https://arxiv.org/pdf/2111.04668">pdf</a>, <a href="https://arxiv.org/format/2111.04668">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.106.014508">10.1103/PhysRevD.106.014508 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> $蟺-蟺$ scattering, QED and finite-volume quantization </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Karpie%2C+J">Joseph Karpie</a>, <a href="/search/hep-lat?searchtype=author&query=Nguyen%2C+T">Tuan Nguyen</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2111.04668v1-abstract-short" style="display: inline;"> Using the Coulomb gauge formulation of QED we present a lattice QCD procedure to calculate the $蟺^+蟺^+$ scattering phase shift including the effects of the Coulomb potential which appears in this formulation. The approach described here incorporates the effects of relativity and avoids finite-volume corrections that vanish as a power of the volume in which the lattice calculation is performed. Thi… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.04668v1-abstract-full').style.display = 'inline'; document.getElementById('2111.04668v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2111.04668v1-abstract-full" style="display: none;"> Using the Coulomb gauge formulation of QED we present a lattice QCD procedure to calculate the $蟺^+蟺^+$ scattering phase shift including the effects of the Coulomb potential which appears in this formulation. The approach described here incorporates the effects of relativity and avoids finite-volume corrections that vanish as a power of the volume in which the lattice calculation is performed. This is the first step in developing a complete lattice QCD calculation of the electromagnetic and isospin-breaking light-quark mass contributions to $\varepsilon'$, the parameter describing direct CP violating effects in $K_L\to蟺蟺$ decay. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2111.04668v1-abstract-full').style.display = 'none'; document.getElementById('2111.04668v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 November, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">51 pages, 10 figures</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2108.05486">arXiv:2108.05486</a> <span> [<a href="https://arxiv.org/pdf/2108.05486">pdf</a>, <a href="https://arxiv.org/format/2108.05486">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Gauge-Fixed Fourier Acceleration </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Sheta%2C+A">Ahmed Sheta</a>, <a href="/search/hep-lat?searchtype=author&query=Zhao%2C+Y">Yidi Zhao</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2108.05486v1-abstract-short" style="display: inline;"> For an asymptotically free theory, a promising strategy for eliminating Critical Slowing Down (CSD) is na茂ve Fourier acceleration. This requires the introduction of gauge-fixing into the action, in order to isolate the asymptotically decoupled Fourier modes. In this article, we present our approach and results from a gauge-fixed Fourier-accelerated hybrid Monte Carlo algorithm, using an action tha… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.05486v1-abstract-full').style.display = 'inline'; document.getElementById('2108.05486v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2108.05486v1-abstract-full" style="display: none;"> For an asymptotically free theory, a promising strategy for eliminating Critical Slowing Down (CSD) is na茂ve Fourier acceleration. This requires the introduction of gauge-fixing into the action, in order to isolate the asymptotically decoupled Fourier modes. In this article, we present our approach and results from a gauge-fixed Fourier-accelerated hybrid Monte Carlo algorithm, using an action that softly fixes the gauge links to Landau gauge. We compare the autocorrelation times with those of the pure hybrid Monte Carlo algorithm. We work on a small-volume lattice at weak coupling. We present preliminary results and obstacles from working with periodic boundary conditions, and then we present results from using fixed, equilibrated boundary links to avoid $\mathbb{Z}_3$ and other topological barriers and to anticipate applying a similar acceleration to many small cells in a large, physically-relevant lattice volume. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2108.05486v1-abstract-full').style.display = 'none'; document.getElementById('2108.05486v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 11 August, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2021. </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2103.15131">arXiv:2103.15131</a> <span> [<a href="https://arxiv.org/pdf/2103.15131">pdf</a>, <a href="https://arxiv.org/format/2103.15131">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Theory">nucl-th</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.104.114506">10.1103/PhysRevD.104.114506 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Lattice determination of $I= 0$ and 2 $蟺蟺$ scattering phase shifts with a physical pion mass </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">T. Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P+A">P. A. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Bruno%2C+M">M. Bruno</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hoying%2C+D">D. Hoying</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">C. Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">C. Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">R. D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=Meyer%2C+A+S">A. S. Meyer</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">C. T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Soni%2C+A">A. Soni</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+T">T. Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2103.15131v3-abstract-short" style="display: inline;"> Phase shifts for $s$-wave $蟺蟺$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3\times 64$. These results support our recent study of direct CP violation in $K\to蟺蟺$ decay \cite{Abbott:2020hxn}, improving our earlier 2015 calcula… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.15131v3-abstract-full').style.display = 'inline'; document.getElementById('2103.15131v3-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2103.15131v3-abstract-full" style="display: none;"> Phase shifts for $s$-wave $蟺蟺$ scattering in both the $I=0$ and $I=2$ channels are determined from a lattice QCD calculation performed on 741 gauge configurations obeying G-parity boundary conditions with a physical pion mass and lattice size of $32^3\times 64$. These results support our recent study of direct CP violation in $K\to蟺蟺$ decay \cite{Abbott:2020hxn}, improving our earlier 2015 calculation \cite{Bai:2015nea}. The phase shifts are determined for both stationary and moving $蟺蟺$ systems, at three ($I=0$) and four ($I=2$) different total momenta. We implement several $蟺蟺$ interpolating operators including a scalar bilinear "$蟽$" operator and paired single-pion bilinear operators with the constituent pions carrying various relative momenta. Several techniques, including correlated fitting and a bootstrap determination of p-values have been used to refine the results and a comparison with the generalized eigenvalue problem (GEVP) method is given. A detailed systematic error analysis is performed which allows phase shift results to be presented at a fixed energy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2103.15131v3-abstract-full').style.display = 'none'; document.getElementById('2103.15131v3-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 March, 2022; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 March, 2021; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2021. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">v3: Add a subsection "Higher partial wave correction", and correct the unit of scattering length. 88 pages and 14 figures v2: 1). Add reference 29 as an example of pipi scattering calculation above 4mpi threshold. 2). Modify the wording on page 3 for the footage. 3). Correct the 蟽operator on page 17</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CERN-TH-2021-039 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2009.08287">arXiv:2009.08287</a> <span> [<a href="https://arxiv.org/pdf/2009.08287">pdf</a>, <a href="https://arxiv.org/ps/2009.08287">ps</a>, <a href="https://arxiv.org/format/2009.08287">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.103.014507">10.1103/PhysRevD.103.014507 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Finite-volume effects in long-distance processes with massless leptonic propagators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Lu-Chang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2009.08287v1-abstract-short" style="display: inline;"> In Ref. [1], a method was proposed to calculate QED corrections to hadronic self energies from lattice QCD without power-law finite-volume errors. In this paper, we extend the method to processes which occur at second-order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. We demonstrate that, in spite of the presence of the propagator of an almost… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.08287v1-abstract-full').style.display = 'inline'; document.getElementById('2009.08287v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2009.08287v1-abstract-full" style="display: none;"> In Ref. [1], a method was proposed to calculate QED corrections to hadronic self energies from lattice QCD without power-law finite-volume errors. In this paper, we extend the method to processes which occur at second-order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decay $K^+\to蟺^+谓\bar谓$ from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2009.08287v1-abstract-full').style.display = 'none'; document.getElementById('2009.08287v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 17 September, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">21 pages, 3 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 103, 014507 (2021) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2004.09440">arXiv:2004.09440</a> <span> [<a href="https://arxiv.org/pdf/2004.09440">pdf</a>, <a href="https://arxiv.org/format/2004.09440">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.102.054509">10.1103/PhysRevD.102.054509 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Direct CP violation and the $螖I=1/2$ rule in $K\to蟺蟺$ decay from the Standard Model </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Abbott%2C+R">Ryan Abbott</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P+A">Peter A. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Bruno%2C+M">Mattia Bruno</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hoying%2C+D">Daniel Hoying</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">Christopher Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">Robert D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">David J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Soni%2C+A">Amarjit Soni</a>, <a href="/search/hep-lat?searchtype=author&query=Tomii%2C+M">Masaaki Tomii</a>, <a href="/search/hep-lat?searchtype=author&query=Wang%2C+T">Tianle Wang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2004.09440v2-abstract-short" style="display: inline;"> We present a lattice QCD calculation of the $螖I=1/2$, $K\to蟺蟺$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\to蟺蟺$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.09440v2-abstract-full').style.display = 'inline'; document.getElementById('2004.09440v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2004.09440v2-abstract-full" style="display: none;"> We present a lattice QCD calculation of the $螖I=1/2$, $K\to蟺蟺$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\to蟺蟺$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $蟺蟺$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find ${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and ${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ${\rm Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain ${\rm Re}(\varepsilon'/\varepsilon)=21.7(2.6)(6.2)(5.0) \times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2) = 19.9(2.3)(4.4)$. The first agrees well with the experimental result of ${\rm Re}(\varepsilon'/\varepsilon)=16.6(2.3)\times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2) = 22.45(6)$, demonstrates the Standard Model origin of this "$螖I = 1/2$ rule" enhancement. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2004.09440v2-abstract-full').style.display = 'none'; document.getElementById('2004.09440v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 November, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 April, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Updated to published version. 95 pages, 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> CERN-TH-2020-058, MIT-CTP/5197 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 102, 054509 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/2001.05642">arXiv:2001.05642</a> <span> [<a href="https://arxiv.org/pdf/2001.05642">pdf</a>, <a href="https://arxiv.org/format/2001.05642">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Calculating the Two-photon Contribution to $蟺^0 \rightarrow e^+ e^-$ Decay Amplitude </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Tu%2C+C">Cheng Tu</a>, <a href="/search/hep-lat?searchtype=author&query=Zhao%2C+Y">Yidi Zhao</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="2001.05642v1-abstract-short" style="display: inline;"> We develop a new method that allows us to deal with two-photon intermediate states in a lattice QCD calculation. We apply this method to perform a first-principles calculation of the $蟺^0 \rightarrow e^+ e^-$ decay amplitude. Both the real and imaginary parts of amplitude are calculated. The imaginary part is compared with the prediction of optical theorem to demonstrate the effectiveness of this… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.05642v1-abstract-full').style.display = 'inline'; document.getElementById('2001.05642v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="2001.05642v1-abstract-full" style="display: none;"> We develop a new method that allows us to deal with two-photon intermediate states in a lattice QCD calculation. We apply this method to perform a first-principles calculation of the $蟺^0 \rightarrow e^+ e^-$ decay amplitude. Both the real and imaginary parts of amplitude are calculated. The imaginary part is compared with the prediction of optical theorem to demonstrate the effectiveness of this method. Our result for the real part of decay amplitude is $19.68(52)(1.10) \ \text{eV}$, where the first error is statistical and the second is systematic. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('2001.05642v1-abstract-full').style.display = 'none'; document.getElementById('2001.05642v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 15 January, 2020; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2020. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 4 figures, Proceedings of the 37th Annual International Symposium on Lattice Field Theory (Lattice 2019), 16-22 June 2019, Wuhan, China</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1911.08123">arXiv:1911.08123</a> <span> [<a href="https://arxiv.org/pdf/1911.08123">pdf</a>, <a href="https://arxiv.org/format/1911.08123">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.124.132002">10.1103/PhysRevLett.124.132002 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1911.08123v2-abstract-short" style="display: inline;"> We report the first result for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment with all errors systematically controlled. Several ensembles using 2+1 flavors of physical mass M枚bius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.08123v2-abstract-full').style.display = 'inline'; document.getElementById('1911.08123v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1911.08123v2-abstract-full" style="display: none;"> We report the first result for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment with all errors systematically controlled. Several ensembles using 2+1 flavors of physical mass M枚bius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find $a_渭^{\rm HLbL} = 7.87(3.06)_\text{stat}(1.77)_\text{sys}\times 10^{-10}$. Our value is consistent with previous model results and leaves little room for this notoriously difficult hadronic contribution to explain the difference between the Standard Model and the BNL experiment. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1911.08123v2-abstract-full').style.display = 'none'; document.getElementById('1911.08123v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 March, 2020; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 19 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 124, 132002 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1910.10644">arXiv:1910.10644</a> <span> [<a href="https://arxiv.org/pdf/1910.10644">pdf</a>, <a href="https://arxiv.org/format/1910.10644">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.100.114506">10.1103/PhysRevD.100.114506 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Lattice QCD study of the rare kaon decay $K^+\to蟺^+谓\bar谓$ at a near-physical pion mass </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">Antonin Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1910.10644v2-abstract-short" style="display: inline;"> The rare kaon decay $K^+\to蟺^+谓\bar谓$ is an ideal process in which to search for signs of new physics and is the primary goal of the NA62 experiment at CERN. In this paper we report on a lattice QCD calculation of the long-distance contribution to the $K^+\to蟺^+谓\bar谓$ decay amplitude at the near-physical pion mass $m_蟺=170$ MeV. The calculations are however, performed on a coarse lattice and henc… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.10644v2-abstract-full').style.display = 'inline'; document.getElementById('1910.10644v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1910.10644v2-abstract-full" style="display: none;"> The rare kaon decay $K^+\to蟺^+谓\bar谓$ is an ideal process in which to search for signs of new physics and is the primary goal of the NA62 experiment at CERN. In this paper we report on a lattice QCD calculation of the long-distance contribution to the $K^+\to蟺^+谓\bar谓$ decay amplitude at the near-physical pion mass $m_蟺=170$ MeV. The calculations are however, performed on a coarse lattice and hence with a lighter charm quark mass ($m_c^{\bar{\mathrm{MS}}}(\mbox{3 GeV})=750$ MeV) than the physical one. The main aims of this study are two-fold. Firstly we study the momentum dependence of the amplitude and conclude that it is very mild so that a computation at physical masses even at a single kinematic point would provide a good estimate of the long-distance contribution to the decay rate. Secondly we compute the contribution to the branching ratio from the two-pion intermediate state whose energy is below the kaon mass and find that it is less than 1% after its exponentially growing unphysical contribution has been removed and that the corresponding non-exponential finite-volume effects are negligibly small. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1910.10644v2-abstract-full').style.display = 'none'; document.getElementById('1910.10644v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 23 October, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">17 pages, 6 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 100, 114506 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1908.08640">arXiv:1908.08640</a> <span> [<a href="https://arxiv.org/pdf/1908.08640">pdf</a>, <a href="https://arxiv.org/ps/1908.08640">ps</a>, <a href="https://arxiv.org/format/1908.08640">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.101.014506">10.1103/PhysRevD.101.014506 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Lattice simulations with G-parity Boundary Conditions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">Christopher Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+D">Daiqian Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1908.08640v1-abstract-short" style="display: inline;"> We discuss G-parity lattice boundary conditions as a means to impose momentum on the pion ground state without breaking isospin symmetry. This technique is expected to be critical for the precision measurement of $K\rightarrow(蟺蟺)_{I=0}$ matrix elements where physical kinematics demands moving pions in the final state and the statistical noise caused by disconnected contributions will make it diff… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.08640v1-abstract-full').style.display = 'inline'; document.getElementById('1908.08640v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1908.08640v1-abstract-full" style="display: none;"> We discuss G-parity lattice boundary conditions as a means to impose momentum on the pion ground state without breaking isospin symmetry. This technique is expected to be critical for the precision measurement of $K\rightarrow(蟺蟺)_{I=0}$ matrix elements where physical kinematics demands moving pions in the final state and the statistical noise caused by disconnected contributions will make it difficult to use multi-exponential fits to isolate this as an excited state. We present a formalism for computing hadronic Green's functions with G-parity boundary conditions, derive the discretized action and its symmetries, discuss how the strange quark can be introduced and detail techniques for the numerical implementation of these boundary conditions. We demonstrate and test these methods using several $16^3\times 32$ dynamical domain wall ensembles with a $420$ MeV pion mass and G-parity boundary conditions in one and two spatial directions. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1908.08640v1-abstract-full').style.display = 'none'; document.getElementById('1908.08640v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 August, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">76 pages, 11 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 101, 014506 (2020) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1907.00864">arXiv:1907.00864</a> <span> [<a href="https://arxiv.org/pdf/1907.00864">pdf</a>, <a href="https://arxiv.org/format/1907.00864">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Hadronic light-by-light contribution to the muon anomalous magnetic moment from lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1907.00864v1-abstract-short" style="display: inline;"> We report preliminary results for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment. Several ensembles using 2+1 flavors of M枚bius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find $a_渭^{\rm HLbL} = (7.41\pm6.33)\times 10^{-10}$ </span> <span class="abstract-full has-text-grey-dark mathjax" id="1907.00864v1-abstract-full" style="display: none;"> We report preliminary results for the hadronic light-by-light scattering contribution to the muon anomalous magnetic moment. Several ensembles using 2+1 flavors of M枚bius domain-wall fermions, generated by the RBC/UKQCD collaborations, are employed to take the continuum and infinite volume limits of finite volume lattice QED+QCD. We find $a_渭^{\rm HLbL} = (7.41\pm6.33)\times 10^{-10}$ <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1907.00864v1-abstract-full').style.display = 'none'; document.getElementById('1907.00864v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 1 July, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 19 figures, to appear in the proceedings of Rencontres de Moriond (EW)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1904.09725">arXiv:1904.09725</a> <span> [<a href="https://arxiv.org/pdf/1904.09725">pdf</a>, <a href="https://arxiv.org/format/1904.09725">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Nuclear Experiment">nucl-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="Computational Physics">physics.comp-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1140/epja/i2019-12919-7">10.1140/epja/i2019-12919-7 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Status and Future Perspectives for Lattice Gauge Theory Calculations to the Exascale and Beyond </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Jo%C3%B3%2C+B">B谩lint Jo贸</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Detmold%2C+W">William Detmold</a>, <a href="/search/hep-lat?searchtype=author&query=Edwards%2C+R+G">Robert G. Edwards</a>, <a href="/search/hep-lat?searchtype=author&query=Savage%2C+M">Martin Savage</a>, <a href="/search/hep-lat?searchtype=author&query=Shanahan%2C+P">Phiala Shanahan</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1904.09725v2-abstract-short" style="display: inline;"> In this and a set of companion whitepapers, the USQCD Collaboration lays out a program of science and computing for lattice gauge theory. These whitepapers describe how calculation using lattice QCD (and other gauge theories) can aid the interpretation of ongoing and upcoming experiments in particle and nuclear physics, as well as inspire new ones. </span> <span class="abstract-full has-text-grey-dark mathjax" id="1904.09725v2-abstract-full" style="display: none;"> In this and a set of companion whitepapers, the USQCD Collaboration lays out a program of science and computing for lattice gauge theory. These whitepapers describe how calculation using lattice QCD (and other gauge theories) can aid the interpretation of ongoing and upcoming experiments in particle and nuclear physics, as well as inspire new ones. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.09725v2-abstract-full').style.display = 'none'; document.getElementById('1904.09725v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 22 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 22 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">44 pages. 1 of USQCD whitepapers,</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Eur. Phys. J. A (2019) 55: 199 </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1904.09479">arXiv:1904.09479</a> <span> [<a href="https://arxiv.org/pdf/1904.09479">pdf</a>, <a href="https://arxiv.org/format/1904.09479">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1140/epja/i2019-12891-2">10.1140/epja/i2019-12891-2 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Opportunities for lattice QCD in quark and lepton flavor physics </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Meinel%2C+S">Stefan Meinel</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Tom Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=El-Khadra%2C+A+X">Aida X. El-Khadra</a>, <a href="/search/hep-lat?searchtype=author&query=Hansen%2C+M+T">Maxwell T. Hansen</a>, <a href="/search/hep-lat?searchtype=author&query=Kronfeld%2C+A+S">Andreas S. Kronfeld</a>, <a href="/search/hep-lat?searchtype=author&query=Laiho%2C+J">Jack Laiho</a>, <a href="/search/hep-lat?searchtype=author&query=Neil%2C+E+T">Ethan T. Neil</a>, <a href="/search/hep-lat?searchtype=author&query=Sharpe%2C+S+R">Stephen R. Sharpe</a>, <a href="/search/hep-lat?searchtype=author&query=Van+de+Water%2C+R+S">Ruth S. Van de Water</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1904.09479v2-abstract-short" style="display: inline;"> This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in quark and lepton flavor physics. New data generated at Belle II, LHCb, BES III, NA62, KOTO, and Fermilab E989, combined with precise calculations of the relevant hadronic physics, may reveal what lies beyond the Standard Model. We outline a path toward improvements of the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.09479v2-abstract-full').style.display = 'inline'; document.getElementById('1904.09479v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1904.09479v2-abstract-full" style="display: none;"> This document is one of a series of whitepapers from the USQCD collaboration. Here, we discuss opportunities for lattice QCD in quark and lepton flavor physics. New data generated at Belle II, LHCb, BES III, NA62, KOTO, and Fermilab E989, combined with precise calculations of the relevant hadronic physics, may reveal what lies beyond the Standard Model. We outline a path toward improvements of the precision of existing lattice-QCD calculations and discuss groundbreaking new methods that allow lattice QCD to access new observables. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1904.09479v2-abstract-full').style.display = 'none'; document.getElementById('1904.09479v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 November, 2019; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 20 April, 2019; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> April 2019. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">USQCD whitepaper</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> FERMILAB-PUB-19-173-T, RBRC-1309 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Eur. Phys. J. A 55, 195 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1812.05281">arXiv:1812.05281</a> <span> [<a href="https://arxiv.org/pdf/1812.05281">pdf</a>, <a href="https://arxiv.org/format/1812.05281">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Fourier acceleration, the HMC algorithm and renormalizability </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Wickenden%2C+E+W">Evan W. Wickenden</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1812.05281v1-abstract-short" style="display: inline;"> The analysis developed by L眉scher and Schaefer of the Hybrid Monte Carlo (HMC) algorithm is extended to include Fourier acceleration. We show for the $蠁^4$ theory that Fourier acceleration substantially changes the structure of the theory for both the Langevin and HMC algorithms. When expanded in perturbation theory, each five-dimensional auto-correlation function of the fields $蠁(x_i, t_i)$,… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.05281v1-abstract-full').style.display = 'inline'; document.getElementById('1812.05281v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1812.05281v1-abstract-full" style="display: none;"> The analysis developed by L眉scher and Schaefer of the Hybrid Monte Carlo (HMC) algorithm is extended to include Fourier acceleration. We show for the $蠁^4$ theory that Fourier acceleration substantially changes the structure of the theory for both the Langevin and HMC algorithms. When expanded in perturbation theory, each five-dimensional auto-correlation function of the fields $蠁(x_i, t_i)$, $1\le i \le N $, corresponding to a specific 4-dimensional Feynman graph separates into two factors: one depending on the Monte-Carlo evolution times $t_i$ and the second depending on the space-time positions $x_i$. This separation implies that only auto-correlation times at the lattice scale appear, eliminating critical slowing down in perturbation theory. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1812.05281v1-abstract-full').style.display = 'none'; document.getElementById('1812.05281v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 13 December, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> December 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 3 figures, Proceedings of the 36th Annual International Symposium on Lattice Field Theory (Lattice 2018), 22-28 July 2018, Michigan State University, East Lansing, Michigan USA</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1811.11238">arXiv:1811.11238</a> <span> [<a href="https://arxiv.org/pdf/1811.11238">pdf</a>, <a href="https://arxiv.org/format/1811.11238">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.99.014515">10.1103/PhysRevD.99.014515 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> $O(4)$-symmetric position-space renormalization of lattice operators </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Tomii%2C+M">Masaaki Tomii</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1811.11238v1-abstract-short" style="display: inline;"> We extend the position-space renormalization procedure, where renormalization factors are calculated from Green's functions in position space, by introducing a technique to take the average of Green's functions over spheres. In addition to reducing discretization errors, this technique enables the resulting position-space correlators to be evaluated at any physical distance, making them continuous… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.11238v1-abstract-full').style.display = 'inline'; document.getElementById('1811.11238v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1811.11238v1-abstract-full" style="display: none;"> We extend the position-space renormalization procedure, where renormalization factors are calculated from Green's functions in position space, by introducing a technique to take the average of Green's functions over spheres. In addition to reducing discretization errors, this technique enables the resulting position-space correlators to be evaluated at any physical distance, making them continuous functions similar to the $O(4)$-symmetric position-space Green's functions in the continuum theory but with a residual dependence on a regularization parameter, the lattice spacing $a$. We can then take the continuum limit of these renormalized quantities calculated at the same physical renormalization scale $|x|$ and investigate the resulting $|x|$-dependence to identify the appropriate renormalization window. As a numerical test of the spherical averaging technique, we determine the renormalized light and strange quark masses by renormalizing the scalar current. We see a substantial reduction of discretization effects on the scalar current correlator and an enhancement of the renormalization window. The numerical simulation is carried out with $2+1$-flavor domain-wall fermions at three lattice cutoffs in the range 1.79--3.15~GeV. