CINXE.COM

<!doctype html><html><head><title>View article</title><meta http-equiv="Content-Type" content="text/html;charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="referrer" content="always"><meta name="viewport" content="width=device-width,initial-scale=1,minimum-scale=1,maximum-scale=2"><meta name="format-detection" content="telephone=no"><link rel="shortcut icon" href="/favicon.ico"><meta name="description" content="‪ATLAS Collaboration atlas. publications@ cern. ch, G Aad, B Abbott, K Abeling, NJ Abicht, SH Abidi, A Aboulhorma, H Abramowicz, H Abreu, Y Abulaiti…‬, ‪The European Physical Journal C, 2024‬ - ‪Cited by 8‬"><meta property="og:description" content="‪ATLAS Collaboration atlas. publications@ cern. ch, G Aad, B Abbott, K Abeling, NJ Abicht, SH Abidi, A Aboulhorma, H Abramowicz, H Abreu, Y Abulaiti…‬, ‪The European Physical Journal C, 2024‬ - ‪Cited by 8‬"><meta property="og:title" content="‪A precise measurement of the Z-boson double-differential transverse momentum and rapidity distributions in the full phase space of the decay leptons with the ATLAS experiment at s= 8 TeV‬"><meta property="og:image" content=""><meta property="og:type" content="website"><meta name="twitter:card" content="summary"><style>html,body,form,table,div,h1,h2,h3,h4,h5,h6,img,ol,ul,li,button{margin:0;padding:0;border:0;}table{border-collapse:collapse;border-width:0;empty-cells:show;}html,body{height:100%}#gs_top{position:relative;box-sizing:border-box;min-height:100%;min-width:964px;-webkit-tap-highlight-color:rgba(0,0,0,0);}#gs_top>*:not(#x){-webkit-tap-highlight-color:rgba(204,204,204,.5);}.gs_el_ph #gs_top,.gs_el_ta #gs_top{min-width:320px;}#gs_top.gs_nscl{position:fixed;width:100%;}body,td,input,button{font-size:13px;font-family:Arial,sans-serif;line-height:1.24;}body{background:#fff;color:#222;-webkit-text-size-adjust:100%;-moz-text-size-adjust:none;}.gs_gray{color:#777777}.gs_red{color:#dd4b39}.gs_grn{color:#006621}.gs_lil{font-size:11px}.gs_med{font-size:16px}.gs_hlt{font-weight:bold;}a:link{color:#1a0dab;text-decoration:none}a:visited{color:#660099;text-decoration:none}a:hover,a:hover .gs_lbl{text-decoration:underline}a:active,a:active .gs_lbl,a .gs_lbl:active{color:#d14836}.gs_el_tc a:hover,.gs_el_tc a:hover .gs_lbl{text-decoration:none}.gs_pfcs a:focus,.gs_pfcs button:focus,.gs_pfcs input:focus,.gs_pfcs label:focus{outline:none}.gs_a,.gs_a a:link,.gs_a a:visited{color:#006621}.gs_a a:active{color:#d14836}a.gs_fl:link,.gs_fl a:link{color:#1a0dab}a.gs_fl:visited,.gs_fl a:visited{color:#660099}a.gs_fl:active,.gs_fl a:active{color:#d14836}.gs_fl{color:#777777}.gs_ctc,.gs_ctu{vertical-align:middle;font-size:11px;font-weight:bold}.gs_ctc{color:#1a0dab}.gs_ctg,.gs_ctg2{font-size:13px;font-weight:bold}.gs_ctg{color:#1a0dab}a.gs_pda,.gs_pda a{padding:7px 0 5px 0}.gs_alrt{background:#f9edbe;border:1px solid #f0c36d;padding:0 16px;text-align:center;box-shadow:0 2px 4px rgba(0,0,0,.2);border-radius:2px;}.gs_alrt:empty{display:none;}.gs_spc{display:inline-block;width:12px}.gs_br{width:0;font-size:0}.gs_ibl{display:inline-block;}.gs_scl:after{content:"";display:table;clear:both;}.gs_ind{padding-left:8px;text-indent:-8px}.gs_ico,.gs_icm{display:inline-block;background:no-repeat url(/intl/en/scholar/images/1x/sprite_20161020.png);background-position:-23px -161px;background-size:169px;width:21px;height:21px;}@media(-webkit-min-device-pixel-ratio:1.5),(min-resolution:144dpi){.gs_ico,.gs_icm{background-image:url(/intl/en/scholar/images/2x/sprite_20161020.png);}}.gs_el_ta .gs_nta,.gs_ota,.gs_el_ph .gs_nph,.gs_oph{display:none}.gs_el_ta .gs_ota,.gs_el_ph .gs_oph{display:inline}.gs_el_ta div.gs_ota,.gs_el_ph div.gs_oph{display:block}.gs_sth_g{visibility:hidden;max-height:0;}.gs_sth_vis .gs_sth_g{max-height:1000px;}.gs_sth_vis .gs_sth_b{position:fixed;top:0;}.gs_sth_trk .gs_sth_b{position:absolute;top:auto;}@keyframes gs_anm_spin{0%{transform:rotate(0deg);}100%{transform:rotate(360deg);}}.gs_invis{visibility:hidden;}.gs_rimg{display:block;background-color:#e5e5e5;border-radius:50%;overflow:hidden;position:relative;z-index:1;}.gs_rimg>img{position:absolute;margin:auto;left:0;top:0;bottom:0;right:0;}.gs_in_txtw{display:inline-block;vertical-align:middle;}.gs_in_txtb{display:block;}.gs_in_txt{color:#000;background-color:#fff;font-size:16px;box-sizing:border-box;height:29px;line-height:23px;border:1px solid #d9d9d9;border-top-color:#c0c0c0;padding:3px 6px 1px 8px;border-radius:1px;outline:none;-webkit-appearance:none;-moz-appearance:none;}.gs_el_tc .gs_in_txt{font-size:18px;}.gs_in_txtb .gs_in_txt{width:100%;}.gs_in_rnd .gs_in_txt{border-radius:14.5px;padding:3px 12px 1px 12px;}.gs_in_txt:hover{border-color:#b9b9b9;border-top-color:#a0a0a0;box-shadow:inset 0 1px 2px rgba(0,0,0,.1);}.gs_in_txte .gs_in_txt{border-color:#dd4b39;}.gs_in_txt:focus{border-color:#4d90fe;box-shadow:inset 0 1px 2px rgba(0,0,0,.3);}.gs_in_txt:disabled{color:#b8b8b8;border-color:#f1f1f1;box-shadow:none;}.gs_in_txtm .gs_in_txt{font-size:13px;height:24px;line-height:16px;padding:3px 6px;}.gs_in_txtm.gs_in_rnd .gs_in_txt{border-radius:12px;}.gs_el_tc .gs_in_txtm .gs_in_txt{height:29px;line-height:21px;}.gs_el_tc .gs_in_txtm.gs_in_rnd .gs_in_txt{border-radius:14.5px;}.gs_in_txtl .gs_in_txt{height:41px;padding:9px 43px;}.gs_in_txtl.gs_in_rnd .gs_in_txt{border-radius:20.5px;}.gs_in_txts{font-size:13px;line-height:18px;color:#666;}.gs_in_txts:not(:empty){margin-top:2px;}.gs_in_txte .gs_in_txts{color:#dd4b39;}button{position:relative;z-index:1;box-sizing:border-box;font-size:13px;cursor:pointer;height:29px;line-height:normal;min-width:72px;padding:0 8px;color:#444;border:1px solid rgba(0,0,0,.1);border-radius:3px;text-align:center;background-color:#f5f5f5;-ms-user-select:none;user-select:none;}button.gs_btn_rnd{border-radius:14px;padding:0 12px;}button.gs_btn_rnd.gs_btn_rndci{padding-left:4px;}button.gs_btn_lrge{height:41px;min-width:82px;padding:0 9px;}button.gs_btn_lrge.gs_btn_lrge_asym{padding-left:5px;padding-right:8px;}button.gs_btn_lrge.gs_btn_rnd{border-radius:20px;padding:0 16px;}button.gs_btn_lrge.gs_btn_rnd.gs_btn_rndci{padding-left:10px;}button.gs_btn_cir{border-radius:14.5px;min-width:29px;}button.gs_btn_lrge.gs_btn_cir{border-radius:20.5px;min-width:41px;}button.gs_btn_mini{padding:0;border:0;}.gs_el_ph button.gs_btn_mph,.gs_el_ta button.gs_btn_mta{height:41px;}button .gs_wr{position:relative;display:inline-block;width:100%;height:100%;}button .gs_wr:before{content:"";width:0;height:100%;}button .gs_wr:before,button .gs_ico,button .gs_rdt,button .gs_lbl,button .gs_icm{display:inline-block;vertical-align:middle;}button .gs_wr{font-size:13px;text-transform:none;}.gs_btn_lrge .gs_wr{font-size:15px;}.gs_btn_lsb .gs_wr{font-size:11px;font-weight:bold;}.gs_btn_lsu .gs_wr{font-size:11px;text-transform:uppercase;}.gs_btn_lrge.gs_btn_lsb .gs_wr,.gs_btn_lrge.gs_btn_lsu .gs_wr,.gs_btn_lrge.gs_btn_lrge_asym .gs_wr{font-size:13px;}.gs_btn_half,.gs_el_ta .gs_btn_hta,.gs_el_ph .gs_btn_hph{min-width:36px;}.gs_btn_lrge.gs_btn_half,.gs_el_ta .gs_btn_lrge.gs_btn_hta,.gs_el_ph .gs_btn_lrge.gs_btn_hph,.gs_el_ta .gs_btn_mta,.gs_el_ph .gs_btn_mph{min-width:41px;}.gs_btn_slt{border-radius:3px 0 0 3px;}.gs_btn_srt{margin-left:-1px;border-radius:0 3px 3px 0;}.gs_btn_smd{margin-left:-1px;border-radius:0;}button:hover{z-index:2;color:#222;border-color:rgba(0,0,0,.2);background-color:#f8f8f8;}button.gs_sel{background-color:#dcdcdc;}button:active{z-index:2;background-color:#f1f1f1;}button:focus{z-index:2;}button::-moz-focus-inner{padding:0;border:0}button:-moz-focusring{outline:1px dotted ButtonText}.gs_pfcs button:-moz-focusring{outline:none}a.gs_in_ib{position:relative;display:inline-block;line-height:16px;padding:6px 0 7px 0;-ms-user-select:none;user-select:none;}a.gs_btn_lrge{height:40px;padding:0;}a.gs_in_bgcw{min-width:41px;}a.gs_btn_lrge.gs_in_bgcw:before{position:absolute;content:"";height:29px;width:29px;top:6px;left:6px;background-color:#fff;box-shadow:0 1px 3px rgb(0,0,0,.4);border-radius:50%;}a.gs_in_bgcw:hover:before{background-color:#f5f5f5;}a.gs_in_bgcw:active:before{background-color:#e5e5e5;}a.gs_in_bgcw.gs_dis:before{background-color:#fff;}a.gs_in_ib .gs_lbl{display:inline-block;padding-left:21px;color:#222;}a.gs_in_ib.gs_in_gray .gs_lbl{color:#444;}a.gs_in_ib .gs_lbl:not(:empty){padding-left:29px;}button.gs_in_ib .gs_lbl:not(:empty){padding-left:4px;}a.gs_in_ib:active .gs_lbl,a.gs_in_ib .gs_lbl:active,a.gs_in_ib :active~.gs_lbl{color:#d14836;}.gs_el_ta .gs_btn_hta .gs_lbl,.gs_el_ph .gs_btn_hph .gs_lbl,.gs_el_ta .gs_btn_mta .gs_lbl,.gs_el_ph .gs_btn_mph .gs_lbl,.gs_el_ta .gs_btn_cta .gs_lbl,.gs_el_ph .gs_btn_cph .gs_lbl{display:none;}a.gs_in_ib .gs_ico{position:absolute;top:3px;left:0;}.gs_in_ib.gs_md_li .gs_ico{left:14px;}.gs_el_tc .gs_in_ib.gs_md_li .gs_ico{top:11px;}.gs_in_ib.gs_md_li.gs_md_lix .gs_ico{top:10px;left:16px;}a.gs_btn_lrge .gs_ico{top:50%;left:50%;margin:-10.5px 0 0 -10.5px;}.gs_in_ib .gs_ico{opacity:.55;}.gs_in_ib:hover .gs_ico{opacity:.72;}.gs_in_ib:active .gs_ico,.gs_in_ib .gs_ico:active,.gs_in_ib :active~.gs_ico{opacity:1;}.gs_in_ib:disabled .gs_ico,.gs_in_ib.gs_dis .gs_ico{opacity:.28;}.gs_in_ib.gs_btn_act .gs_ico,.gs_in_ib.gs_btn_cre .gs_ico{opacity:1;}.gs_btn_act:disabled .gs_ico,.gs_btn_cre:disabled .gs_ico{opacity:.72;}.gs_rdt{position:relative;width:0;height:21px;}a.gs_in_ib .gs_rdt{left:21px;}.gs_rdt:before{content:"";position:absolute;top:1px;right:0;width:5px;height:5px;border:1px solid #fff;border-radius:50%;background-color:#dd4b39;}.gs_notf{display:inline-block;vertical-align:top;margin-left:8px;width:16px;line-height:16px;background-color:#d14836;border-radius:50%;color:#fff;text-align:center;font-size:9px;font-weight:bold;}.gs_notf:empty{display:none;}.gs_ind .gs_notf{text-indent:0;}button.gs_btn_flat{border-color:transparent;background-color:transparent;}button.gs_btn_olact{color:#4d90fe;background-color:transparent;}button.gs_btn_flat:hover,button.gs_btn_olact:hover{background-color:rgba(0,0,0,.05);}button.gs_btn_flat:active,button.gs_btn_olact:active{background-color:rgba(0,0,0,.1);}button.gs_btn_flat.gs_btn_flact{color:#1a0dab;}button.gs_btn_act{color:#fff;background-color:#4d90fe;}button.gs_btn_act:hover{color:#fff;background-color:#3983fe;}button.gs_btn_act.gs_sel{background-color:#2f6bcc;}button.gs_btn_act:active{background-color:#357ae8;}button.gs_btn_cre{color:#fff;background-color:#d14836;}button.gs_btn_cre:hover{color:#fff;background-color:#c53727;}button.gs_btn_cre.gs_sel{background-color:#992b1e;}button.gs_btn_cre:active{background-color:#b0281a;}button.gs_btn_hov_nobg:hover,button.gs_btn_hov_nobg:active{border:none;background:transparent;}button:disabled,button:disabled:hover,button:disabled:active{cursor:default;color:#b8b8b8;border-color:rgba(0,0,0,.05);background-color:transparent;z-index:0;}button.gs_btn_flat:disabled{color:#b8b8b8;border-color:transparent;}button.gs_btn_act:disabled{color:#fff;background-color:#a6c8ff;}button.gs_btn_cre:disabled{color:#fff;background-color:#e8a49b;}a.gs_in_ib.gs_dis{cursor:default;pointer-events:none}a.gs_in_ib.gs_dis .gs_lbl{color:#b8b8b8;text-decoration:none}.gs_ttp{position:absolute;top:100%;right:50%;z-index:10;pointer-events:none;visibility:hidden;opacity:0;transition:visibility 0s .13s,opacity .13s ease-out;}button:hover .gs_ttp,button:focus .gs_ttp,a:hover .gs_ttp,a:focus .gs_ttp{transition:visibility 0s .3s,opacity .13s ease-in .3s;visibility:visible;opacity:1;}.gs_md_tb.gs_sel .gs_ttp{transition:none;visibility:hidden;}button.gs_btn_lrge.gs_btn_cir .gs_ttp{top:75%;}.gs_ttp .gs_aro,.gs_ttp .gs_aru{position:absolute;top:-2px;right:-5px;width:0;height:0;line-height:0;font-size:0;border:5px solid transparent;border-top:none;border-bottom-color:#595959;z-index:1;}.gs_ttp .gs_aro{top:-3px;right:-6px;border-width:6px;border-top:none;border-bottom-color:white;}.gs_ttp .gs_txt{display:block;position:relative;top:2px;right:-50%;padding:4px 6px;background:#595959;color:white;font-size:11px;font-weight:bold;line-height:normal;white-space:nowrap;border:1px solid white;border-radius:3px;box-shadow:inset 0 1px 4px rgba(0,0,0,.2);}.gs_press,.gs_in_se,.gs_tan{touch-action:none;}.gs_in_se .gs_lbl:not(:empty){padding-right:14px;}.gs_in_se .gs_icm{position:absolute;top:50%;margin-top:-5.5px;right:0;width:7px;height:11px;background-position:-21px -88px;opacity:.55;}.gs_in_se:hover .gs_icm{opacity:.72;}.gs_in_se:active .gs_icm{opacity:1;}.gs_in_se:disabled .gs_icm{opacity:.28;}.gs_el_ta .gs_btn_hta .gs_icm,.gs_el_ph .gs_btn_hph .gs_icm,.gs_el_ta .gs_btn_mta .gs_icm,.gs_el_ph .gs_btn_mph .gs_icm,.gs_el_ta .gs_btn_cta .gs_icm,.gs_el_ph .gs_btn_cph .gs_icm{display:none;}.gs_btn_mnu .gs_icm{margin-top:-3.5px;height:7px;background-position:0 -110px;}.gs_in_se.gs_btn_act .gs_icm,.gs_in_se.gs_btn_cre .gs_icm{margin-top:-3.5px;height:7px;background-position:-42px -44px;opacity:1;}.gs_btn_act:disabled .gs_icm,.gs_btn_cre:disabled .gs_icm{opacity:.72;}button.gs_btnG .gs_ico{width:21px;height:21px;background-position:-92px -253px;}button .gs_bs{position:absolute;top:50%;left:50%;margin-top:-10px;margin-left:-10px;box-sizing:border-box;width:20px;height:20px;border-radius:50%;border:2px solid #eee;border-top-color:#4d90fe;visibility:hidden;animation:gs_anm_spin .8s linear infinite;}button.gs_bsp .gs_bs{visibility:visible;transition:visibility 0s .4s;}.gs_md_d{text-transform:none;white-space:nowrap;position:absolute;top:0;left:0;border:1px solid #ccc;border-color:rgba(0,0,0,.2);background:#fff;box-shadow:0 2px 4px rgba(0,0,0,.2);z-index:1100;text-align:left;visibility:hidden;max-height:0;margin-top:-1000px;opacity:0;transition:opacity .13s,visibility 0s .13s,max-height 0s .13s,margin-top 0s .13s;}.gs_md_d.gs_vis{visibility:visible;max-height:10000px;margin-top:0;opacity:1;transition:all 0s;}.gs_el_tc .gs_md_d{transform-origin:100% 0;transform:scale(1,0);transition:opacity .218s ease-out,transform 0s .218s,visibility 0s .218s,max-height 0s .218s,margin-top 0s .218s;}.gs_el_tc .gs_md_d.gs_ttzi{transform-origin:50% 50%;transform:scale(0,0);}.gs_el_tc .gs_md_d.gs_ttzr{transform:scale(0,0);}.gs_el_tc .gs_md_d.gs_vis{transform:scale(1,1);transition:transform .218s ease-out;}.gs_md_r{position:relative;display:inline-block;}.gs_md_rmb>.gs_md_d{top:29px}.gs_md_rmbl>.gs_md_d{top:41px}.gs_md_ul{list-style-type:none;word-wrap:break-word;display:inline-block;vertical-align:top;}.gs_md_ul.gs_md_ul_tb{display:block;}.gs_md_li,.gs_in_cb.gs_md_li,.gs_md_li:link,.gs_md_li:visited{display:block;padding:6px 44px 6px 16px;font-size:13px;line-height:16px;color:#222;cursor:pointer;text-decoration:none;position:relative;z-index:0;}a.gs_md_li:hover .gs_lbl,a.gs_md_li:active .gs_lbl{text-decoration:none}.gs_el_tc .gs_md_li{padding-top:14px;padding-bottom:10px;}.gs_md_li.gs_md_lix{font-size:16px;line-height:20px;padding:12px 16px 8px 16px;}.gs_md_li:before{content:"";background-color:#f1f1f1;position:absolute;left:0;right:0;top:0;bottom:0;opacity:0;transition:opacity .13s;z-index:-1;}.gs_md_li:hover:before,.gs_md_li:focus:before{opacity:1;transition:all 0s;}a.gs_in_ib.gs_md_li .gs_lbl{color:#222}a.gs_in_ib.gs_md_li.gs_in_gray .gs_lbl{color:#444}.gs_md_li:active:before{background-color:#ddd}.gs_md_li.gs_sel,a.gs_in_ib.gs_md_li.gs_sel .gs_lbl{color:#d14836}.gs_md_d:focus,.gs_md_li:focus{outline:none}a.gs_md_lix .gs_lbl,a.gs_md_lix .gs_lbl:not(:empty){padding:0 0 0 40px;}a.gs_in_cb:link,a.gs_in_cb:visited,a.gs_in_cb:active,a.gs_in_cb:hover{cursor:pointer;color:#222;text-decoration:none;}.gs_in_cb,.gs_in_ra{position:relative;line-height:16px;display:inline-block;-ms-user-select:none;user-select:none;}.gs_in_cb.gs_md_li{padding:6px 44px 6px 16px;}.gs_in_cb input,.gs_in_ra input{position:absolute;top:1px;left:1px;width:15px;height:15px;margin:0;padding:0;opacity:0;z-index:2;}.gs_in_ra input{top:0;left:0}.gs_el_tc .gs_in_cb input{top:9px}.gs_el_tc .gs_in_ra input{top:8px}.gs_in_cb.gs_in_cbj input{top:15px;left:15px}.gs_in_cb label,.gs_in_cb .gs_lbl,.gs_in_ra label{display:inline-block;padding-left:21px;min-height:16px;}.gs_in_ra_lrge{font-size:15px;}.gs_in_cb label:empty:before,.gs_in_cb .gs_lbl:empty:before,.gs_in_ra label:empty:before{content:"\200b";}.gs_el_tc .gs_in_cb label,.gs_el_tc .gs_in_cb .gs_lbl,.gs_el_tc .gs_in_ra label{padding-top:8px;padding-bottom:5px;}.gs_in_cb.gs_in_cbj label,.gs_in_cb.gs_in_cbj .gs_lbl{padding:13px 0 12px 41px;}.gs_in_cbb,.gs_in_cbb label,.gs_in_cbb .gs_lbl{display:block;}.gs_in_cb .gs_cbx,.gs_in_ra .gs_cbx{position:absolute}.gs_in_cb .gs_cbx{top:2px;left:2px;width:11px;height:11px;border:1px solid #c6c6c6;border-radius:1px;}.gs_md_li .gs_cbx{top:8px;left:18px}.gs_el_tc .gs_in_cb .gs_cbx{top:10px}.gs_el_tc .gs_md_li .gs_cbx{top:16px}.gs_in_cb.gs_in_cbj .gs_cbx{top:15px;left:15px}.gs_el_tc .gs_in_ra .gs_cbx{top:8px}.gs_in_ra .gs_cbx{top:0;left:0;border:1px solid #c6c6c6;width:13px;height:13px;border-radius:7px;}.gs_in_cb:hover .gs_cbx,.gs_in_ra:hover .gs_cbx{border-color:#666;box-shadow:inset 0 1px 1px rgba(0,0,0,.1);}button.gs_in_cb:hover .gs_cbx{border-color:#c6c6c6;}.gs_in_cb :focus~label,.gs_in_ra :focus~label{outline:1px dotted #222;}.gs_pfcs .gs_in_cb :focus~label,.gs_pfcs .gs_in_ra :focus~label{outline:none;}.gs_in_cb:active .gs_cbx,.gs_in_ra:active .gs_cbx,.gs_in_cb .gs_cbx:active,.gs_in_ra .gs_cbx:active,.gs_in_cb :active~.gs_cbx,.gs_in_ra :active~.gs_cbx{border-color:#666;background-color:#ebebeb;}button.gs_in_cb:active .gs_cbx{border-color:#a6a6a6;}.gs_in_cb :disabled~.gs_cbx,.gs_in_ra :disabled~.gs_cbx,button.gs_in_cb:disabled .gs_cbx{border-color:#f1f1f1;box-shadow:none;}.gs_in_cb :disabled~label,.gs_in_ra :disabled~label{color:#b8b8b8;}.gs_in_cb.gs_err .gs_cbx{border-color:#eda29b;}.gs_in_cb .gs_chk,.gs_in_ra .gs_chk{position:absolute;z-index:1;top:-3px;left:-2px;width:21px;height:21px;}.gs_md_li .gs_chk{top:3px;left:14px}.gs_el_tc .gs_in_cb .gs_chk{top:5px}.gs_el_tc .gs_md_li .gs_chk{top:11px}.gs_in_cb.gs_in_cbj .gs_chk{top:10px;left:11px}.gs_in_ra .gs_chk{top:4px;left:4px;width:7px;height:7px;border-radius:4px;}.gs_el_tc .gs_in_ra .gs_chk{top:12px}.gs_in_cb input:checked~.gs_chk,.gs_in_cb.gs_sel .gs_chk{background:no-repeat url(/intl/en/scholar/images/1x/sprite_20161020.png) -69px -67px;opacity:.62;}.gs_in_ra input:checked~.gs_chk{background-color:#666}.gs_in_cb.gs_par .gs_chk{background:no-repeat url(/intl/en/scholar/images/1x/sprite_20161020.png) -21px -44px;opacity:.55;}@media(-webkit-min-device-pixel-ratio:1.5),(min-resolution:144dpi){.gs_in_cb input:checked~.gs_chk,.gs_in_cb.gs_sel .gs_chk,.gs_in_cb.gs_par .gs_chk{background-image:url(/intl/en/scholar/images/2x/sprite_20161020.png);background-size:169px;}}.gs_in_cb input:checked:disabled~.gs_chk{opacity:.22}.gs_in_ra input:checked:disabled~.gs_chk{background-color:#f1f1f1}.gs_in_cb.gs_bsp .gs_cbx{top:6px;left:16px;border-radius:6px;border-width:3px;animation:gs_cbx_spn .5s infinite linear;}.gs_el_tc .gs_in_cb.gs_md_li.gs_bsp .gs_cbx{top:14px}.gs_in_cb .gs_csp{background:url('/intl/en/scholar/images/spinner.gif') no-repeat;position:absolute;height:25px;width:25px;top:2px;left:12px;display:none;animation:gs_cbx_ah 9s infinite;}.gs_in_cb.gs_bsp .gs_csp{display:block}.gs_el_tc .gs_md_li .gs_csp{top:10px}@keyframes gs_cbx_spn{0%,100%{border-color:#4d90fe #c6c6c6 #c6c6c6 #c6c6c6}40%{border-color:#c6c6c6 #4d90fe #c6c6c6 #c6c6c6}50%{border-color:#c6c6c6 #c6c6c6 #4d90fe #c6c6c6}60%{border-color:#c6c6c6 #c6c6c6 #c6c6c6 #4d90fe}}@keyframes gs_cbx_ah{0%,100%{visibility:hidden}}.gs_ico_x{background-position:-113px -22px;opacity:.55;}.gs_ico_x:hover{opacity:.72;}.gs_ico_x:active{opacity:1;}.gs_ico_X{background-position:-71px 0;opacity:.55;}.gs_ico_X:hover{opacity:.72;}.gs_ico_X:active{opacity:1;}.gs_btnX .gs_ico{background-position:-71px 0;}.gs_el_tc .gs_ico_Xt{background-origin:content-box;background-clip:content-box;padding:10px 6px 10px 14px;}.gs_ico_P{background-position:0 0;opacity:.55;}.gs_ico_P:hover{opacity:.72;}.gs_ico_P:active{opacity:1;}.gs_btnP .gs_ico{background-position:-21px 0;}.gs_btnC .gs_ico{background-position:0 -66px;}.gs_btnL .gs_ico{background-position:-92px -44px;}.gs_ico_LB{background-position:-50px -44px;height:16px;}.gs_btnJ .gs_ico{background-position:-92px -22px;}.gs_btnM .gs_ico{background-position:-92px 0;}.gs_btnMW .gs_ico{background-position:-21px -22px;}.gs_btnSB .gs_ico{background-position:0 -44px;}.gs_btnTSB .gs_ico{background-position:-115px -253px;}.gs_btnPL .gs_ico{background-position:-148px -66px;}.gs_btnPR .gs_ico{background-position:-21px -66px;}.gs_btnPLW .gs_ico{background-position:-0 -230px;}.gs_btnPRW .gs_ico{background-position:-23px -230px;}.gs_btnZI .gs_ico{background-position:-148px -22px;}.gs_btnZO .gs_ico{background-position:-127px -44px;}.gs_btnDE .gs_ico{background-position:-134px 0;}.gs_btnFI .gs_ico{background-position:-50px -66px;}.gs_btnAD .gs_ico{background-position:-141px -88px;opacity:.55;}.gs_btnAD:hover .gs_ico{opacity:.72;}.gs_btnAD:active .gs_ico,.gs_btnAD .gs_ico:active,.gs_btnAD :active~.gs_ico{opacity:1;}.gs_btnBA .gs_ico{background-position:-50px -22px;}.gs_btnADD .gs_ico{background-position:-92px -66px;}.gs_btnMRG .gs_ico{background-position:-113px 0;}.gs_btnLBL .gs_ico{background-position:0 -161px;}.gs_btnCNCL .gs_ico{background-position:-71px 0;}.gs_btnDWL .gs_ico{background-position:-28px -88px;}.gs_btnMNU .gs_ico{background-position:0 -88px;}.gs_btnMNT .gs_ico{background-position:-46px -161px;}.gs_btnALT .gs_ico{background-position:-92px -161px;}.gs_btnART .gs_ico{background-position:-115px -161px;}.gs_btnGSL .gs_ico{background-position:-69px -161px;}.gs_btnCLS .gs_ico{background-position:-138px -161px;}.gs_btnXBLU .gs_ico{background-position:-138px -253px;}.gs_btnSSB .gs_ico{background-position:0 -276px;}.gs_btnSSW .gs_ico{background-position:-23px -276px;}.gs_btnFLT .gs_ico{background-position:0 -184px;}.gs_btnXT .gs_ico{background-position:-46px -184px;}.gs_btnPD .gs_ico{background-position:-69px -184px;}.gs_btnPU .gs_ico {background-position:-92px -276px;}.gs_btnCP .gs_ico{background-position:-92px -184px;}.gs_btnTP .gs_ico{background-position:-138px -184px;}.gs_btnML .gs_ico{background-position:-115px -276px;}.gs_btnCHK .gs_ico{background-position:-71px -66px;}.gs_btnDNB .gs_ico{background-position:-115px -230px;}.gs_btnDNW .gs_ico{background-position:0 -207px;}.gs_btnACA .gs_ico{background-position:-23px -207px;}.gs_btnAPT .gs_ico{background-position:-46px -207px;}.gs_btnAPTW .gs_ico{background-position:-92px -230px;}.gs_btnAFL .gs_ico{background-position:-69px -207px;}.gs_btnAN .gs_ico{background-position:-46px -276px;}.gs_btnAI .gs_ico{background-position:-69px -276px;}.gs_btnPBL .gs_ico{background-position:-92px -207px;}.gs_btnUCT .gs_ico{background-position:-115px -207px;}.gs_btnVRF .gs_ico{background-position:-138px -207px;}.gs_btnLSI .gs_ico{background-position:-46px -230px;}.gs_btnLSG .gs_ico{background-position:-69px -230px;}.gs_btnMOR .gs_ico{background-position:-23px -253px;}.gs_btnADV .gs_ico{background-position:-46px -253px;}.gs_btnPRO .gs_ico{background-position:-69px -253px;}.gs_ico_star{background-position:-71px -44px;width:13px;height:13px;}.gs_btnPLSW .gs_ico{background-position:-138px -230px;}.gs_btnPDF .gs_ico{background-position:0 -253px;}.gs_btnS .gs_ico{background-position:-138px -276px;}.gs_btnUNS .gs_ico{background-position:0 -299px;}.gs_btnMORR .gs_ico{background-position:-23px -299px;}.gs_btnTW .gs_ico{background-position:-46px -299px;}.gs_btnIN .gs_ico{background-position:-69px -299px;}.gs_btnFB .gs_ico{background-position:-92px -299px;}.gs_btnET .gs_ico{background-position:-115px -299px;}.gs_btnARC .gs_ico{background-position:-138px -299px;}.gs_btnOL .gs_ico{background-position:0px -322px;}.gs_btnFA .gs_ico{background-position:-23px -322px;}.gs_btnFAD .gs_ico{background-position:-46px -322px;}.gs_btnHP .gs_ico{background-position:-69px -322px;}.gs_btnPLM .gs_ico{background-position:-92px -322px;}.gs_btnPRM .gs_ico{background-position:-115px -322px;}.gs_btnRN .gs_ico{background-position:-138px -322px;}.gs_btnVF .gs_ico{background-position:0px -345px;}.gs_btnVP .gs_ico{background-position:-23px -345px;}.gs_btnSRT .gs_ico{background-position:-46px -345px;}#gs_md_s.gs_hdr_drs{transition:opacity .15s,visibility 0s .15s;}#gs_md_s.gs_hdr_drs.gs_vis{transition:opacity .15s,visibility 0s;}.gs_el_tc #gs_md_s.gs_hdr_drs{transition:opacity .218s,visibility 0s .218s;}.gs_el_tc #gs_md_s.gs_hdr_drs.gs_vis{transition:opacity .218s,visibility 0s;}#gs_hdr_drw{position:fixed;top:0;left:0;height:100%;z-index:1200;visibility:hidden;overflow:auto;width:228px;background-color:#fff;box-shadow:2px 2px 4px rgba(0,0,0,.15);outline:none;transform:translate(-100%,0);transition:transform .15s ease-in-out,visibility 0s .15s;}#gs_hdr_drw.gs_vis{visibility:visible;transform:translate(0,0);transition:transform .15s ease-in-out,visibility 0s;}.gs_el_tc #gs_hdr_drw{transition:transform .3s cubic-bezier(.4,0,.6,1),visibility 0s .3s;}.gs_el_tc #gs_hdr_drw.gs_vis{transition:transform .225s cubic-bezier(0,0,.2,1),visibility 0s;}#gs_top #gs_hdr_drw.gs_abt,#gs_top #gs_md_s.gs_abt{transition:none;}#gs_hdr_drw_in{position:relative;box-sizing:border-box;min-height:100%;padding:0 0 8px 0;}.gs_el_ta #gs_hdr_drw_in,.gs_el_ph #gs_hdr_drw_in{padding:0 0 65px 0;}#gs_hdr_drw_top{position:relative;height:63px;border-bottom:1px solid #e5e5e5;margin-bottom:8px;}.gs_el_ta #gs_hdr_drw_top,.gs_el_ph #gs_hdr_drw_top{height:57px;}#gs_hdr_drw_mnu,#gs_hdr_drw_lgo{position:absolute;top:0;height:100%;}#gs_hdr_drw_mnu{left:0;width:55px;}#gs_hdr_drw_lgo{left:56px;}.gs_hdr_drw_sec:before{display:block;content:" ";height:0;border-bottom:1px solid #e5e5e5;margin:8px 0;}.gs_hdr_drw_sec:first-child:before{display:none;}#gs_hdr_drw_bot{display:none;}.gs_el_ta #gs_hdr_drw_bot,.gs_el_ph #gs_hdr_drw_bot{display:block;position:absolute;left:0;bottom:0;width:100%;height:65px;}#gs_hdr_drw_bot .gs_md_li:before{opacity:0;}#gs_hdr_drw_bot .gs_hdr_pp{display:block;position:absolute;bottom:14px;left:15px;pointer-events:none;}#gs_hdr_drw_bot .gs_lbl{display:block;white-space:nowrap;overflow:hidden;text-overflow:ellipsis;}#gs_hdr{position:relative;height:63px;background-color:#f5f5f5;border-bottom:1px solid #e5e5e5;display:flex;}.gs_el_ta #gs_hdr,.gs_el_ph #gs_hdr{height:57px;}#gs_hdr_mnu,#gs_hdr_bck,#gs_hdr_lgo,#gs_hdr_lgt,#gs_hdr_md,#gs_hdr_sre,#gs_hdr_act{display:inline-block;vertical-align:top;position:relative;height:100%;flex:0 0 auto;}#gs_hdr_md{flex:1 1 auto;}#gs_hdr .gs_hdr_mbo,#gs_hdr .gs_hdr_mbo,.gs_el_ta #gs_hdr .gs_hdr_dso,.gs_el_ph #gs_hdr .gs_hdr_dso{display:none;}.gs_el_ta #gs_hdr .gs_hdr_mbo,.gs_el_ph #gs_hdr .gs_hdr_mbo{display:inline-block;}#gs_hdr_mnu,#gs_hdr_bck,#gs_hdr_sre{width:55px;margin-right:1px;}#gs_hdr_lgo,#gs_hdr_drw_lgo{width:149px;background:no-repeat url('/intl/en/scholar/images/1x/scholar_logo_24dp.png') 0% 50%;background-size:149px;}@media(-webkit-min-device-pixel-ratio:1.5),(min-resolution:144dpi){#gs_hdr_lgo,#gs_hdr_drw_lgo{background-image:url('/intl/en/scholar/images/2x/scholar_logo_24dp.png');}}#gs_hdr_lgo{margin-right:31px;}.gs_el_ph #gs_hdr_lgo{margin-right:0;}#gs_hdr_lgt{min-width:164px;margin-right:16px;}#gs_hdr_md{margin-right:16px;min-width:1px;}#gs_hdr_lgt,#gs_hdr_md h1{padding:19px 0 0 0;white-space:nowrap;overflow:hidden;text-overflow:ellipsis;font-size:20px;line-height:25px;font-weight:normal;color:#666;max-width:100%;text-align:left;}.gs_el_ta #gs_hdr_md h1,.gs_el_ph #gs_hdr_md h1{padding:16px 0 0 0;}#gs_hdr_srch{padding:14px 0 0 0;max-width:600px;}.gs_el_ta #gs_hdr_srch,.gs_el_ph #gs_hdr_srch{padding:10px 0 0 0;max-width:none;}#gs_hdr_frm{position:relative;padding-right:39px;}#gs_hdr_tsi{height:38px;border-radius:2px 0 0 2px;}#gs_hdr_tsi::-ms-clear{display:none;}#gs_hdr_tsc{display:none;position:absolute;top:3px;right:41px;width:21px;height:21px;padding:6px 10px 7px 10px;}.gs_in_acw[dir="rtl"]~#gs_hdr_tsc{right:auto;left:1px;}#gs_hdr_tsb{position:absolute;top:0;right:0;width:40px;height:38px;border-radius:0 2px 2px 0;}#gs_hdr_frm_ac{top:37px;right:40px;}.gs_el_ph #gs_hdr_frm_ac{right:0;}.gs_el_ph .gs_hdr_ifc #gs_hdr_mnu,.gs_el_ph .gs_hdr_ifc #gs_hdr_bck,.gs_hdr_src #gs_hdr_srch,.gs_hdr_src #gs_hdr_lgt,.gs_hdr_srx #gs_hdr_sre,.gs_hdr_srx #gs_hdr_md h1,.gs_hdr_srx #gs_hdr_md h1.gs_hdr_mbo,.gs_hdr_srx #gs_hdr_md h1.gs_hdr_dso,.gs_el_ta .gs_hdr_srx #gs_hdr_lgo,.gs_el_ph .gs_hdr_srx #gs_hdr_lgo,.gs_el_ph .gs_hdr_srx #gs_hdr_mnu,.gs_el_ph .gs_hdr_srx #gs_hdr_bck{display:none;}.gs_el_ph .gs_hdr_ifc #gs_hdr_md,.gs_el_ph .gs_hdr_srx #gs_hdr_md{margin-left:16px;}.gs_el_tc .gs_hdr_tsc #gs_hdr_tsi[dir="ltr"]{padding-right:41px;}.gs_el_tc .gs_hdr_tsc #gs_hdr_tsi[dir="rtl"]{padding-left:41px;}.gs_el_tc .gs_hdr_tsc .gs_in_acw~#gs_hdr_tsc{display:block;}#gs_hdr_act{min-width:64px;max-width:200px;text-align:right;float:right;}.gs_el_ta #gs_hdr_act,.gs_el_ph #gs_hdr_act{display:none;}#gs_hdr_act_i,#gs_hdr_act_s{display:inline-block;padding:23px 24px 23px 16px;max-width:100%;box-sizing:border-box;font-size:13px;line-height:17px;white-space:nowrap;overflow:hidden;text-overflow:ellipsis;color:#444;}#gs_hdr_act_s{text-transform:uppercase;}.gs_el_sm #gs_hdr_act_i,.gs_el_sm #gs_hdr_act_s{padding:23px 16px;}.gs_el_ta #gs_hdr_act_i,.gs_el_ta #gs_hdr_act_s,.gs_el_ph #gs_hdr_act_i,.gs_el_ph #gs_hdr_act_s{padding:20px 16px;}#gs_hdr_act_i:active,#gs_hdr_act_s:active{color:#d14836;}#gs_hdr_act_i,.gs_el_sm #gs_hdr_act_i{padding-top:15px;padding-bottom:16px;}.gs_el_ta #gs_hdr_act_i,.gs_el_ph #gs_hdr_act_i{padding-top:12px;padding-bottom:13px;}#gs_hdr_act_i .gs_hdr_pp{vertical-align:top;}#gs_hdr_act_d{top:63px;left:auto;right:24px;min-width:288px;max-width:400px;}.gs_el_sm #gs_hdr_act_d{right:16px;}.gs_el_ta #gs_hdr_act_d{top:57px;}.gs_el_ph #gs_hdr_act_d{top:57px;min-width:280px;max-width:280px;max-width:90vw;}/* Account dialog body. */#gs_hdr_act_aw,#gs_hdr_act_ap,.gs_hdr_act_am,#gs_hdr_act_ab{display:block;padding:10px 20px;word-wrap:break-word;white-space:normal;}#gs_hdr_act_aw{background-color:#fef9db;font-size:11px;}#gs_hdr_act_ap,.gs_hdr_act_am{border-bottom:1px solid #ccc;}#gs_hdr_act_ap{padding:20px;}.gs_el_ph #gs_hdr_act_ap{padding:10px;}#gs_hdr_act_apb{margin-top:12px;}#gs_hdr_act_aa:link,#gs_hdr_act_aa:visited{float:right;margin-left:8px;color:#1a0dab;}#gs_hdr_act_aa:active{color:#d14836}.gs_hdr_act_am:link,.gs_hdr_act_am:visited{color:#222;text-decoration:none;background:#fbfbfb;}.gs_hdr_act_am:hover,.gs_hdr_act_am:focus{background:#f1f1f1;}.gs_hdr_act_am:active{background:#eee;}#gs_hdr_act_ab{background:#fbfbfb;padding:10px 0;display:table;width:100%;white-space:nowrap;}#gs_hdr_act_aba,#gs_hdr_act_abs{display:table-cell;padding:0 20px;}#gs_hdr_act_abs{text-align:right;}.gs_el_ph #gs_hdr_act_aba,.gs_el_ph #gs_hdr_act_abs{display:block;padding:10px;text-align:center;}.gs_el_ph #gs_hdr_act_aba button,.gs_el_ph #gs_hdr_act_abs button{width:100%;}#gs_hdr_act_a1,#gs_hdr_act_a2{position:absolute;top:-9px;right:7.5px;width:0;height:0;z-index:1;border:8.5px solid transparent;border-top:none;border-bottom-color:#333;border-bottom-color:rgba(0,0,0,.2);}#gs_hdr_act_a2{top:-8px;border-bottom-color:#fff;}.gs_hdr_act_mw #gs_hdr_act_a2{border-bottom-color:#fef9db;}.gs_hdr_pp{border-radius:50%;overflow:hidden;}#gs_hdr_act_ap .gs_hdr_pp,.gs_hdr_act_am .gs_hdr_pp{float:left;}#gs_hdr_act_ap .gs_hdr_pm{margin-left:116px;}.gs_hdr_act_am .gs_hdr_pm{margin:6px 0 0 58px;}#gs_ab{position:relative;height:41px;border-bottom:1px solid #e5e5e5;display:flex;white-space:nowrap;background-color:#fff;z-index:1000;}.gs_el_ta #gs_ab.gs_nta,.gs_el_ph #gs_ab.gs_nph{display:none;}.gs_sth_vis #gs_ab{position:fixed;}#gs_ab_ico,#gs_ab_ttl,#gs_ab_md,#gs_ab_btns{display:inline-block;vertical-align:top;position:relative;height:100%;flex:0 0 auto;}.gs_el_ph #gs_ab_md{display:block;}#gs_ab_ico{width:55px;margin-right:1px;}#gs_ab_ico .gs_ico{position:absolute;top:50%;left:50%;margin:-10.5px 0 0 -10.5px;}#gs_ab_ttl{min-width:172px;padding-right:8px;}.gs_el_sm #gs_ab_ttl{min-width:68px;}.gs_el_ta #gs_ab_ttl,.gs_el_ph #gs_ab_ttl{min-width:0;}#gs_ab_ttl,#gs_ab_ttll{font-size:18px;color:#666;text-transform:none;}.gs_el_sm #gs_ab_ttl,.gs_el_sm #gs_ab_ttll{font-size:16px;}#gs_ab_ttll{overflow:hidden;text-overflow:ellipsis;max-width:200px;}#gs_ab_md{flex:1 0 auto;}.gs_ab_st #gs_ab_md{flex:1 1 auto;font-size:13px;line-height:17px;padding:0 8px;color:#999;overflow:hidden;text-overflow:ellipsis;}.gs_el_ph .gs_ab_st #gs_ab_md{visibility:hidden;padding:0;}#gs_ab_btns{margin-right:8px;}.gs_el_sm #gs_ab_btns{margin-right:0;}.gs_el_ta #gs_ab_btns,.gs_el_ph #gs_ab_btns{margin-right:4px;}#gs_ab_ttl:before,#gs_ab_md:before,#gs_ab_btns:before{content:"";display:inline-block;width:0;height:100%;vertical-align:middle;}#gs_ab_md>button,#gs_ab_btns>button,#gs_ab_md>.gs_in_ib,#gs_ab_btns>.gs_in_ib,#gs_ab_md>.gs_md_r,#gs_ab_btns>.gs_md_r,#gs_ab .gs_ab_mdw,#gs_ab .gs_ab_btw{margin:0 8px;vertical-align:middle;}#gs_ab .gs_ab_mdw,.gs_ab_btw{display:inline-block;margin:0;}#gs_ab_btns>.gs_in_ib{margin:0 16px 0 8px;}#gs_ab .gs_ab_btw{margin:0 12px 0 16px;}.gs_el_ta .gs_ab_sel #gs_ab_ico,.gs_el_ph .gs_ab_sel #gs_ab_ico,.gs_el_ta .gs_ab_sel #gs_ab_ttl,.gs_el_ph .gs_ab_sel #gs_ab_ttl,.gs_el_ta .gs_ab_sel #gs_ab_btns,.gs_el_ph .gs_ab_sel #gs_ab_btns{display:none;}#gs_bdy{display:table;table-layout:fixed;width:100%;}#gs_bdy_sb{vertical-align:top;width:228px;word-wrap:break-word;display:table-cell;}.gs_el_sm #gs_bdy_sb{}.gs_el_ta #gs_bdy_sb,.gs_el_ph #gs_bdy_sb{display:none;}.gs_bdy_sb_sec{margin:0 40px 0 56px;}.gs_bdy_sb_sec:before{display:block;content:" ";height:0;margin:13px 0;border-top:1px solid #eee;}.gs_bdy_sb_sec:first-child:before{margin:21px 0 0 0;border:none;}#gs_bdy_sb ul{list-style-type:none;}.gs_bdy_sb_sec a:link,.gs_bdy_sb_sec a:visited{color:#222;}.gs_bdy_sb_sec a:active{color:#d14836;}.gs_bdy_sb_sel a:link,.gs_bdy_sb_sel a:visited{color:#d14836;text-decoration:none;}.gs_el_tc .gs_bdy_sb_sec li.gs_ind,.gs_el_tc .gs_bdy_sb_sec li.gs_ind a{padding-top:8px;padding-bottom:5px;}.gs_el_tc .gs_bdy_sb_sec:first-child li.gs_ind:first-child{margin-top:-8px;}#gs_bdy_sb .gs_ind,#gs_bdy_sb .gs_inw{margin-bottom:6px;}.gs_el_tc #gs_bdy_sb .gs_ind,.gs_el_tc #gs_bdy_sb .gs_inw{margin-bottom:0;}#gs_bdy_ccl{display:table-cell;vertical-align:top;padding:0 24px 0 16px;}.gs_el_sm #gs_bdy_ccl{padding:0 16px;}.gs_el_ta #gs_bdy_ccl,.gs_el_ph #gs_bdy_ccl{padding:0 16px 0 56px;}.gs_el_ph #gs_bdy_ccl{padding:0 16px;padding:0;}#gs_ftr_sp{height:62px;}.gs_el_sm #gs_ftr_sp{height:57px;}#gs_ftr{position:absolute;bottom:0;left:0;width:100%;white-space:nowrap;border-top:1px solid #e4e4e4;background-color:#f2f2f2;display:flex;}#gs_ftr.gs_pfix{position:fixed;}#gs_ftr_rt{box-sizing:border-box;max-width:100%;overflow-x:auto;margin-left:auto;padding:0 12px;}.gs_el_sm #gs_ftr_rt{padding:0 8px;}.gs_el_ph #gs_ftr_rt:after{content:" ";position:absolute;top:0;right:0;width:16px;height:100%;background-image:linear-gradient(to right,rgba(242,242,242,0),rgba(242,242,242,1) 80%);}#gs_ftr_rt>a{display:inline-block;line-height:16px;padding:12px;white-space:nowrap;}.gs_el_sm #gs_ftr_rt>a{padding:12px 8px;}#gs_ftr_rt>a:link,#gs_ftr_rt>a:visited{color:#666}#gs_ftr_rt>a:active{color:#d14836}#gs_ftr_mnu{top:auto;bottom:48px;left:auto;right:24px;padding:8px 0;}.gs_el_sm #gs_ftr_mnu{right:16px;}#gsc_sb_ui{text-align:center;margin-bottom:16px;}#gsc_sb_ui img{max-width:120px;height:auto;}.gs_el_sm #gsc_sb_ui img{max-width:100px;}.gsc_sb_addl{text-align:right;padding:0 8px;color:#777777;min-width:60px;}#gsc_ccl{max-width:862px;margin:21px 0 0 0;}.gs_el_sm #gsc_ccl{margin:16px 0 0 0;}.gsc_art_mm{font-size:24px;line-height:16px;display:inline-block;margin:-10px 0 0 4px;position:relative;top:8px;}.gs_pp_tn,.gs_el_ta .gs_pp_mo_tn,.gs_el_ph .gs_pp_mo_tn{width:32px;height:32px;}.gs_pp_sm,.gs_el_ta .gs_pp_mo_sm,.gs_el_ph .gs_pp_mo_sm{width:56px;height:56px;}.gs_pp_nm,.gs_el_ta .gs_pp_mo_nm,.gs_el_ph .gs_pp_mo_nm{width:128px;height:128px;}#gsc_vcpb{max-width:870px;padding-top:21px;}.gs_el_ph #gsc_vcpb{padding:16px 8px;}#gsc_vcpb_btns{padding-bottom:16px;}#gsc_vcpb_btns:empty{display:none;}#gsc_vcpb_btns>button{margin-right:16px;}.gs_el_ph #gsc_vcpb_btns>button{margin-right:8px;}#gsc_oci_title_wrapper{font-size:16px;margin:0 0 16px 0;}#gsc_oci_title{font-size:20px;}.gs_el_sm #gsc_oci_title{font-size:18px;}#gsc_oci_title_gg{float:right;padding:0 0 8px 16px;}.gs_el_ph #gsc_oci_title_gg{float:none;text-align:right;padding:0;margin:-4px 0 8px 0;}.gsc_oci_title_ggt{font-size:13px;font-weight:bold;}.gsc_oci_title_ggut{font-size:13px;color:#777;padding-bottom:8px;}.gsc_oci_field{float:left;width:100px;text-align:right;color:#777;}.gs_el_ph .gsc_oci_field{float:none;width:auto;text-align:left;margin-bottom:4px;font-size:16px;color:black;}.gsc_oci_value{margin-left:116px;max-width:512px;margin-bottom:16px;}.gs_el_ph .gsc_oci_value{margin-left:0;}.gsc_oci_merged_snippet{margin-bottom:1em;}#gsc_oci_graph_wrapper{height:100px;overflow-x:auto;overflow-y:hidden;direction:rtl;}#gsc_oci_graph{position:relative;min-width:100%;}#gsc_oci_graph_x{position:absolute;top:57px;left:0;width:100%;height:13px;border-top:1px solid #777;}.gsc_oci_g_t{position:absolute;top:60px;color:#777;font-size:11px;}#gsc_oci_graph_bars{position:absolute;top:0;right:0;width:100%;height:100px;}.gsc_oci_g_a{position:absolute;bottom:13px;width:15px;background:#777;}.gsc_oci_g_a:hover{background:#1a0dab;text-decoration:none;}.gsc_oci_g_a:active{background:#d14836;}.gsc_oci_g_al{position:absolute;bottom:15px;left:7px;color:#222;background:white;text-align:center;font-size:11px;min-width:11px;padding:1px;border:1px solid #777;border-radius:1px;visibility:hidden;opacity:0;}.gsc_oci_g_a:hover .gsc_oci_g_al{visibility:visible;opacity:1;}.gsc_oci_g_a{transition:all .218s;}.gsc_oci_g_al{transition:opacity .218s,visibility 0s .218s;}.gsc_oci_g_a:hover,.gsc_oci_g_a:hover .gsc_oci_g_al{transition:all 0s;}a.gsc_oci_lbx:link,a.gsc_oci_lbx:visited{white-space:nowrap;display:inline-block;vertical-align:middle;font-size:11px;background-color:#e5e5e5;color:#777;padding:2px 6px;text-decoration:none;}a.gsc_oci_lbx:hover{color:#e5e5e5;background-color:#777;}a.gsc_oci_lbx:active{color:#d14836;}.gsc_oms_mm{font-size:24px;line-height:16px;display:inline-block;margin:-10px 0 0 4px;position:relative;top:8px;}.gsc_oms_link{white-space:nowrap;margin-right:12px;}.gsc_oms_link:last-child{margin-right:0;}.gs_fsvg line{stroke:#222222}a:link .gs_fsvg{fill:#1a0dab;}a:link .gs_fsvg line{stroke:#1a0dab;}a:visited .gs_fsvg{fill:#660099;}a:visited .gs_fsvg line{stroke:#660099;}a:active .gs_fsvg{fill:#d14836;}a:active .gs_fsvg line{stroke:#d14836;}a .gs_fsvg{border-bottom:1px solid transparent;}a:hover .gs_fsvg,a:focus .gs_fsvg{border-bottom-color:inherit;}.gs_fsml{font-size:13px}.gs_fscp{font-variant:small-caps}.gsh_clim{display:table-row}.gsh_clil,.gsh_clic{display:table-cell;padding-bottom:8px}.gsh_clil{padding-right:8px;}.gsh_lla{list-style-type:lower-alpha}.gsh_lua{list-style-type:upper-alpha}.gsh_llr{list-style-type:lower-roman}.gsh_lur{list-style-type:upper-roman}.gsh_l>li{margin-left:32px;}.gs_fma .gsh_l>li{margin-left:16px;}.gsh_h3{font-size:inherit;font-weight:normal}.gsh_h3,.gsh_csp{margin:16px 0}.gsh_h3+.gsh_csp{margin-top:-8px}.gs_fma .gsh_h3{margin:12px 0 0 0;font-size:15px;font-weight:bold;}.gs_fma_abs .gsh_csp{margin:0 0 12px 0;}.gs_fma b,.gs_fma .gsh_h3{color:#444;}.gs_fma .gsh_h3+.gsh_csp{margin:4px 0 0 0;}.gs_fma .gsh_csp:last-child,.gs_fma .gsh_h3.gsh_flh{margin:0;}.gs_fma ul .gsh_clim:last-child .gsh_clic{padding-bottom:0;}.gs_fma ul,.gs_fma ol{margin:12px 0;}.gsh_ovln{text-decoration:overline}.gsh_small .gsh_l .gsh_csp{margin:8px 0}.gsh_small .gsh_csp:first-child,.gsh_small .gsh_h3.gsh_flh{margin-top:0}.gsh_small .gsh_csp:last-child{margin-bottom:0}.gsh_dspfr{text-align:center}.gsh_dspfr svg{margin:8px 0}</style><script>!function(GSP){var aa=function(a){var b=0;return function(){return b<a.length?{done:!1,value:a[b++]}:{done:!0}}},ba=typeof Object.defineProperties=="function"?Object.defineProperty:function(a,b,c){if(a==Array.prototype||a==Object.prototype)return a;a[b]=c.value;return a},ca=function(a){a=["object"==typeof globalThis&&globalThis,a,"object"==typeof window&&window,"object"==typeof self&&self,"object"==typeof global&&global];for(var b=0;b<a.length;++b){var c=a[b];if(c&&c.Math==Math)return c}throw Error("Cannot find global object"); },da=ca(this),h=function(a,b){if(b)a:{var c=da;a=a.split(".");for(var d=0;d<a.length-1;d++){var e=a[d];if(!(e in c))break a;c=c[e]}a=a[a.length-1];d=c[a];b=b(d);b!=d&&b!=null&&ba(c,a,{configurable:!0,writable:!0,value:b})}}; h("Symbol",function(a){if(a)return a;var b=function(f,g){this.ba=f;ba(this,"description",{configurable:!0,writable:!0,value:g})};b.prototype.toString=function(){return this.ba};var c="jscomp_symbol_"+(Math.random()*1E9>>>0)+"_",d=0,e=function(f){if(this instanceof e)throw new TypeError("Symbol is not a constructor");return new b(c+(f||"")+"_"+d++,f)};return e});var ea=typeof Object.create=="function"?Object.create:function(a){var b=function(){};b.prototype=a;return new b},fa; if(typeof Object.setPrototypeOf=="function")fa=Object.setPrototypeOf;else{var ha;a:{var ia={a:!0},ka={};try{ka.__proto__=ia;ha=ka.a;break a}catch(a){}ha=!1}fa=ha?function(a,b){a.