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1811.11238v1-abstract-full').style.display = 'none'; document.getElementById('1811.11238v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 27 November, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">34 pages, 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 99, 014515 (2019) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1806.11520">arXiv:1806.11520</a> <span> [<a href="https://arxiv.org/pdf/1806.11520">pdf</a>, <a href="https://arxiv.org/format/1806.11520">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.98.074509">10.1103/PhysRevD.98.074509 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exploratory lattice QCD study of the rare kaon decay $K^+\to蟺^+谓\bar谓$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Bai%2C+Z">Ziyuan Bai</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Lawson%2C+A">Andrew Lawson</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">Antonin Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1806.11520v1-abstract-short" style="display: inline;"> In Ref [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^+\to蟺^+谓\bar谓$ decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The $K^+\to蟺^+谓\bar谓$ decay amplitude is dominated by short-distance contributions which can be computed in… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.11520v1-abstract-full').style.display = 'inline'; document.getElementById('1806.11520v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1806.11520v1-abstract-full" style="display: none;"> In Ref [1] we have presented the results of an exploratory lattice QCD computation of the long-distance contribution to the $K^+\to蟺^+谓\bar谓$ decay amplitude. In the present paper we describe the details of this calculation, which includes the implementation of a number of novel techniques. The $K^+\to蟺^+谓\bar谓$ decay amplitude is dominated by short-distance contributions which can be computed in perturbation theory with the only required non-perturbative input being the relatively well-known form factors of semileptonic kaon decays. The long-distance contributions, which are the target of this work, are expected to be of O(5%) in the branching ratio. Our study demonstrates the feasibility of lattice QCD computations of the $K^+\to蟺^+谓\bar谓$ decay amplitude, and in particular of the long-distance component. Though this calculation is performed on a small lattice ($16^3\times32$) and at unphysical pion, kaon and charm quark masses, $m_蟺=420$ MeV, $m_K=563$ MeV and $m_c^{\overline{\mathrm{MS}}}(\mbox{2 GeV})=863$ MeV, the techniques presented in this work can readily be applied to a future realistic calculation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1806.11520v1-abstract-full').style.display = 'none'; document.getElementById('1806.11520v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 29 June, 2018; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> June 2018. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">74 pages, 12 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 98, 074509 (2018) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1711.09339">arXiv:1711.09339</a> <span> [<a href="https://arxiv.org/pdf/1711.09339">pdf</a>, <a href="https://arxiv.org/format/1711.09339">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1051/epjconf/201817513016">10.1051/epjconf/201817513016 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Including electromagnetism in $K\to蟺蟺$ decay calculations </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1711.09339v1-abstract-short" style="display: inline;"> Because of the small size of the ratio A_2/A_0 of the I=2 to I=0 K -> pipi decay amplitudes (the Delta I=1/2 rule) the effects of electromagnetism on A_2 may be a factor of 20 larger than given by a naive O(alpha) estimate. Thus, if future calculations of A_2 and epsilon'/epsilon are to achieve 10% accuracy, these effects need to be included. Here we present the first steps toward including electr… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1711.09339v1-abstract-full').style.display = 'inline'; document.getElementById('1711.09339v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1711.09339v1-abstract-full" style="display: none;"> Because of the small size of the ratio A_2/A_0 of the I=2 to I=0 K -> pipi decay amplitudes (the Delta I=1/2 rule) the effects of electromagnetism on A_2 may be a factor of 20 larger than given by a naive O(alpha) estimate. Thus, if future calculations of A_2 and epsilon'/epsilon are to achieve 10% accuracy, these effects need to be included. Here we present the first steps toward including electromagnetism in a calculation of the standard model K -> pipi decay amplitudes using lattice QCD. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1711.09339v1-abstract-full').style.display = 'none'; document.getElementById('1711.09339v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 November, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 1 figures, presented at the 35th International Symposium on Lattice Field Theory (Lattice 2017)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1710.11094">arXiv:1710.11094</a> <span> [<a href="https://arxiv.org/pdf/1710.11094">pdf</a>, <a href="https://arxiv.org/format/1710.11094">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1051/epjconf/201817509010">10.1051/epjconf/201817509010 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Lattice QCD Application Development within the US DOE Exascale Computing Project </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Brower%2C+R">Richard Brower</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=DeTar%2C+C">Carleton DeTar</a>, <a href="/search/hep-lat?searchtype=author&query=Edwards%2C+R">Robert Edwards</a>, <a href="/search/hep-lat?searchtype=author&query=Mackenzie%2C+P">Paul Mackenzie</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1710.11094v1-abstract-short" style="display: inline;"> In October, 2016, the US Department of Energy launched the Exascale Computing Project, which aims to deploy exascale computing resources for science and engineering in the early 2020's. The project brings together application teams, software developers, and hardware vendors in order to realize this goal. Lattice QCD is one of the applications. Members of the US lattice gauge theory community with… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1710.11094v1-abstract-full').style.display = 'inline'; document.getElementById('1710.11094v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1710.11094v1-abstract-full" style="display: none;"> In October, 2016, the US Department of Energy launched the Exascale Computing Project, which aims to deploy exascale computing resources for science and engineering in the early 2020's. The project brings together application teams, software developers, and hardware vendors in order to realize this goal. Lattice QCD is one of the applications. Members of the US lattice gauge theory community with significant collaborators abroad are developing algorithms and software for exascale lattice QCD calculations. We give a short description of the project, our activities, and our plans. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1710.11094v1-abstract-full').style.display = 'none'; document.getElementById('1710.11094v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 30 October, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">35th International Symposium on Lattice Field Theory (Lattice 2017)</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1710.07036">arXiv:1710.07036</a> <span> [<a href="https://arxiv.org/pdf/1710.07036">pdf</a>, <a href="https://arxiv.org/format/1710.07036">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1051/epjconf/201817502008">10.1051/epjconf/201817502008 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Testing algorithms for critical slowing down </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Cossu%2C+G">Guido Cossu</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P">Peter Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=J%C3%BCttner%2C+A">Andreas J眉ttner</a>, <a href="/search/hep-lat?searchtype=author&query=Sanfilippo%2C+F">Francesco Sanfilippo</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1710.07036v1-abstract-short" style="display: inline;"> We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1710.07036v1-abstract-full').style.display = 'inline'; document.getElementById('1710.07036v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1710.07036v1-abstract-full" style="display: none;"> We present the preliminary tests on two modifications of the Hybrid Monte Carlo (HMC) algorithm. Both algorithms are designed to travel much farther in the Hamiltonian phase space for each trajectory and reduce the autocorrelations among physical observables thus tackling the critical slowing down towards the continuum limit. We present a comparison of costs of the new algorithms with the standard HMC evolution for pure gauge fields, studying the autocorrelation times for various quantities including the topological charge. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1710.07036v1-abstract-full').style.display = 'none'; document.getElementById('1710.07036v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 19 October, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">8 pages, 2 figures, Lattice 2017 conference proceedings</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1705.01067">arXiv:1705.01067</a> <span> [<a href="https://arxiv.org/pdf/1705.01067">pdf</a>, <a href="https://arxiv.org/ps/1705.01067">ps</a>, <a href="https://arxiv.org/format/1705.01067">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.96.034515">10.1103/PhysRevD.96.034515 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Using infinite volume, continuum QED and lattice QCD for the hadronic light-by-light contribution to the muon anomalous magnetic moment </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1705.01067v1-abstract-short" style="display: inline;"> In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g - 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD collaboration. However, the calculation is expected to suffer from a significant finite volume error that scales like $1/L^2$ where $L$ is the sp… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.01067v1-abstract-full').style.display = 'inline'; document.getElementById('1705.01067v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1705.01067v1-abstract-full" style="display: none;"> In our previous work, the connected and leading disconnected hadronic light-by-light contributions to the muon anomalous magnetic moment (g - 2) have been computed using lattice QCD ensembles corresponding to physical pion mass generated by the RBC/UKQCD collaboration. However, the calculation is expected to suffer from a significant finite volume error that scales like $1/L^2$ where $L$ is the spatial size of the lattice. In this paper, we demonstrate that this problem is cured by treating the muon and photons in infinite volume, continuum QED, resulting in a weighting function that is pre-computed and saved with affordable cost and sufficient accuracy. We present numerical results for the case when the quark loop is replaced by a muon loop, finding the expected exponential approach to the infinite volume limit and consistency with the known analytic result. We have implemented an improved weighting function which reduces both discretization and finite volume effects arising from the hadronic part of the amplitude. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1705.01067v1-abstract-full').style.display = 'none'; document.getElementById('1705.01067v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 2 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">12 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 96, 034515 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1701.02858">arXiv:1701.02858</a> <span> [<a href="https://arxiv.org/pdf/1701.02858">pdf</a>, <a href="https://arxiv.org/format/1701.02858">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Experiment">hep-ex</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.118.252001">10.1103/PhysRevLett.118.252001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Exploratory Lattice QCD Study of the Rare Kaon Decay $K^+\to蟺^+谓\bar谓$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Bai%2C+Z">Ziyuan Bai</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Lawson%2C+A">Andrew Lawson</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">Antonin Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1701.02858v2-abstract-short" style="display: inline;"> We report a first, complete lattice QCD calculation of the long-distance contribution to the $K^+\to蟺^+谓\bar谓$ decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics there is a long-distan… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1701.02858v2-abstract-full').style.display = 'inline'; document.getElementById('1701.02858v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1701.02858v2-abstract-full" style="display: none;"> We report a first, complete lattice QCD calculation of the long-distance contribution to the $K^+\to蟺^+谓\bar谓$ decay within the standard model. This is a second-order weak process involving two four-Fermi operators that is highly sensitive to new physics and being studied by the NA62 experiment at CERN. While much of this decay comes from perturbative, short-distance physics there is a long-distance part, perhaps as large as the planned experimental error, which involves nonperturbative phenomena. The calculation presented here, with unphysical quark masses, demonstrates that this contribution can be computed using lattice methods by overcoming three technical difficulties: (i) a short-distance divergence that results when the two weak operators approach each other, (ii) exponentially growing, unphysical terms that appear in Euclidean, second-order perturbation theory, and (iii) potentially large finite-volume effects. A follow-on calculation with physical quark masses and controlled systematic errors will be possible with the next generation of computers. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1701.02858v2-abstract-full').style.display = 'none'; document.getElementById('1701.02858v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 May, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 January, 2017; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> January 2017. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">5 pages, 2 figures, 1 table; v2, version accepted for publication in PRL</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 118, 252001 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1611.08685">arXiv:1611.08685</a> <span> [<a href="https://arxiv.org/pdf/1611.08685">pdf</a>, <a href="https://arxiv.org/format/1611.08685">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> The connected and leading disconnected diagrams of the hadronic light-by-light contribution to muon $g - 2$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1611.08685v1-abstract-short" style="display: inline;"> We report our recent lattice calculation of hadronic light-by-light contribution to muon $g-2$ using our recently developed moment method. The connected diagrams and the leading disconnected diagrams are included. The calculation is performed on a $48^3 \times 96$ lattice with physical pion mass and 5.5 fm box size. We expect sizable finite volume and finite lattice spacing corrections to the resu… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.08685v1-abstract-full').style.display = 'inline'; document.getElementById('1611.08685v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1611.08685v1-abstract-full" style="display: none;"> We report our recent lattice calculation of hadronic light-by-light contribution to muon $g-2$ using our recently developed moment method. The connected diagrams and the leading disconnected diagrams are included. The calculation is performed on a $48^3 \times 96$ lattice with physical pion mass and 5.5 fm box size. We expect sizable finite volume and finite lattice spacing corrections to the results of these calculations which will be estimated in calculations to be carried out over the next 1-2 years. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1611.08685v1-abstract-full').style.display = 'none'; document.getElementById('1611.08685v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 26 November, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">34th annual International Symposium on Lattice Field Theory, 24-30 July 2016, University of Southampton, UK. 7 pages</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1610.04603">arXiv:1610.04603</a> <span> [<a href="https://arxiv.org/pdf/1610.04603">pdf</a>, <a href="https://arxiv.org/format/1610.04603">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.118.022005">10.1103/PhysRevLett.118.022005 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Connected and leading disconnected hadronic light-by-light contribution to the muon anomalous magnetic moment with physical pion mass </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">Chulwoo Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1610.04603v1-abstract-short" style="display: inline;"> We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the $48^3 \times 96$ ensemble generated with a physical… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1610.04603v1-abstract-full').style.display = 'inline'; document.getElementById('1610.04603v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1610.04603v1-abstract-full" style="display: none;"> We report a lattice QCD calculation of the hadronic light-by-light contribution to the muon anomalous magnetic moment at physical pion mass. The calculation includes the connected diagrams and the leading, quark-line-disconnected diagrams. We incorporate algorithmic improvements developed in our previous work. The calculation was performed on the $48^3 \times 96$ ensemble generated with a physical-pion-mass and a 5.5 fm spatial extent by the RBC and UKQCD collaborations using the chiral, domain wall fermion (DWF) formulation. We find $a_渭^{\text{HLbL}} = 5.35 (1.35) \times 10^{- 10}$, where the error is statistical only. The finite-volume and finite lattice-spacing errors could be quite large and are the subject of on-going research. The omitted disconnected graphs, while expected to give a correction of order 10\%, also need to be computed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1610.04603v1-abstract-full').style.display = 'none'; document.getElementById('1610.04603v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 October, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">6 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 118, 022005 (2017) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1608.07585">arXiv:1608.07585</a> <span> [<a href="https://arxiv.org/pdf/1608.07585">pdf</a>, <a href="https://arxiv.org/format/1608.07585">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.94.114516">10.1103/PhysRevD.94.114516 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> First exploratory calculation of the long-distance contributions to the rare kaon decays $K\to蟺\ell^+\ell^-$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Juttner%2C+A">Andreas Juttner</a>, <a href="/search/hep-lat?searchtype=author&query=Lawson%2C+A">Andrew Lawson</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">Antonin Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1608.07585v2-abstract-short" style="display: inline;"> The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential New Physics. The CP conserving $K\to蟺\ell^+\ell^-$ decay channels however are dominated by a single photon exchange; this… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1608.07585v2-abstract-full').style.display = 'inline'; document.getElementById('1608.07585v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1608.07585v2-abstract-full" style="display: none;"> The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential New Physics. The CP conserving $K\to蟺\ell^+\ell^-$ decay channels however are dominated by a single photon exchange; this involves a sizeable long-distance hadronic contribution which represents the current major source of theoretical uncertainty. Here we outline our methodology for the computation of the long-distance contributions to these rare decay amplitudes using lattice QCD and present the numerical results of the first exploratory studies of these decays in which all but the disconnected diagrams are evaluated. The domain wall fermion ensembles of the RBC and UKQCD collaborations are used, with a pion mass of $M_蟺\sim 430\,\mathrm{MeV}$ and a kaon mass of $M_{K}\sim 625\,\mathrm{MeV}$. In particular we determine the form factor, $V(z)$, of the $K^+\to蟺^+\ell^+\ell^-$ decay from the lattice at small values of $z=q^2/M_{K}^{2}$, obtaining $V(z)=1.37(36),\, 0.68(39),\, 0.96(64)$ for the three values of $z=-0.5594(12),\, -1.0530(34),\, -1.4653(82)$ respectively. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1608.07585v2-abstract-full').style.display = 'none'; document.getElementById('1608.07585v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 April, 2017; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 26 August, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> August 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">40 pages, 14 figures, 4 tables</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 94, 114516 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1605.04442">arXiv:1605.04442</a> <span> [<a href="https://arxiv.org/pdf/1605.04442">pdf</a>, <a href="https://arxiv.org/format/1605.04442">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.93.114517">10.1103/PhysRevD.93.114517 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Prospects for a lattice computation of rare kaon decay amplitudes II $K\to蟺谓\bar谓$ decays </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">Norman H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">Antonin Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">Christopher T. Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1605.04442v1-abstract-short" style="display: inline;"> The rare kaon decays $K\to蟺谓\bar谓$ are strongly suppressed in the standard model and widely regarded as processes in which new phenomena, not predicted by the standard model, may be observed. Recognizing such new phenomena requires precise standard model prediction for the braching ratio of $K\to蟺谓\bar谓$ with controlled uncertainty for both short-distance and long-distance contributions. In this w… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1605.04442v1-abstract-full').style.display = 'inline'; document.getElementById('1605.04442v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1605.04442v1-abstract-full" style="display: none;"> The rare kaon decays $K\to蟺谓\bar谓$ are strongly suppressed in the standard model and widely regarded as processes in which new phenomena, not predicted by the standard model, may be observed. Recognizing such new phenomena requires precise standard model prediction for the braching ratio of $K\to蟺谓\bar谓$ with controlled uncertainty for both short-distance and long-distance contributions. In this work we demonstrate the feasibility of lattice QCD calculation of the long-distance contribution to rare kaon decays with the emphasis on $K^+\to蟺^+谓\bar谓$. Our methodology covers the calculation of both $W$-$W$ and $Z$-exchange diagrams. We discuss the estimation of the power-law, finite-volume corrections and two methods to consistently combine the long distance contribution determined by the lattice methods outlined here with the short distance parts that can be reliably determined using perturbation theory. It is a subsequent work of our first methodology paper on $K\to蟺\ell^+\ell^-$, where the focus was made on the $纬$-exchange diagrams. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1605.04442v1-abstract-full').style.display = 'none'; document.getElementById('1605.04442v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 14 May, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">47 pages, 5 figures</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 93, 114517 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1603.03065">arXiv:1603.03065</a> <span> [<a href="https://arxiv.org/pdf/1603.03065">pdf</a>, <a href="https://arxiv.org/ps/1603.03065">ps</a>, <a href="https://arxiv.org/format/1603.03065">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> Erratum: Standard-model prediction for direct CP violation in $K\to蟺蟺$ decay </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Bai%2C+Z">Z. Bai</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">T. Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P+A">P. A. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Frison%2C+J">J. Frison</a>, <a href="/search/hep-lat?searchtype=author&query=Garron%2C+N">N. Garron</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">T. Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">C. Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">C. Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">C. Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">R. D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">C. T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Soni%2C+A">A. Soni</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+D">D. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1603.03065v1-abstract-short" style="display: inline;"> In this document we address an error discovered in the ensemble generation for our calculation of the $I=0$ $K\to蟺蟺$ amplitude (Phys. Rev. Lett. 115, 212001 (2015), arXiv:1505.07863) whereby the same random numbers were used for the two independent quark flavors, resulting in small but measurable correlations between gauge observables separated by 12 units in the y-direction. We conclude that the… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1603.03065v1-abstract-full').style.display = 'inline'; document.getElementById('1603.03065v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1603.03065v1-abstract-full" style="display: none;"> In this document we address an error discovered in the ensemble generation for our calculation of the $I=0$ $K\to蟺蟺$ amplitude (Phys. Rev. Lett. 115, 212001 (2015), arXiv:1505.07863) whereby the same random numbers were used for the two independent quark flavors, resulting in small but measurable correlations between gauge observables separated by 12 units in the y-direction. We conclude that the effects of this error are negligible compared to the overall errors on our calculation. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1603.03065v1-abstract-full').style.display = 'none'; document.getElementById('1603.03065v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 8 March, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> March 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">2 pages, 1 figure</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1602.01374">arXiv:1602.01374</a> <span> [<a href="https://arxiv.org/pdf/1602.01374">pdf</a>, <a href="https://arxiv.org/format/1602.01374">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Long distance contributions to the rare kaon decay $K\to蟺\ell^{+}\ell^{-}$ </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">Xu Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Juttner%2C+A">Andreas Juttner</a>, <a href="/search/hep-lat?searchtype=author&query=Lawson%2C+A">Andrew Lawson</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">Antonin Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C">Christopher Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1602.01374v1-abstract-short" style="display: inline;"> The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential New Physics. To discern such New Physics one must be able to control the errors on the Standard Model prediction of the d… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1602.01374v1-abstract-full').style.display = 'inline'; document.getElementById('1602.01374v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1602.01374v1-abstract-full" style="display: none;"> The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavour changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential New Physics. To discern such New Physics one must be able to control the errors on the Standard Model prediction of the decay amplitude. These particular decay channels however are dominated by a single photon exchange; this involves a sizeable long-distance hadronic contribution which represents the current major source of theoretical uncertainty. Here we outline our methodology for the computation of the long distance contributions to these rare decay amplitudes using lattice QCD, and present the numerical results of some exploratory studies using the Domain Wall Fermion ensembles of the RBC and UKQCD collaborations. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1602.01374v1-abstract-full').style.display = 'none'; document.getElementById('1602.01374v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 3 February, 2016; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> February 2016. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 4 figures. Talk presented at the 33rd International Symposium on Lattice Field Theory (Lattice 2015), 14-18 July 2015, Kobe International Conference Center, Kobe, Japan</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1511.05198">arXiv:1511.05198</a> <span> [<a href="https://arxiv.org/pdf/1511.05198">pdf</a>, <a href="https://arxiv.org/ps/1511.05198">ps</a>, <a href="https://arxiv.org/format/1511.05198">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Hadronic Light by Light Contributions to the Muon Anomalous Magnetic Moment With Physical Pions </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1511.05198v1-abstract-short" style="display: inline;"> The current measurement of muonic $g - 2$ disagrees with the theoretical calculation by about 3 standard deviations. Hadronic vacuum polarization (HVP) and hadronic light by light (HLbL) are the two types of processes that contribute most to the theoretical uncertainty. The current value for HLbL is still given by models. I will describe results from a first-principles lattice calculation with a 1… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.05198v1-abstract-full').style.display = 'inline'; document.getElementById('1511.05198v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1511.05198v1-abstract-full" style="display: none;"> The current measurement of muonic $g - 2$ disagrees with the theoretical calculation by about 3 standard deviations. Hadronic vacuum polarization (HVP) and hadronic light by light (HLbL) are the two types of processes that contribute most to the theoretical uncertainty. The current value for HLbL is still given by models. I will describe results from a first-principles lattice calculation with a 139 MeV pion in a box of 5.5 fm extent. Our current numerical strategies, including noise reduction techniques, evaluating the HLbL amplitude at zero external momentum transfer, and important remaining challenges, in particular those associated with finite volume effects, will be discussed. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.05198v1-abstract-full').style.display = 'none'; document.getElementById('1511.05198v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 16 November, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">The 33rd International Symposium on Lattice Field Theory, 14 -18 July 2015, Kobe International Conference Center, Kobe, Japan</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1511.01950">arXiv:1511.01950</a> <span> [<a href="https://arxiv.org/pdf/1511.01950">pdf</a>, <a href="https://arxiv.org/format/1511.01950">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.93.054502">10.1103/PhysRevD.93.054502 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> The Low Energy Constants of $SU(2)$ Partially Quenched Chiral Perturbation Theory from $N_{f}=2+1$ Domain Wall QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P+A">P. A. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Garron%2C+N">N. Garron</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">C. Jung</a>, <a href="/search/hep-lat?searchtype=author&query=J%C3%BCttner%2C+A">A. J眉ttner</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">C. Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">R. D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=McGlynn%2C+G">G. McGlynn</a>, <a href="/search/hep-lat?searchtype=author&query=Murphy%2C+D+J">D. J. Murphy</a>, <a href="/search/hep-lat?searchtype=author&query=Ohta%2C+S">S. Ohta</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">A. Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">C. T. Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1511.01950v1-abstract-short" style="display: inline;"> We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to othe… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.01950v1-abstract-full').style.display = 'inline'; document.getElementById('1511.01950v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1511.01950v1-abstract-full" style="display: none;"> We have performed fits of the pseudoscalar masses and decay constants, from a variety of RBC-UKQCD domain wall fermion ensembles, to $SU(2)$ partially quenched chiral perturbation theory at next-to leading order (NLO) and next-to-next-to leading order (NNLO). We report values for 9 NLO and 8 linearly independent combinations of NNLO partially quenched low energy constants, which we compare to other lattice and phenomenological determinations. We discuss the size of successive terms in the chiral expansion and use our large set of low energy constants to make predictions for mass splittings due to QCD isospin breaking effects and the S-wave $蟺蟺$ scattering lengths. We conclude that, for the range of pseudoscalar masses explored in this work, $115~\mathrm{MeV} \lesssim m_{\rm PS} \lesssim 430~\mathrm{MeV}$, the NNLO $SU(2)$ expansion is quite robust and can fit lattice data with percent-scale accuracy. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.01950v1-abstract-full').style.display = 'none'; document.getElementById('1511.01950v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 5 November, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 93, 054502 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1511.01493">arXiv:1511.01493</a> <span> [<a href="https://arxiv.org/pdf/1511.01493">pdf</a>, <a href="https://arxiv.org/ps/1511.01493">ps</a>, <a href="https://arxiv.org/format/1511.01493">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> </div> <p class="title is-5 mathjax"> On calculating disconnected-type hadronic light-by-light scattering diagrams from lattice QCD </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1511.01493v2-abstract-short" style="display: inline;"> For reliable comparison of the standard model prediction to the muon g-2 with its experimental value, the hadronic light-by-light scattering (HLbL) contribution must be calculated by lattice QCD simulation. HLbL contribution has many types of disconnected-type diagrams. Here, we start with recalling the point that must be taken care of in every method to calculate them by lattice QCD, and present… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.01493v2-abstract-full').style.display = 'inline'; document.getElementById('1511.01493v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1511.01493v2-abstract-full" style="display: none;"> For reliable comparison of the standard model prediction to the muon g-2 with its experimental value, the hadronic light-by-light scattering (HLbL) contribution must be calculated by lattice QCD simulation. HLbL contribution has many types of disconnected-type diagrams. Here, we start with recalling the point that must be taken care of in every method to calculate them by lattice QCD, and present one concrete method called nonperturbative QED method. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1511.01493v2-abstract-full').style.display = 'none'; document.getElementById('1511.01493v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 18 November, 2015; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 4 November, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> November 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">7 pages, 12 figures. 2 tables, Proceedings of the 33rd International Symposium on Lattice Field Theory, July 14-18, 2015, Kobe, Japan</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1510.07100">arXiv:1510.07100</a> <span> [<a href="https://arxiv.org/pdf/1510.07100">pdf</a>, <a href="https://arxiv.org/ps/1510.07100">ps</a>, <a href="https://arxiv.org/format/1510.07100">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.93.014503">10.1103/PhysRevD.93.014503 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Lattice Calculation of Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1510.07100v1-abstract-short" style="display: inline;"> The quark-connected part of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of thes… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.07100v1-abstract-full').style.display = 'inline'; document.getElementById('1510.07100v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1510.07100v1-abstract-full" style="display: none;"> The quark-connected part of the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment is computed using lattice QCD with chiral fermions. We report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical, $171$ MeV pion mass on a $(4.6\;\mathrm{fm})^3$ spatial volume using the $32^3\times 64$ Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1510.07100v1-abstract-full').style.display = 'none'; document.getElementById('1510.07100v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 23 October, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> October 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">52 pages</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 93, 014503 (2016) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1509.08372">arXiv:1509.08372</a> <span> [<a href="https://arxiv.org/pdf/1509.08372">pdf</a>, <a href="https://arxiv.org/ps/1509.08372">ps</a>, <a href="https://arxiv.org/format/1509.08372">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> </div> </div> <p class="title is-5 mathjax"> Lattice Calculation of the Connected Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Jin%2C+L">Luchang Jin</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">Thomas Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N">Norman Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Hayakawa%2C+M">Masashi Hayakawa</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">Taku Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">Christoph Lehner</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1509.08372v1-abstract-short" style="display: inline;"> The anomalous magnetic moment of muon, $g-2$, is a very precisely measured quantity. However, the current measurement disagrees with standard model by about 3 standard deviations. Hadronic vacuum polarization and hadronic light by light are the two types of processes that contribute most to the theoretical uncertainty. I will describe how lattice methods are well-suited to provide a first-principl… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1509.08372v1-abstract-full').style.display = 'inline'; document.getElementById('1509.08372v1-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1509.08372v1-abstract-full" style="display: none;"> The anomalous magnetic moment of muon, $g-2$, is a very precisely measured quantity. However, the current measurement disagrees with standard model by about 3 standard deviations. Hadronic vacuum polarization and hadronic light by light are the two types of processes that contribute most to the theoretical uncertainty. I will describe how lattice methods are well-suited to provide a first-principle's result for the hadronic light by light contribution, the various numerical strategies that are presently being used to evaluate it, our current results and the important remaining challenges which must be overcome. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1509.08372v1-abstract-full').style.display = 'none'; document.getElementById('1509.08372v1-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 September, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> September 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Twelfth Conference on the Intersections of Particle and Nuclear Physics. Vail Colorado at the Vail Marriott from May 19-24, 2015</span> </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1507.03094">arXiv:1507.03094</a> <span> [<a href="https://arxiv.org/pdf/1507.03094">pdf</a>, <a href="https://arxiv.org/format/1507.03094">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevD.92.094512">10.1103/PhysRevD.92.094512 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Prospects for a lattice computation of rare kaon decay amplitudes: $K\to蟺\ell^+\ell^-$ decays </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Feng%2C+X">X. Feng</a>, <a href="/search/hep-lat?searchtype=author&query=Portelli%2C+A">A. Portelli</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">C. T. Sachrajda</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1507.03094v2-abstract-short" style="display: inline;"> The rare kaon decays $K\to蟺\ell^+\ell^-$ and $K\to蟺谓\bar谓$ are flavor changing neutral current (FCNC) processes and hence promising channels with which to probe the limits of the standard model and to look for signs of new physics. In this paper we demonstrate the feasibility of lattice calculations of $K\to蟺\ell^+\ell^-$ decay amplitudes for which long-distance contributions are very significant.… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1507.03094v2-abstract-full').style.display = 'inline'; document.getElementById('1507.03094v2-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1507.03094v2-abstract-full" style="display: none;"> The rare kaon decays $K\to蟺\ell^+\ell^-$ and $K\to蟺谓\bar谓$ are flavor changing neutral current (FCNC) processes and hence promising channels with which to probe the limits of the standard model and to look for signs of new physics. In this paper we demonstrate the feasibility of lattice calculations of $K\to蟺\ell^+\ell^-$ decay amplitudes for which long-distance contributions are very significant. We show that the dominant finite-volume corrections (those decreasing as powers of the volume) are negligibly small and that, in the four-flavor theory, no new ultraviolet divergences appear as the electromagnetic current $J$ and the effective weak Hamiltonian $H_W$ approach each other. In addition, we demonstrate that one can remove the unphysical terms which grow exponentially with the range of the integration over the time separation between $J$ and $H_W$. We will now proceed to exploratory numerical studies with the aim of motivating further experimental measurements of these decays. Our work extends the earlier study by Isidori, Turchetti and Martinelli which focussed largely on the renormalization of ultraviolet divergences. In a companion paper we discuss the evaluation of the long-distance contributions to $K\to蟺谓\bar谓$ decays; these contributions are expected to be at the level of a few percent for $K^+$ decays. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1507.03094v2-abstract-full').style.display = 'none'; document.getElementById('1507.03094v2-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 28 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 11 July, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> July 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">Version published in Phys. Rev. D</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. D 92, 094512 (2015) </p> </li> <li class="arxiv-result"> <div class="is-marginless"> <p class="list-title is-inline-block"><a href="https://arxiv.org/abs/1505.07863">arXiv:1505.07863</a> <span> [<a href="https://arxiv.org/pdf/1505.07863">pdf</a>, <a href="https://arxiv.org/ps/1505.07863">ps</a>, <a href="https://arxiv.org/format/1505.07863">other</a>] </span> </p> <div class="tags is-inline-block"> <span class="tag is-small is-link tooltip is-tooltip-top" data-tooltip="High Energy Physics - Lattice">hep-lat</span> <span class="tag is-small is-grey tooltip is-tooltip-top" data-tooltip="High Energy Physics - Phenomenology">hep-ph</span> </div> <div class="is-inline-block" style="margin-left: 0.5rem"> <div class="tags has-addons"> <span class="tag is-dark is-size-7">doi</span> <span class="tag is-light is-size-7"><a class="" href="https://doi.org/10.1103/PhysRevLett.115.212001">10.1103/PhysRevLett.115.212001 <i class="fa fa-external-link" aria-hidden="true"></i></a></span> </div> </div> </div> <p class="title is-5 mathjax"> Standard-model prediction for direct CP violation in $K\to蟺蟺$ decay </p> <p class="authors"> <span class="search-hit">Authors:</span> <a href="/search/hep-lat?searchtype=author&query=Bai%2C+Z">Z. Bai</a>, <a href="/search/hep-lat?searchtype=author&query=Blum%2C+T">T. Blum</a>, <a href="/search/hep-lat?searchtype=author&query=Boyle%2C+P+A">P. A. Boyle</a>, <a href="/search/hep-lat?searchtype=author&query=Christ%2C+N+H">N. H. Christ</a>, <a href="/search/hep-lat?searchtype=author&query=Frison%2C+J">J. Frison</a>, <a href="/search/hep-lat?searchtype=author&query=Garron%2C+N">N. Garron</a>, <a href="/search/hep-lat?searchtype=author&query=Izubuchi%2C+T">T. Izubuchi</a>, <a href="/search/hep-lat?searchtype=author&query=Jung%2C+C">C. Jung</a>, <a href="/search/hep-lat?searchtype=author&query=Kelly%2C+C">C. Kelly</a>, <a href="/search/hep-lat?searchtype=author&query=Lehner%2C+C">C. Lehner</a>, <a href="/search/hep-lat?searchtype=author&query=Mawhinney%2C+R+D">R. D. Mawhinney</a>, <a href="/search/hep-lat?searchtype=author&query=Sachrajda%2C+C+T">C. T. Sachrajda</a>, <a href="/search/hep-lat?searchtype=author&query=Soni%2C+A">A. Soni</a>, <a href="/search/hep-lat?searchtype=author&query=Zhang%2C+D">D. Zhang</a> </p> <p class="abstract mathjax"> <span class="has-text-black-bis has-text-weight-semibold">Abstract</span>: <span class="abstract-short has-text-grey-dark mathjax" id="1505.07863v4-abstract-short" style="display: inline;"> We report the first lattice QCD calculation of the complex kaon decay amplitude $A_0$ with physical kinematics, using a $32^3\times 64$ lattice volume and a single lattice spacing $a$, with $1/a= 1.3784(68)$ GeV. We find Re$(A_0) = 4.66(1.00)(1.26) \times 10^{-7}$ GeV and Im$(A_0) = -1.90(1.23)(1.08) \times 10^{-11}$ GeV, where the first error is statistical and the second systematic. The first va… <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.07863v4-abstract-full').style.display = 'inline'; document.getElementById('1505.07863v4-abstract-short').style.display = 'none';">▽ More</a> </span> <span class="abstract-full has-text-grey-dark mathjax" id="1505.07863v4-abstract-full" style="display: none;"> We report the first lattice QCD calculation of the complex kaon decay amplitude $A_0$ with physical kinematics, using a $32^3\times 64$ lattice volume and a single lattice spacing $a$, with $1/a= 1.3784(68)$ GeV. We find Re$(A_0) = 4.66(1.00)(1.26) \times 10^{-7}$ GeV and Im$(A_0) = -1.90(1.23)(1.08) \times 10^{-11}$ GeV, where the first error is statistical and the second systematic. The first value is in approximate agreement with the experimental result: Re$(A_0) = 3.3201(18) \times 10^{-7}$ GeV while the second can be used to compute the direct CP violating ratio Re$(\varepsilon'/\varepsilon)=1.38(5.15)(4.59)\times 10^{-4}$, which is $2.1蟽$ below the experimental value $16.6(2.3)\times 10^{-4}$. The real part of $A_0$ is CP conserving and serves as a test of our method while the result for Re$(\varepsilon'/\varepsilon)$ provides a new test of the standard-model theory of CP violation, one which can be made more accurate with increasing computer capability. <a class="is-size-7" style="white-space: nowrap;" onclick="document.getElementById('1505.07863v4-abstract-full').style.display = 'none'; document.getElementById('1505.07863v4-abstract-short').style.display = 'inline';">△ Less</a> </span> </p> <p class="is-size-7"><span class="has-text-black-bis has-text-weight-semibold">Submitted</span> 20 January, 2016; <span class="has-text-black-bis has-text-weight-semibold">v1</span> submitted 28 May, 2015; <span class="has-text-black-bis has-text-weight-semibold">originally announced</span> May 2015. </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Comments:</span> <span class="has-text-grey-dark mathjax">9 pages, 3 figures. Updated to match published version</span> </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Report number:</span> RBRC 1141 </p> <p class="comments is-size-7"> <span class="has-text-black-bis has-text-weight-semibold">Journal ref:</span> Phys. Rev. Lett. 115, 212001 (2015) </p> </li> </ol> <nav class="pagination is-small is-centered breathe-horizontal" role="navigation" aria-label="pagination"> <a href="" class="pagination-previous is-invisible">Previous </a> <a href="/search/?searchtype=author&query=Christ%2C+N&start=50" class="pagination-next" >Next </a> <ul class="pagination-list"> <li> <a href="/search/?searchtype=author&query=Christ%2C+N&start=0" class="pagination-link is-current" aria-label="Goto page 1">1 </a> </li> <li> <a href="/search/?searchtype=author&query=Christ%2C+N&start=50" class="pagination-link " aria-label="Page 2" aria-current="page">2 </a> </li> <li> <a href="/search/?searchtype=author&query=Christ%2C+N&start=100" class="pagination-link " aria-label="Page 3" aria-current="page">3 </a> </li> </ul> </nav> <div class="is-hidden-tablet">  <span class="help" style="display: inline-block;"><a href="https://github.com/arXiv/arxiv-search/releases">Search v0.5.6 released 2020-02-24</a>  </span> </div> </div> </main> <footer> <div class="columns is-desktop" role="navigation" aria-label="Secondary">  <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/about">About</a></li> <li><a href="https://info.arxiv.org/help">Help</a></li> </ul> </div> <div class="column"> <ul class="nav-spaced"> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>contact arXiv</title><desc>Click here to contact arXiv</desc><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg> <a href="https://info.arxiv.org/help/contact.html"> Contact</a> </li> <li> <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><title>subscribe to arXiv mailings</title><desc>Click here to subscribe</desc><path d="M476 3.2L12.5 270.6c-18.1 10.4-15.8 35.6 2.2 43.2L121 358.4l287.3-253.2c5.5-4.9 13.3 2.6 8.6 8.3L176 407v80.5c0 23.6 28.5 32.9 42.5 15.8L282 426l124.6 52.2c14.2 6 30.4-2.9 33-18.2l72-432C515 7.8 493.3-6.8 476 3.2z"/></svg> <a href="https://info.arxiv.org/help/subscribe"> Subscribe</a> </li> </ul> </div> </div> </div>   <div class="column"> <div class="columns"> <div class="column"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/license/index.html">Copyright</a></li> <li><a href="https://info.arxiv.org/help/policies/privacy_policy.html">Privacy Policy</a></li> </ul> </div> <div class="column sorry-app-links"> <ul class="nav-spaced"> <li><a href="https://info.arxiv.org/help/web_accessibility.html">Web Accessibility Assistance</a></li> <li> <p class="help"> <a class="a11y-main-link" href="https://status.arxiv.org" target="_blank">arXiv Operational Status <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 256 512" class="icon filter-dark_grey" role="presentation"><path d="M224.3 273l-136 136c-9.4 9.4-24.6 9.4-33.9 0l-22.6-22.6c-9.4-9.4-9.4-24.6 0-33.9l96.4-96.4-96.4-96.4c-9.4-9.4-9.4-24.6 0-33.9L54.3 103c9.4-9.4 24.6-9.4 33.9 0l136 136c9.5 9.4 9.5 24.6.1 34z"/></svg></a><br> Get status notifications via <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/email/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512" class="icon filter-black" role="presentation"><path d="M502.3 190.8c3.9-3.1 9.7-.2 9.7 4.7V400c0 26.5-21.5 48-48 48H48c-26.5 0-48-21.5-48-48V195.6c0-5 5.7-7.8 9.7-4.7 22.4 17.4 52.1 39.5 154.1 113.6 21.1 15.4 56.7 47.8 92.2 47.6 35.7.3 72-32.8 92.3-47.6 102-74.1 131.6-96.3 154-113.7zM256 320c23.2.4 56.6-29.2 73.4-41.4 132.7-96.3 142.8-104.7 173.4-128.7 5.8-4.5 9.2-11.5 9.2-18.9v-19c0-26.5-21.5-48-48-48H48C21.5 64 0 85.5 0 112v19c0 7.4 3.4 14.3 9.2 18.9 30.6 23.9 40.7 32.4 173.4 128.7 16.8 12.2 50.2 41.8 73.4 41.4z"/></svg>email</a> or <a class="is-link" href="https://subscribe.sorryapp.com/24846f03/slack/new" target="_blank"><svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 448 512" class="icon filter-black" role="presentation"><path d="M94.12 315.1c0 25.9-21.16 47.06-47.06 47.06S0 341 0 315.1c0-25.9 21.16-47.06 47.06-47.06h47.06v47.06zm23.72 0c0-25.9 21.16-47.06 47.06-47.06s47.06 21.16 47.06 47.06v117.84c0 25.9-21.16 47.06-47.06 47.06s-47.06-21.16-47.06-47.06V315.1zm47.06-188.98c-25.9 0-47.06-21.16-47.06-47.06S139 32 164.9 32s47.06 21.16 47.06 47.06v47.06H164.9zm0 23.72c25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06H47.06C21.16 243.96 0 222.8 0 196.9s21.16-47.06 47.06-47.06H164.9zm188.98 47.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06s-21.16 47.06-47.06 47.06h-47.06V196.9zm-23.72 0c0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06V79.06c0-25.9 21.16-47.06 47.06-47.06 25.9 0 47.06 21.16 47.06 47.06V196.9zM283.1 385.88c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06-25.9 0-47.06-21.16-47.06-47.06v-47.06h47.06zm0-23.72c-25.9 0-47.06-21.16-47.06-47.06 0-25.9 21.16-47.06 47.06-47.06h117.84c25.9 0 47.06 21.16 47.06 47.06 0 25.9-21.16 47.06-47.06 47.06H283.1z"/></svg>slack</a> </p> </li> </ul> </div> </div> </div>  </div> </footer> <script src="https://static.arxiv.org/static/base/1.0.0a5/js/member_acknowledgement.js"></script> </body> </html>

CINXE.COM

Search | arXiv e-print repository