__proto__=b;if(a.__proto__!==b)throw new TypeError(a+" is not extensible");return a}:null} var la=fa,ma=function(a,b){a.prototype=ea(b.prototype);a.prototype.constructor=a;if(la)la(a,b);else for(var c in b)if(c!="prototype")if(Object.defineProperties){var d=Object.getOwnPropertyDescriptor(b,c);d&&Object.defineProperty(a,c,d)}else a[c]=b[c];a.qa=b.prototype};h("Symbol.dispose",function(a){return a?a:Symbol("Symbol.dispose")}); h("Math.trunc",function(a){return a?a:function(b){b=Number(b);if(isNaN(b)||b===Infinity||b===-Infinity||b===0)return b;var c=Math.floor(Math.abs(b));return b<0?-c:c}});var na=function(a){a=Math.trunc(a)||0;a<0&&(a+=this.length);if(!(a<0||a>=this.length))return this[a]};h("Array.prototype.at",function(a){return a?a:na});var n=function(a){return a?a:na};h("Int8Array.prototype.at",n);h("Uint8Array.prototype.at",n);h("Uint8ClampedArray.prototype.at",n);h("Int16Array.prototype.at",n); h("Uint16Array.prototype.at",n);h("Int32Array.prototype.at",n);h("Uint32Array.prototype.at",n);h("Float32Array.prototype.at",n);h("Float64Array.prototype.at",n);h("String.prototype.at",function(a){return a?a:na});/* Copyright The Closure Library Authors. SPDX-License-Identifier: Apache-2.0 */ var oa=function(a,b){var c=Array.prototype.slice.call(arguments,1);return function(){var d=c.slice();d.push.apply(d,arguments);return a.apply(this,d)}};var t=function(){this.C=this.C;this.H=this.H};t.prototype.C=!1;t.prototype.isDisposed=function(){return this.C};t.prototype.dispose=function(){this.C||(this.C=!0,this.K())};t.prototype[Symbol.dispose]=function(){this.dispose()};t.prototype.K=function(){if(this.H)for(;this.H.length;)this.H.shift()()};var pa=function(){};function u(a,b){a.classList.add(b)}function v(a,b){a.classList.remove(b)}function w(a,b){return a.classList?a.classList.contains(b):!1}function x(a,b,c){c=c!==void 0?c:!w(a,b);(c?u:v)(a,b)};function z(a){return(navigator.userAgent||"").indexOf(a)>=0}var qa=z("iPhone")||z("iPad")||z("iPod"),ra=z("iPhone")||z("Android")&&z("Mobile");function sa(){if(b===void 0){var a=window.screen;a={width:window.innerWidth,height:window.innerHeight,pa:a.width,oa:a.height}}else a=b;var b=a;a=b.width;var c=b.height,d=b.pa;b=b.oa;var e=4;if(a<600||d*b<48E4||ra)e=1;else if(a<982)e=2;else if(a<1136||c<590)e=3;return e}var ta,ua=/[?&]tc=([01])/.exec(location.search||""); ta=ua?+ua[1]>0:z("Android")?!0:window.matchMedia&&window.matchMedia("(pointer)").matches?window.matchMedia("(pointer:coarse)").matches:!z("Firefox")||z("Mobile")||z("Tablet")?qa||"ontouchstart"in window||(navigator.msMaxTouchPoints||0)>0:!1;function va(){if(wa==void 0){wa=!1;try{var a=Object.defineProperty({},"passive",{get:function(){wa=!0}});window.addEventListener("testPassive",pa,a);window.removeEventListener("testPassive",pa,a)}catch(b){}}return wa}var wa;var xa=new function(){this.aa="INPUT"};function D(a){return document.getElementById(a)}function E(a){return a.id||(a.id="gs_id"+ya++)}function za(a){a=(a===void 0?null:a)||document.body;return(a?window.getComputedStyle(a,null):null).direction=="rtl"}function Aa(a){var b=[];a=a.elements;for(var c=a.length,d=0;d<c;d++){var e=a[d],f=encodeURIComponent(e.name||""),g=e.type;!f||e.disabled||!(g!="checkbox"&&g!="radio"||e.checked)||b.push(f+"="+encodeURIComponent(e.value||""))}return b.join("&")} function Ba(a,b){var c=a.elements[b];c||(c=document.createElement(xa.aa),c.type="hidden",c.name=b,a.appendChild(c));return c}var ya=100,Ca=/\S+/g,Da=/^(?:https?:|[^:/?#]*(?:[/?#]|$))/i,Ea=/^(?:#|\/[a-z0-9_-]*(?:[?].*)?$)/i;function F(a){return a.hasOwnProperty("gs_uid")?a.gs_uid:a.gs_uid=++Ga}var Ga=0;var G=function(){this.o=[];this.F={};this.S=this.I=0};G.prototype.add=function(a){var b=F(a);this.F[b]||(this.o.push(a),this.F[b]=this.o.length,++this.I)};G.prototype.remove=function(a){a=F(a);var b=this.F[a];b&&(this.o[b-1]=null,delete this.F[a],--this.I*2<this.o.length&&!this.S&&Ha(this))};G.prototype.notify=function(a){var b=this.o;try{++this.S;for(var c=0;c<b.length;c++){var d=b[c];d&&d.apply(null,arguments)}}finally{!--this.S&&this.I*2<b.length&&Ha(this)}};G.prototype.getSize=function(){return this.I}; var Ha=function(a){var b=a.o,c=b.length;a=a.F;for(var d=0,e=0;e<c;e++){var f=b[e];f&&(b[d]=f,a[F(f)]=++d)}b.length=d};function H(a,b,c,d,e){Ia(a,b,c,d===void 0?!1:d,e===void 0?!1:e,Ja)}function I(a,b,c,d){Ia(a,b,c,d===void 0?!1:d,!1,Ka)}function La(a,b,c,d){function e(g){I(f,a,e,c);b(g)}var f=document;c=c===void 0?!1:c;H(f,a,e,c,d===void 0?!1:d)}function Ma(a){Na?Na.add(a):a()}var Oa=window.requestAnimationFrame?function(a){window.requestAnimationFrame(a)}:function(a){setTimeout(function(){return a(window.performance&&performance.now?performance.now():Date.now())},33)}; function Pa(a){a.stopPropagation();a.preventDefault()}function Qa(a){return(a.ctrlKey?1:0)|(a.altKey?2:0)|(a.metaKey?4:0)|(a.shiftKey?8:0)}function Ja(a,b,c,d,e){var f=a.addEventListener;e=e&&va();f.call(a,b,c,e?{passive:e,capture:d}:d)}function Ka(a,b,c,d){a.removeEventListener(b,c,d)}function Ia(a,b,c,d,e,f){if(typeof b==="string")f(a,b,c,d,e);else for(var g=b.length,m=0;m<g;m++)f(a,b[m],c,d,e)}function Ra(){Na.notify();Na=null} function Sa(){document.readyState=="complete"&&(I(document,"readystatechange",Sa),Ra())}var Na,Ta=!!document.attachEvent,Ua=document.readyState;if(Ta?Ua!="complete":Ua=="loading")Na=new G,Ta?H(document,"readystatechange",Sa):La("DOMContentLoaded",Ra);function Va(){La(["mousedown","touchstart"],function(){x(document.documentElement,"gs_pfcs",!0);H(document,"keydown",Wa,!0)},!0,!0)}function Wa(a){a.keyCode==9&&(x(document.documentElement,"gs_pfcs",!1),I(document,"keydown",Wa,!0),Va())}Va();function Xa(a,b,c,d,e){var f=D(a);Ya(f,function(){u(f,"gs_vis");b&&b()},function(){v(f,"gs_vis");c&&c()},d,e)}function Za(a){a=J[a]||[0];return a[a.length-1]} function Ya(a,b,c,d,e,f){f=f===void 0?"":f;var g=E(a),m=Za(g);if(!m||m<Za(f)){var k=document.activeElement;f=D(f);$a(ab(f||a),!0);b&&b();K.push(function(l){J[g].pop();J[g].length||delete J[g];if(!l){(l=e)||k==document.body||(l=k);var p=document.activeElement;if(l)try{l.focus()}catch(A){}else p&&a.contains(p)&&p.blur()}c&&c()});J[g]||(J[g]=[]);J[g].push(K.length);k&&a.contains(k)||setTimeout(function(){var l=d,p=l&&l.type=="text";if(!l||p&&ta)l=a;try{l.focus(),p&&(l.value=l.value)}catch(A){}},0)}} function L(a){$a((Za(a)||1E6)-1,!1)}function bb(a){a=a===void 0?!1:a;K.pop()(a)}function $a(a,b){for(b=b===void 0?!1:b;K.length>a;)bb(b||K.length>a+1)}function ab(a){for(var b=0;a&&!(b=Za(a.id));)a=a.parentNode;return b}var K=[],J={};H(document,"click",function(a){var b=K.length;b&&!Qa(a)&&b>ab(a.target)&&bb(!0)});H(document,"keydown",function(a){a.keyCode==27&&!Qa(a)&&K.length&&bb()}); H(document,"focus",function(a){var b=K.length;if(b)for(var c=ab(a.target);c<b;){var d="",e;for(e in J)if(Za(e)==b){d=e;break}a:{d=(D(d).getAttribute("data-wfc")||"").match(Ca)||[];for(var f=0;f<d.length;f++){var g=D(d[f]);if(g&&g.offsetWidth){d=g;break a}}d=void 0}if(d){Pa(a);d.focus();break}else bb(!0),--b}},!0);var cb={},db={},eb;try{eb=window.sessionStorage}catch(a){};function M(a){return typeof a=="object"?a:null}function fb(){var a=gb(),b=hb();b=ib(b);a=jb(a);a=kb(a)||"#";N=M(b);lb?window.history.replaceState(b,"",a):window.location.replace(a)}function kb(a){var b=[],c;for(c in a)b.push(encodeURIComponent(c)+"="+encodeURIComponent(a[c]));return(a=b.sort().join("&"))?"#"+a:""} function mb(a){var b={};a=a.split("&");for(var c=0;c<a.length;c++){var d=a[c],e=d.indexOf("=");if(e+1){var f=d.substr(0,e);d=d.substr(e+1)}else f=d,d="";f&&(b[decodeURIComponent(f)]=decodeURIComponent(d))}return b}function nb(){var a=window.location.hash,b=a.indexOf("#")+1;return mb(b?a.substr(b):"")}function ob(a,b){for(var c in b){var d=b[c];d!==void 0?a[c]=d:delete a[c]}}function jb(a){var b=nb();ob(b,a);return b} function ib(a){var b=N||M(window.history.state),c={},d;for(d in b)c[d]=b[d];ob(c,a);return c}function pb(){setTimeout(function(){if(!qb){var a=window.history.state;qb=!0;N=M(a);rb.notify()}sb=!1},0)}var rb=new G,N,qb=!1,sb=!0,lb="pushState"in window.history,tb; if(typeof GSP=="undefined")tb=!1;else{var ub=.001*Date.now(),vb=GSP.eventId,wb=!1,O,xb=eb;if(!("nh"in cb)){var yb=xb&&xb.getItem("nh"),zb;if(yb)try{zb=JSON.parse(yb)}catch(a){}db.nh=zb}O=db.nh;O instanceof Array||(O=[]);for(var Ab=O.length,Bb=0,Cb=0;Cb<Ab;Cb++){var Db=O[Cb];if(Db instanceof Array&&Db.length==2){var Eb=Db[1]==vb;wb=wb||Eb;Ab-Cb<=10&&+Db[0]>ub-86400&&!Eb&&(O[Bb++]=Db)}}O.length=Bb;O.push([ub,vb]);var Fb=O,Gb=eb;db.nh=Fb;try{Gb&&Gb.setItem("nh",JSON.stringify(Fb))}catch(a){}tb=wb} var Hb=tb;"onpageshow"in window?H(window,"pageshow",pb):Ma(pb);H(window,lb?"popstate":"hashchange",function(a){document.readyState!="loading"&&(a=a.state,qb=!0,N=M(a),rb.notify())});function Ib(){Jb&&(I(D("gs_alrt_l"),"click",Jb),Jb=void 0)}function Kb(){var a=Lb();u(a,"gs_anm");u(a,"gs_vis");H(document,"click",Mb);clearTimeout(Nb);Nb=setTimeout(Mb,4E3);++Ob;setTimeout(Pb,0)}function Mb(){Ob||(I(document,"click",Mb),clearTimeout(Nb),Nb=void 0,Ib(),v(Lb(),"gs_vis"))}function Lb(){return D("gs_alrt")}function Pb(){Ob=0}var Nb,Ob=0,Jb;Ma(function(){var a=D("gs_alrt_m");a&&(a.innerHTML&&!Hb&&Kb(),H(window,"pagehide",function(){Ob=0;Mb();v(Lb(),"gs_anm")}))});function Qb(a,b,c){var d=new XMLHttpRequest;d.onreadystatechange=function(){if(d.readyState==4){var e=d.status,f=d.responseText,g=d.getResponseHeader("Content-Type"),m=d.responseURL,k=window.location,l=k.protocol;k="//"+k.host+"/";m&&m.indexOf(l+k)&&m.indexOf("https:"+k)&&(e=0,g=f="");c(e,f,g||"")}};d.open(b?"POST":"GET",a,!0);d.setRequestHeader("X-Requested-With","XHR");b&&d.setRequestHeader("Content-Type","application/x-www-form-urlencoded");b?d.send(b):d.send();return d} function Rb(a){a&&(a.onreadystatechange=function(){},a.abort())};var Sb=function(a,b,c){this.type=a;this.currentTarget=this.target=b;this.i=c===void 0?null:c;this.U=!1};Sb.prototype.stopPropagation=function(){this.i&&this.i.stopPropagation();this.U=!0};var P=function(a){a.i&&Pa(a.i);a.U=!0};var Q=function(a,b){this.V=a;this.na=b},Tb=function(a,b,c){this.V=a;this.types=b;this.listener=c};function Ub(a,b){var c=b.length;if(c){var d=F(a),e=Vb[d];if(!e){e=Vb[d]=[];d=Wb(b[0].V);for(var f in d){var g=Xb[f];g||(g=Xb[f]=Object.create(null));for(var m in d[f]){var k=g[m];k||(k=g[m]=[]);k.push(a)}}Yb(a,e,b[0],Zb);for(f=1;f<c;f++)Yb(a,e,b[f],$b)}}}function S(a,b,c){ac(new Sb(a,b,c===void 0?null:c))} function T(a,b,c){var d=bc;typeof b==="string"&&(cc[0]=b,b=cc);var e=b.length;a=Wb(a);for(var f in a)for(var g in a[f])for(var m=0;m<e;m++)d(f,g,b[m],c)}function Wb(a){typeof a==="string"&&(dc[0]=a,a=dc);for(var b=a.length,c=Object.create(null),d=0;d<b;d++){var e=a[d],f=e.charAt(0),g=e.substr(1);if(f!="#"&&f!="."||!g)throw Error("bad selector: "+e);(e=c[f])||(e=c[f]=Object.create(null));e[g]=!0}return c} function bc(a,b,c,d){var e=ec[c];e||(c!="touchstart"&&c!="mouseover"&&c!="mouseout"&&H(document,c,fc,c=="focus"||c=="blur"),e=ec[c]=Object.create(null));(c=e[a])||(c=e[a]=Object.create(null));(a=c[b])||(a=c[b]=new G);a.add(d)}function fc(a){var b=a.target;b&&b.nodeType==3&&(b=b.parentNode);ac(new Sb(a.type,b,a))} function ac(a){for(var b=a.target;b&&b!=document&&!b.disabled&&!w(b,"gs_dis");){a.currentTarget=b;var c=b.id;if(c&&!gc("#",c,a))break;c=b.classList||[];for(var d=c.length,e=0;e<d;e++)if(!gc(".",c[e],a))return;b=b.parentNode}}function gc(a,b,c){var d=ec[c.type];(b=(a=d&&d[a])&&a[b])&&b.notify(c);return!c.U}function Yb(a,b,c,d){var e=c.V;c=c.na;for(var f in c){var g=oa(d,a,c[f]);T(e,f,g);b.push(new Tb(e,f,g))}}function Zb(a,b,c){var d=c.currentTarget;a=hc(a,d)||a;a=ic(a,d);b.call(a,c)} function $b(a,b,c){a:{for(var d=c.currentTarget;d&&d!=document;){var e=hc(a,d);if(e){a=ic(e,d);break a}d=d.parentNode}a=void 0}a&&b.call(a,c)}function ic(a,b){var c=jc(b),d=kc[c];d||(d=kc[c]=[]);for(var e=d.length,f=0;f<e;f++){var g=d[f];if(g instanceof a)return g}b=new a(b);d.push(b);a=F(a);(d=lc[a])||(d=lc[a]=[]);d.push(c);return b}function hc(a,b){var c,d=b.id;d&&(c=mc(a,c,"#",d));b=b.classList||[];d=b.length;for(var e=0;e<d;e++)c=mc(a,c,".",b[e]);return c} function mc(a,b,c,d){c=(d=(c=Xb[c])&&c[d])?d.length:0;for(var e=0;e<c;e++){var f=d[e];!(f===a||f.prototype instanceof a)||b&&!(f===b||f.prototype instanceof b)||(b=f)}return b}function jc(a){var b=a.getAttribute("data-duid");b||a.setAttribute("data-duid",b=""+nc++);return b}var ec=Object.create(null),dc=[""],cc=[""],Xb=Object.create(null),Vb=Object.create(null),lc=Object.create(null),kc=Object.create(null),nc=100;window.gs_evt_dsp=fc;function oc(){var a=".gs_md_li";if(typeof a==="string"){var b=a.charAt(0),c=a.slice(1);if(b=="#")a=function(d){return d.id==c&&d.offsetWidth>0};else if(b==".")a=function(d){return w(d,c)&&d.offsetWidth>0};else throw Error("bad selector: "+a);}return a}function pc(a,b){return a&&((b===void 0?0:b)?a.lastElementChild:a.firstElementChild)}function qc(a,b){return a&&((b===void 0?0:b)?a.previousElementSibling:a.nextElementSibling)}function rc(a,b,c){c=c===void 0?!1:c;return sc(a,b,oc(),c,!1)} function sc(a,b,c,d,e){for(var f;b&&a;){if(c(b)){if(e)return b}else for(f=pc(b,d);f;f=qc(f,d))if(e=sc(f,f,c,d,!0))return e;for(e=!0;;){if(b==a)return null;f=b.parentNode;if(b=qc(b,d))break;b=f}}return null};var tc=["false","true","mixed"];var U=function(){this.D=Object.create(null)};U.prototype.clear=function(){this.D=Object.create(null)};U.prototype.has=function(a){return a in this.D};U.prototype.get=function(a){return this.D[a]};U.prototype.set=function(a,b){this.has(a);this.D[a]=b};U.prototype.delete=function(a){this.has(a)&&delete this.D[a]};var uc=function(a){var b=window,c=this;this.o=new G;this.Y=0;this.W=[b,a,function(){c.Y++||Oa(d)},!1];var d=function(){c.Y=0;c.o.notify()}};uc.prototype.addListener=function(a){this.o.getSize()||H.apply(null,this.W);this.o.add(a)};uc.prototype.removeListener=function(a){this.o.remove(a);this.o.getSize()||I.apply(null,this.W)};var vc=new uc("scroll"),wc=new uc("resize");var xc=new G;function yc(){var a=document.documentElement,b=sa();b={gs_el_ph:b==1,gs_el_ta:b==2,gs_el_sm:b!=4,gs_el_tc:ta||b==1};var c;for(c in b){var d=b[c];if(w(a,c)!=d){var e=!0;x(a,c,d)}}e&&xc.notify()}x(document.documentElement,"gs_el_ios",qa);yc();wc.addListener(yc);H(window,["pageshow","load"],yc);var zc=function(a,b,c,d,e,f){this.g=a;this.B=b;this.v=c;this.A=d;this.T=e;this.s=f;this.m=null},Ac=function(a,b){a.m=b},Bc=function(){this.l=[];this.j=-1};Bc.prototype.push=function(a){++this.j;this.j==this.l.length?this.l.push(a):(this.l[this.j]=a,this.l.splice(this.j+1,this.l.length-this.j))};Bc.prototype.pop=function(){--this.j};var Ec=function(a){for(var b=W;b.j>a;)L(b.top().g)},Fc=function(a,b){for(var c=0;c<a.l.length&&!(a.l[c].s>=b);++c);return c};Bc.prototype.top=function(){return this.at(this.j)}; Bc.prototype.at=function(a){return this.l[a]||null};function Gc(a,b){var c=a==W.j;W.j=a;b&&!N&&!M(window.history.state)&&fb();c||Hc()}function Ic(a,b){b=b===void 0?"":b;var c=c===void 0?"":c;var d=d===void 0?"":d;var e=W.top();e&&a==e.g&&b==e.B&&c==e.v||(W.push(new zc(a,b,c,d,e&&e.g==a?e.T+1:1,Date.now())),b=gb(),a=hb(),a=ib(a),b=jb(b),b=kb(b)||"#",N=M(a),lb?window.history.pushState(a,"",b):window.location.assign(b),Hc())} function Jc(a){a=Kc(D(a));return!!a&&w(a,"gs_md_wmw")&&w(document.documentElement,"gs_el_ph")}function Lc(){var a=D("gs_top"),b=document.documentElement;a=a.scrollHeight>b.clientHeight;for(var c=!1,d=0;d<=W.j&&!c;++d)c=!Jc(W.at(d).g);x(D("gs_md_s"),"gs_vis",c);c=W.j;c>=1&&(c=W.at(c-1).g,d=Jc(c),x(D(c),"gs_md_ins_vis",!d));b.style.overflowY=a&&!Jc(W.top().g)?"scroll":""} function Hc(){function a(){var y=c.clientHeight,q=+B.getAttribute("data-h");q||(g.style.maxHeight="none",q=f.offsetHeight);var r=f.querySelector(".gs_md_ftr");q=Math.max((y-q)/2,10);y=Math.max(y-48-(r?r.offsetHeight:0)-2*q,10);r=Jc(e);f.style.top=r?"auto":q+"px";g.style.maxHeight=r?"none":y+"px";Mc(g)}var b=W.top(),c=document.documentElement,d=D("gs_top"),e=b.g,f=D(e),g=D(e+"-bdy"),m=1200+W.j,k=D(f.getAttribute("data-cid")||f.id+"-bdy")||f,l=b.A,p=b.v,A=b.B,C=D("gs_md_s"),V=D(e).getAttribute("data-shd")|| "",B=Kc(f),R=window.pageYOffset,Cc=A&&A[0]!="#"&&!l,Dc=W.j>0?W.at(W.j-1).g:"",ja=!!J[e];Cc?(ja?x(k,"gs_md_ldg",!0):Nc(f,k,'<div class="gs_md_prg">'+D("gs_md_ldg").innerHTML+"</div>",b),S("gs-md-ldin",k)):(l&&Nc(f,k,l,b),S("gs-md-lded",k));ja&&e==Dc||Ya(f,function(){(B||f).style.zIndex=m;Oc(V);if(!ja){B&&u(B,"gs_vis");u(f,"gs_vis");x(f,"gs_abt",sb);x(C,"gs_abt",sb);Pc(e);if(W.j==0){var y=Lc;xc.add(y);y()}else Lc();B&&g&&(a(),wc.addListener(a))}W.j==0&&(u(d,"gs_nscl"),d.style.top=-R+"px")},function(){ja|| (wc.removeListener(a),B&&v(B,"gs_vis"),v(f,"gs_vis"),v(f,"gs_abt"));for(var y=W.top()?W.top().T:0;W.top()&&W.top().g==e;){var q=W.top();Rb(q.m);q.m=null;W.pop()}if(W.top()){if(q=W.top().g,Oc(D(q).getAttribute("data-shd")||""),v(D(q),"gs_md_ins_vis"),ja){a:{q=W;for(var r=q.j;r>=0;r--)if(q.l[r].g==e){q=r;break a}q=-1}r=W.at(q);(B||f).style.zIndex=1200+q;Nc(f,k,r.A,r)}}else v(C,"gs_vis"),v(C,"gs_abt");W.j==-1?(xc.remove(Lc),c.style.overflowY="",v(d,"gs_nscl"),d.style.top="auto",window.scrollTo(0,R)): Lc();Qc||(y>0?window.history.go(-y):fb())},Rc(f),Sc(f),Dc);Cc&&(Rb(b.m),b.m=null,Ac(b,Qb(A,p,function(y,q,r){b.m=null;r=(y=y==200&&r.match(/^text\/html(;.*)?$/i))?q:Tc();Nc(f,k,r,b);if(y)for(y=e,r=0;r<W.l.length;++r){var Fa=W.at(r);y==Fa.g&&A==Fa.B&&p==Fa.v&&(Fa.A=q,r==W.j&&fb())}S("gs-md-lded",k)})))}function Kc(a){a=a.parentNode;return w(a,"gs_md_wnw")?a:null}function Rc(a){return(a=a.getAttribute("data-ifc"))?D(a):null}function Sc(a){return(a=a.getAttribute("data-cfc"))?D(a):null} function Nc(a,b,c,d){x(b,"gs_md_ldg",!1);for(var e=b.querySelectorAll("[data-duid]"),f=e.length,g={},m=0;m<f;m++){for(var k=jc(e[m]),l=kc[k],p=l?l.length:0,A=0;A<p;A++){var C=l[A],V=F(C.constructor),B=g[V];B||(B=g[V]={});B[k]=!0;C&&typeof C.dispose=="function"&&C.dispose()}delete kc[k]}for(var R in g){R=+R;e=g[R];m=(f=lc[R])?f.length:0;for(l=k=0;l<m;l++)p=f[l],p in e||(f[k++]=p);k?f.length=k:delete lc[R]}b.innerHTML=c;d.A=c;Pc(a.id);Rb(d.m);d.m=null} function Pc(a){if(a=document.querySelector("#"+a+">.gs_md_bdy"))a.scrollTop=a.scrollLeft=0,Mc(a)}function Mc(a){var b=a.style,c="padding"+(za(a)?"Left":"Right");b[c]="";var d=a.offsetWidth-a.clientWidth;d>2&&(a=parseInt(window.getComputedStyle(a,null)[c],10)||0,b[c]=Math.max(a-d,0)+"px")}function Tc(){return'<div class="gs_md_prg"><div class="gs_alrt">'+D("gs_md_err").innerHTML+"</div></div>"} function gb(){var a=W.top();return{d:a&&a.g||void 0,u:a&&a.B||void 0,p:a&&a.v?"1":void 0,t:a&&a.s||void 0}}function hb(){var a=W.top();return{n:a&&a.T||0,p:a&&a.v||"",h:a&&a.A||""}}function Oc(a){if(Uc!=a){var b=D("gs_md_s");Uc&&v(b,Uc);(Uc=a)&&u(b,a)}}var Qc=0,Uc="",W=new Bc; rb.add(function(){var a=nb(),b=a.d||"",c=b?D(b):null;++Qc;if(c){var d=a.u||"";c=+a.p>0;var e=+a.t||0,f=N||M(window.history.state)||{};a=+f.n||0;var g=""+(f.p||"");f=""+(f.h||"");d.match(Ea)||(d="");for(var m=Fc(W,e),k=m;k<W.l.length;++k){var l=W.at(k);if(e<l.s&&l.g!=b)break}for(l=m-1;l>=0;--l){var p=W.at(l);if(e>p.s&&p.g!=b)break}Ec(k-1);for(k=0;k<=l;++k)p=W.at(k).g,J[p]||Gc(l,!1);if(l=m<W.l.length)l=W.at(m),l=b==l.g&&d==l.B&&c==!!l.v&&e==l.s;l?Gc(m,!0):(a==0&&(Ec(-1),W=new Bc,e=Date.now()),c!=!!g&& (d=g="",f=Tc()),b=new zc(b,d,g,f,a,e),c=W,e=b.s,a=Fc(c,e),e=a<c.l.length&&e==c.at(a).s,c.l.splice(a,e?1:0,b),W.j=a,fb(),Hc())}else Ec(-1);--Qc});var Vc=function(a){t.call(this);this.G=a;this.R=Object.create(null);this.m=null;a=a.querySelectorAll(".gs_in_txtw>input[type=text]");for(var b=a.length;b--;){var c=a[b],d=c.parentNode.querySelector(".gs_in_txts");c=c.name;d&&c&&(this.R[c]=d.innerHTML)}};ma(Vc,t);Vc.prototype.K=function(){Rb(this.m);this.G=this.m=null;t.prototype.K.call(this)}; Vc.prototype.ja=function(a){var b=this;P(a);if((a=this.G)&&!this.m){var c="json=&"+Aa(a);Wc(this,!0);this.m=Qb(a.action,c,function(d,e){b.m=null;Wc(b,!1);var f=b.G,g=f.getAttribute("data-alrt");if(g=g?D(g):null)g.innerHTML="";try{var m=d==200&&JSON.parse(e)}catch(B){}d=!1;m&&typeof m=="object"||(Xc(g,D("gs_md_err").innerHTML),m={},d=!0);f.setAttribute("data-p",""+(m.P||""));S("gs-ajax-form-done",f);if(e=m.L){var k=""+e;k.match(Da)&&(window.location.href=k)}else{if(e=m.M)Xc(g,e),d=!0;e=1E6;g&&g.innerHTML&& (k=g,e=g.getBoundingClientRect().top);g=f.elements;m=m.E;typeof m=="object"||(m=Object.create(null));for(var l in b.R){var p=g[l],A=void 0,C=""+(m[l]||""),V=p.parentNode.querySelector(".gs_in_txts");x(p.parentNode,"gs_in_txte",!!C);V&&(V.innerHTML=C||b.R[l]||"");C&&(A=p.getBoundingClientRect().top)<e&&(k=p,e=A);d=d||!!C}(f=f.getAttribute("data-d"))&&!d&&L(f);k&&k.scrollIntoView&&(e<0||e+20>window.innerHeight)&&k.scrollIntoView()}})}}; var Wc=function(a,b){a=a.G;var c=a.getAttribute("data-bsel");a=c?document.querySelectorAll(c):a.querySelectorAll("button");for(c=a.length;c--;){var d=a[c];d.disabled=b;x(d,"gs_bsp",b)}},Xc=function(a,b){if(a)a.innerHTML=b;else{var c=c===void 0?"":c;var d=d===void 0?"":d;var e=e===void 0?[]:e;D("gs_alrt_m").innerHTML=b;Lb().action=d.match(Da)?d:"";a=D("gs_alrt_l");a.textContent=c;c=D("gs_alrt_h");c.innerHTML="";for(var f in e)b=document.createElement(xa.aa),b.type="hidden",b.name=f,b.value=e[f],c.appendChild(b); Ib();x(a,"gs_fm_s",!0);Kb()}};Ub(Vc,[new Q(".gs_ajax_frm",{submit:Vc.prototype.ja})]);var Yc=[[1,0,1],[2,0,1]];T(".gs_cb_gen","click",function(a){var b=a.currentTarget,c=(w(b,"gs_sel")?1:0)+2*(w(b,"gs_par")?1:0),d=+b.getAttribute("data-s")==2;c=Yc[+d][c];d=!0;d=d===void 0?!1:d;x(b,"gs_sel",c==1);x(b,"gs_par",c==2);b.setAttribute("aria-checked",tc[c]);d||b.setAttribute("data-s",""+c);S("gs-change",b,a.i)});T(".gs_cb_gen",["keydown","keyup"],function(a){var b=a.currentTarget,c=a.i.keyCode;b.tagName!="BUTTON"||c!=13&&c!=32||(P(a),a.type=="keydown"&&b.click())});T([".gs_cb_gen",".gs_md_li"],"keydown",function(a){var b=a.currentTarget,c=b.tagName,d=a.i.keyCode;c!="BUTTON"&&(d==32||d==13&&c!="A")&&(P(a),b.click())});var Zc=["click","contextmenu","mouseup"].concat(navigator.sendBeacon?[]:["mousedown","touchstart"]),$c="",ad=null;function bd(){ad=null}function cd(a){navigator.sendBeacon?navigator.sendBeacon(a):ad&&a==ad.src||((ad=new Image).src=a,setTimeout(bd,1E3))} function dd(){var a=document.location.href,b=a.indexOf("?")+1;a=b?a.substr(b):"";b=a.indexOf("#");a=mb(b+1?a.substr(0,b):a).hl||"";a="/scholar_bfnav?url="+encodeURIComponent(document.location.href)+"&hl="+encodeURIComponent(a)+"&ei="+GSP.eventId;cd(a)}Ma(function(){$c=Hb?"&bn=1":"";Hb&&dd()});H(window,"pageshow",function(a){a.persisted&&($c="&bn=1",dd())}); H(document,Zc,function(a){if(!(a.type=="click"&&a.button||a.type=="mouseup"&&a.button!=1)){var b,c;a:{for(a=a.target;a;){var d=a.nodeName;if(d=="A")break a;if(d=="SPAN"||d=="B"||d=="I"||d=="EM"||d=="IMG")a=a.parentNode;else break}a=null}a&&(b=a.getAttribute("href"))&&(c=a.getAttribute("data-clk"))&&(b="/scholar_url?url="+encodeURIComponent(b)+"&"+c+"&ws="+window.innerWidth+"x"+window.innerHeight+"&at=",c=encodeURIComponent,a=(a=a.getAttribute("data-clk-atid"))?D(a):null,b=b+c(a&&a.innerText||"")+ $c,cd(b))}},!1,!0);T(".gs_fm_s","click",function(a){a=a.currentTarget.getAttribute("data-fm")||"";(a=D(a))&&a.submit()});var X=function(a){this.g=E(a.querySelector(".gs_md_d"));this.J=E(a.querySelector(".gs_md_tb"))};X.prototype.N=function(a){var b=D(this.g);return a!==void 0?rc(b,b,a):null};X.prototype.open=function(a){a=this.N(a);if(w(D(this.J),"gs_sel"))try{a&&a.focus()}catch(c){}else{var b=D(this.J);Xa(this.g,function(){u(b,"gs_sel")},function(){v(b,"gs_sel")},a,b)}};X.prototype.close=function(){L(this.g)};X.prototype.ca=function(a){P(a);w(D(this.J),"gs_sel")?this.close():this.open(a.i.type=="keydown"?!1:void 0)}; X.prototype.X=function(a){var b=a.i.keyCode;if(b==38||b==40)P(a),this.open(b==38)};X.prototype.ea=function(a){a.target.id==this.g&&this.X(a)};Ub(X,[new Q(".gs_md_rmb",{}),new Q(".gs_md_tb",{"gs-press":X.prototype.ca,keydown:X.prototype.X}),new Q(".gs_md_d",{keydown:X.prototype.ea})]);var Y=function(a){X.call(this,a);this.la=E(a.querySelector(".gs_md_in"));this.ma=E(a.querySelector(".gs_md_tb .gs_lbl"))};ma(Y,X);Y.prototype.N=function(){return D(this.g).querySelector(".gs_md_li[aria-selected]")};Y.prototype.fa=function(a){ed(this,a)};Y.prototype.O=function(a){var b=a.i.keyCode;b!=13&&b!=32||ed(this,a)}; var ed=function(a,b){var c=b.currentTarget,d=D(a.la),e=a.N();c!=e&&(d.value=c.getAttribute("data-v"),D(a.ma).innerHTML=c.innerHTML,e&&fd(e,!1),fd(c,!0));P(b);a.close();S("gs-change",d,b.i)},fd=function(a,b){x(a,"gs_sel",b);b?a.setAttribute("aria-selected","true"):a.removeAttribute("aria-selected")};Ub(Y,[new Q(".gs_md_ris",{}),new Q(".gs_md_li",{click:Y.prototype.fa,keydown:Y.prototype.O})]);T("#gs_lp","click",function(a){P(a);Ic("gs_lp_d")});T("#gs_lp_cur","click",function(a){P(a);L("gs_lp_d")});var gd=function(a){this.Z=E(a)};gd.prototype.O=function(a){var b=a.currentTarget,c=a.i.keyCode;if(c==38||c==40){var d=D(this.Z);d=rc(d,b,c==38)||rc(d,d,c==38)}else if(c==37||c==39)a:{c=c==37!=za(b.parentNode);d=b.parentNode;var e=d.children,f=e.length;if(d.id!=this.Z){for(;e[--f]!=b;);d=qc(d,c)||pc(d.parentNode,c);e=d.children;if(f=Math.min(f+1,e.length))if(d=e[f-1],w(d,"gs_md_li")&&d.offsetLeft!=b.offsetLeft)break a}d=void 0}d&&(P(a),d.focus())};Ub(gd,[new Q(".gs_md_ulr",{}),new Q(".gs_md_li",{keydown:gd.prototype.O})]);T("#gs_hdr_mnu","click",function(a){P(a);Ic("gs_hdr_drw")});T("#gs_hdr_drw_mnu","click",function(a){P(a);L("gs_hdr_drw")});T("#gs_hdr_act_i","click",function(a){P(a);sa()==1?(a=document.querySelector("#gs_hdr_drw_bot>a").href,a.match(Da)&&(window.location.href=a)):Xa("gs_hdr_act_d")});T("#gs_hdr_drw","keydown",function(a){var b=a.i.keyCode;if(b==38||b==40){var c=a.currentTarget;if(b=rc(c,c,b==38))P(a),b.focus()}}); T("#gs_hdr_tsi",["focus","blur"],function(a){function b(){var g=d.getBoundingClientRect().top-10;Math.abs(g)>10&&window.scrollBy(0,g);clearTimeout(e);c()}function c(){I(window,f,b)}var d=a.target;a=a.type=="focus";x(D("gs_hdr"),"gs_hdr_ifc",a);if(a&&ta&&!(window.innerHeight>749)){var e=setTimeout(c,1E3),f=["scroll","resize"];H(window,f,b)}});T("#gs_hdr_tsi",["input","gs-change"],function(a){x(D("gs_hdr_frm"),"gs_hdr_tsc",!!a.currentTarget.value)}); T("#gs_hdr_tsc","mousedown",function(a){P(a);var b=D("gs_hdr_tsi");b.value="";b.focus();S("input",b,a.i)});T("#gs_hdr_sre","click",function(a){P(a);var b=D("gs_hdr");Xa("gs_hdr_frm",function(){v(b,"gs_hdr_src");u(b,"gs_hdr_srx")},function(){u(b,"gs_hdr_src");v(b,"gs_hdr_srx")},D("gs_hdr_tsi"))});T(".gs_md_x","click",function(a){(a=a.currentTarget.getAttribute("data-mdx"))&&L(a)});var Z=function(){},hd,id;Z.prototype.da=function(a){a.i.button||(P(a),jd(a))};Z.prototype.ga=function(a){kd(a)&&(P(a),jd(a))};Z.prototype.ha=function(a){kd(a)&&P(a)};Z.prototype.ia=function(a){if(!a.i.button){P(a);var b=a.i;b&&(ld=b.clientX||0,md=b.clientY||0,H(document,nd,od,!0),clearTimeout(hd),hd=setTimeout(pd,2E3));jd(a)}}; Z.prototype.ka=function(a){P(a);if(qd){var b=a.i;b=b&&b.touches||[];if(b=b.length==1?b[0]:null)rd=b.clientX,sd=b.clientY,H(document,td,ud,!0),clearTimeout(id),id=setTimeout(vd,2E3)}jd(a)}; var kd=function(a){a=a.i.keyCode;return a==32||a==13},jd=function(a){S("gs-press",a.currentTarget,a.i)},pd=function(){I(document,nd,od,!0);clearTimeout(hd);hd=void 0},od=function(a){a.type!="mousedown"&&Math.abs(a.clientX-ld)<10&&Math.abs(a.clientY-md)<10?(Pa(a),a.type=="click"&&pd()):pd()},vd=function(){I(document,td,ud,!0);clearTimeout(id);id=void 0},ud=function(a){a.type!="touchstart"&&Math.abs(a.clientX-rd)<10&&Math.abs(a.clientY-sd)<10?(Pa(a),a.type=="click"&&vd()):vd()},ld=0,md=0,nd=["mousedown", "mouseup","click"],qd=z("Android")&&!z("Chrome"),rd=0,sd=0,td=["touchstart","mousedown","mouseup","click"];Ub(Z,[new Q(".gs_press",{click:Z.prototype.da,keydown:Z.prototype.ga,keyup:Z.prototype.ha,mousedown:Z.prototype.ia,touchstart:Z.prototype.ka})]);function wd(a){xd.style.left=yd&&zd===Ad?a.left+"px":"auto";xd.style.width=yd?a.width+"px":"auto";S("gs-sth-change",D("gs_sth"))}function Bd(){var a=Cd.getBoundingClientRect(),b=a.top,c=xd.offsetHeight,d=b<0,e;if(e=d&&qa)e=document.activeElement,e=!!e&&e.tagName=="INPUT"&&e.type=="text";b=e?-b-a.height:Ad;var f=yd!=d||zd!==Ad!=e;b!==zd&&(zd=b,xd.style.transform=b===Ad?"none":"translate3d(0,"+b+"px,0)");f&&(yd=d,x(Dd,"gs_sth_vis",d),x(Dd,"gs_sth_trk",e),wd(a),Cd.style.height=yd?c+"px":"auto")} function Ed(){yd&&wd(Cd.getBoundingClientRect())}var Ad,Dd,Cd,xd,yd=!1,zd;Ma(function(){if(Dd=D("gs_sth"))Cd=Dd.querySelector(".gs_sth_g"),xd=Dd.querySelector(".gs_sth_b"),vc.addListener(Bd),wc.addListener(Ed),Bd()});(function(a){Ma(function(){return setTimeout(a,0)})})(function(){var a=document.querySelectorAll(".gs_invis");var b=typeof Symbol!="undefined"&&Symbol.iterator&&a[Symbol.iterator];if(b)a=b.call(a);else if(typeof a.length=="number")a={next:aa(a)};else throw Error(String(a)+" is not an iterable or ArrayLike");for(b=a.next();!b.done;b=a.next())v(b.value,"gs_invis")});new U;new U;var Fd=(new Date).getTimezoneOffset();T("#gs_vcpb_cita_edit","click",function(a){a.i&&Pa(a.i);a=D("gsc_vcpb").getAttribute("data-edit-link")+"&tzom="+Fd;Ic("gs_md_cita-d",a)});T("#gs_md_cita-b-save","click",function(){var a=D("gsc_ecd_form");Ba(a,"continue").value=window.location.pathname+window.location.search;S("submit",a)}); T(".gsc_ecd_form_tsel","click",function(a){var b=D("gsc_ecd_form"),c=D("gsc_ecd_table");b=Ba(b,"articletype");a=a.currentTarget;b.value=a.getAttribute("data-type")||"";c.className=a.getAttribute("data-class")||"";c=document.querySelectorAll("#gsc_ecd_citation_type button");for(b=c.length;b--;)x(c[b],"gs_sel",c[b]==a)}); }({"customAC":0,"eventId":"EKRHZ_m0OfO_y9YPm4_bqAY"});</script></head><body><div id="gs_top" onclick=""><style>#gs_md_s,.gs_md_wnw{z-index:1200;position:fixed;top:0;left:0;width:100%;height:100%;visibility:hidden;}.gs_md_ds:before{content:'';position:absolute;background-color:#fff;z-index:100;opacity:0;visibility:hidden;top:0;bottom:0;right:0;left:0;}.gs_md_ds.gs_md_d:not(.gs_el_ph .gs_md_wmw):before{top:-1px;bottom:-1px;right:-1px;left:-1px;}#gs_md_s{background-color:#fff;opacity:0;}.gs_el_ta #gs_md_s,.gs_el_ph #gs_md_s,.gs_el_ta .gs_md_ds:before,.gs_el_ph .gs_md_ds:before{background-color:#666;}#gs_md_s.gs_vis,.gs_md_ds.gs_md_ins_vis:before{opacity:.5;visibility:visible;}.gs_md_wnw{transition:all 0s .218s;}.gs_md_wnw.gs_vis{visibility:visible;transition:all 0s;}.gs_el_tc .gs_md_ds:before{transition:opacity .15s,visibility 0s .15s;}.gs_el_tc .gs_md_ds.gs_md_ins_vis:before{transition:opacity .218s,visibility 0s;}.gs_md_wnw>.gs_md_d{position:relative;margin:0 auto;width:464px;box-shadow:2px 2px 8px rgba(0,0,0,.2);white-space:normal;}.gs_el_ta .gs_md_wnw>.gs_md_d,.gs_el_ph .gs_md_wnw>.gs_md_d{box-shadow:2px 2px 8px rgba(0,0,0,.65);}.gs_el_ph .gs_md_wnw>.gs_md_d{width:80%;max-width:440px;}.gs_el_ph .gs_md_wmw>.gs_md_d{display:flex;flex-direction:column;width:100%;height:100%;max-width:none;border:none;box-shadow:none;transform:translate(0,100%);transform:translate(0,100vh);transition:transform .27s cubic-bezier(.4,0,.6,1),opacity 0s .27s,visibility 0s .27s,max-height 0s .27s;}.gs_el_ph .gs_md_wmw>.gs_md_d.gs_vis{transform:translate(0,0);transition:transform .3s cubic-bezier(0,0,.2,1);}.gs_md_wmw>.gs_md_d.gs_abt,.gs_el_ph .gs_md_wmw>.gs_md_d.gs_abt{transition:none;}.gs_md_hdr{display:flex;align-items:center;height:47px;border-bottom:1px solid #e0e0e0;border-bottom-color:rgba(0,0,0,.12);background-color:#f5f5f5;}.gs_md_hdr>a,.gs_md_hdr>a.gs_btn_lrge{flex:0 0 auto;width:41px;height:47px;}.gs_el_ph .gs_md_hdr>a{margin:0 2px 0 0;}.gs_el_ph a.gs_md_hdr_c{margin:0 0 0 2px;}.gs_md_hdr_b{margin:0 41px 0 16px;}.gs_el_ph .gs_md_hdr_b{margin:0 16px;}.gs_md_hdr_t:empty~.gs_md_hdr_b{margin-left:0;}.gs_md_hdr_b:empty{width:41px;margin:0;}.gs_el_ph .gs_md_hdr_b:empty{margin-right:2px;}.gs_md_hdr_b:empty:not(:last-child){display:none;}.gs_md_hdr_b>button{min-width:51px;height:33px;}.gs_md_hdr_t{flex:1 1 auto;font-size:18px;font-weight:normal;color:#666;overflow:hidden;text-overflow:ellipsis;white-space:nowrap;text-align:center;}.gs_md_bdy{position:relative;overflow-y:auto;box-sizing:border-box;padding:24px 41px 0 41px;}.gs_md_bdy:after{display:block;content:"";clear:both;padding-bottom:24px;}.gs_el_ph .gs_md_bdy{padding:16px 16px 0 16px;}.gs_el_ph .gs_md_bdy:after{padding-bottom:16px;}.gs_el_ph .gs_md_wmw .gs_md_bdy{flex:1;}.gs_md_ftr{border-top:1px solid #e0e0e0;}.gs_md_lbl{display:block;font-size:16px;margin:0 0 16px 0;word-wrap:break-word;}.gs_md_btns{margin:24px 0 0 0;white-space:nowrap;}.gs_el_ph .gs_md_btns{margin:16px 0 0 0;}.gs_md_btns button{margin-right:16px;}.gs_md_btns button:last-child{margin-right:0;}.gs_md_prg{margin:24px 0;text-align:center;}.gs_md_prg .gs_alrt{padding:4px 16px;}.gs_md_ldg:before{content:"";position:absolute;top:0;left:0;bottom:0;right:0;background-color:#fff;opacity:.5;z-index:100;}</style><div id="gs_md_ldg" style="display:none">Loading...</div><div id="gs_md_err" style="display:none">The system can't perform the operation now. Try again later.</div><div id="gs_md_s"></div><div data-h="800" class="gs_md_wnw gs_md_ds gs_md_wmw"><div id="gs_md_cita-d" class="gs_md_d gs_md_ds gs_ttzi" role="dialog" tabindex="-1" aria-labelledby="gs_md_cita-d-t" data-cid="gs_md_cita-l" data-wfc="gs_md_cita-d-x"><div class="gs_md_hdr"><a href="javascript:void(0)" id="gs_md_cita-d-x" role="button" aria-label="Cancel" data-mdx="gs_md_cita-d" class="gs_btnCLS gs_md_x gs_md_hdr_c gs_in_ib gs_btn_lrge"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl"></span></a><h2 id="gs_md_cita-d-t" class="gs_md_hdr_t"></h2><div class="gs_md_hdr_b"><button type="button" id="gs_md_cita-b-save" aria-label="Save" class="gs_btnDNW gs_in_ib gs_btn_act gs_btn_half gs_btn_lsb"><span class="gs_wr"><span class="gs_ico"></span><span class="gs_lbl"></span></span></button></div></div><div id="gs_md_cita-d-bdy" class="gs_md_bdy"><style>#gs_md_cita-d{width:90%;max-width:1000px;}.gs_el_ph #gs_md_cita-d{width:100%;max-width:none;}#gs_md_cita-d .gs_md_prg{min-height:600px;}</style><div id="gs_md_cita-l" aria-live="assertive"></div></div></div></div><div id="gs_hdr_drw" class="gs_md_ulr gs_md_ds" role="dialog" tabindex="-1" data-shd="gs_hdr_drs" data-wfc="gs_hdr_drw_mnu" data-cfc="gs_hdr_mnu"><div id="gs_hdr_drw_in"><div id="gs_hdr_drw_top"><a href="javascript:void(0)" id="gs_hdr_drw_mnu" role="button" aria-controls="gs_hdr_drw" aria-label="Options" class="gs_btnMNT gs_in_ib gs_btn_lrge"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl"></span></a><a id="gs_hdr_drw_lgo" href="/schhp?hl=en" aria-label="Homepage"></a></div><div><div class="gs_hdr_drw_sec"><a href="/citations?hl=en" role="menuitem" class="gs_btnPRO gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">My profile</span></a><a href="/scholar?scilib=1&hl=en" role="menuitem" class="gs_btnL gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">My library</span></a><a href="/citations?view_op=metrics_intro&hl=en" role="menuitem" class="gs_btnJ gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">Metrics</span></a><a href="/scholar_alerts?view_op=list_alerts&hl=en" role="menuitem" class="gs_btnM gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">Alerts</span></a></div><div class="gs_hdr_drw_sec"><a href="/scholar_settings?hl=en" role="menuitem" class="gs_btnP gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">Settings</span></a></div></div><div id="gs_hdr_drw_bot" class="gs_hdr_drw_sec"><a href="https://accounts.google.com/Login?hl=en&continue=https://scholar.google.com/schhp%3Fhl%3Den" class=" gs_in_ib gs_md_li gs_md_lix gs_in_gray"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl">Sign in</span></a></div></div></div><div id="gs_hdr" role="banner"><a href="/citations?view_op=list_works&hl=en&hl=en&user=co9WE00AAAAJ&sortby=title" id="gs_hdr_bck" role="button" class="gs_btnALT gs_in_ib gs_btn_lrge"><span class="gs_ico"></span><span class="gs_ia_notf"></span><span class="gs_lbl"></span></a><div id="gs_hdr_md"><h1 dir="ltr">View article</h1></div><div id="gs_hdr_act"><a id="gs_hdr_act_s" href="https://accounts.google.com/Login?hl=en&continue=https://scholar.google.com/schhp%3Fhl%3Den">Sign in</a></div></div><style>#gs_alrt{position:fixed;bottom:48px;left:16px;max-width:384px;z-index:1250;display:flex;justify-content:space-between;align-items:center;font-size:13px;line-height:16px;color:#e2e2e2;background:#333;text-align:left;border-radius:3px;box-shadow:0 3px 5px -1px rgba(0,0,0,.2),0 6px 10px 0 rgba(0,0,0,.14),0 1px 18px 0 rgba(0,0,0,.12);visibility:hidden;transform-origin:center;transform:scale(0.8,0.8) translate(0,100%);}.gs_el_ph #gs_alrt{bottom:0;left:0;width:100%;max-width:none;border-radius:0;box-shadow:none;transform:scale(1,1) translate(0,100%);}#gs_alrt.gs_vis{visibility:visible;transform:scale(1,1) translate(0,0);}#gs_alrt.gs_anm{transition:transform .067s cubic-bezier(.4,0,1,1),visibility 0s .067s;}#gs_alrt.gs_vis.gs_anm{transition:transform .067s cubic-bezier(0,0,.2,1);}.gs_el_ph #gs_alrt.gs_anm{transition:transform .084s cubic-bezier(.4,0,1,1),visibility 0s .084s;}.gs_el_ph #gs_alrt.gs_vis.gs_anm{transition:transform .1s cubic-bezier(0,0,.2,1);}#gs_alrt_m{display:block;padding:16px;}#gs_alrt_l{display:block;padding:8px;margin:0 8px 0 -8px;border-radius:3px;color:#fcc934;text-transform:uppercase;text-decoration:none;}#gs_alrt_l:hover{background-color:rgba(255,255,255,.05)}#gs_alrt_l:active{background-color:rgba(255,255,255,.1)}#gs_alrt_l:empty{display:none}#gs_alrt_m a{padding:8px 0;color:#e2e2e2;text-decoration:underline;}#gs_alrt_m a:active{color:#f6aea9}</style><form action="" method="post" id="gs_alrt"><span id="gs_alrt_m"></span><span id="gs_alrt_h"></span><a id="gs_alrt_l" href="javascript:void(0)" class="gs_fm_s" data-fm="gs_alrt"></a></form><div id="gs_bdy"><div id="gs_bdy_sb" role="navigation"><div id="gs_bdy_sb_in"><div id="gsc_sb_ui" class="gs_bdy_sb_sec"><a href="/citations?user=co9WE00AAAAJ&hl=en" class="gs_ibl"><span class="gs_rimg gs_pp_sm"><img alt="Ivor Fleck" sizes="56px" src="/citations/images/avatar_scholar_56.png" srcset="/citations/images/avatar_scholar_56.png 56w,/citations/images/avatar_scholar_128.png 128w" width="56" height="56"></span></a><div><a href="/citations?user=co9WE00AAAAJ&hl=en">Ivor Fleck</a></div></div></div></div><div id="gs_bdy_ccl" role="main"><div id="gsc_vcpb" data-edit-link="/citations?view_op=edit_citation&hl=en&user=co9WE00AAAAJ&sortby=title&citation_for_view=co9WE00AAAAJ:1aiWeP-z6tUC&citation_for_view=co9WE00AAAAJ:1aiWeP-z6tUC&back_view_op=view_citation"><form method="post" id="gsc_vcpb_btns" action="/citations?view_op=view_citation&hl=en"><input type="hidden" name="xsrf" value="ADIE8skAAAAAZ0j1kLb7eJp2RRQ7bO9zQgpVgN0"><input type="hidden" name="s" value="co9WE00AAAAJ:1aiWeP-z6tUC"><input type="hidden" name="continue" value="/citations?view_op=list_works&hl=en&hl=en&user=co9WE00AAAAJ&sortby=title"></form><div id="gsc_oci_title_wrapper"><div id="gsc_oci_title_gg"><div class="gsc_oci_title_ggi"><a href="https://link.springer.com/article/10.1140/epjc/s10052-024-12438-w" data-clk="hl=en&sa=T&ei=EKRHZ_m0OfO_y9YPm4_bqAY"><span class='gsc_vcd_title_ggt'>[HTML]</span> from springer.com</a></div><div class="gsc_oci_title_ggi"><a href="https://link.springer.com/content/pdf/10.1140/epjc/s10052-024-12438-w.pdf" data-clk="hl=en&sa=T&ei=EKRHZ_m0OfO_y9YPm4_bqAY">Full View</a></div></div><div id="gsc_oci_title"><a class="gsc_oci_title_link" href="https://link.springer.com/article/10.1140/epjc/s10052-024-12438-w" data-clk="hl=en&sa=T&ei=EKRHZ_m0OfO_y9YPm4_bqAY">A precise measurement of the <i>Z</i>-boson double-differential transverse momentum and rapidity distributions in the full phase space of the decay leptons with the ATLAS …</a></div></div><div id="gsc_oci_table"><div class="gs_scl"><div class="gsc_oci_field">Authors</div><div class="gsc_oci_value">ATLAS Collaboration atlas. publications@ cern. ch, G Aad, B Abbott, K Abeling, NJ Abicht, SH Abidi, A Aboulhorma, H Abramowicz, H Abreu, Y Abulaiti, AC Abusleme Hoffman, BS Acharya, C Adam Bourdarios, L Adamczyk, L Adamek, SV Addepalli, MJ Addison, J Adelman, A Adiguzel, T Adye, AA Affolder, Y Afik, MN Agaras, J Agarwala, A Aggarwal, C Agheorghiesei, A Ahmad, F Ahmadov, WS Ahmed, S Ahuja, X Ai, G Aielli, M Ait Tamlihat, B Aitbenchikh, I Aizenberg, M Akbiyik, TPA Åkesson, AV Akimov, D Akiyama, NN Akolkar, K Al Khoury, GL Alberghi, J Albert, P Albicocco, GL Albouy, S Alderweireldt, M Aleksa, IN Aleksandrov, C Alexa, T Alexopoulos, A Alfonsi, F Alfonsi, M Algren, M Alhroob, B Ali, HMJ Ali, S Ali, SW Alibocus, M Aliev, G Alimonti, W Alkakhi, C Allaire, BMM Allbrooke, JF Allen, CA Allendes Flores, PP Allport, A Aloisio, F Alonso, C Alpigiani, M Alvarez Estevez, A Alvarez Fernandez, MG Alviggi, M Aly, Y Amaral Coutinho, A Ambler, C Amelung, M Amerl, CG Ames, D Amidei, SP Amor Dos Santos, KR Amos, V Ananiev, C Anastopoulos, T Andeen, JK Anders, SY Andrean, A Andreazza, S Angelidakis, A Angerami, AV Anisenkov, A Annovi, C Antel, MT Anthony, E Antipov, M Antonelli, DJA Antrim, F Anulli, M Aoki, T Aoki, JA Aparisi Pozo, MA Aparo, L Aperio Bella, C Appelt, A Apyan, N Aranzabal, C Arcangeletti, ATH Arce, E Arena, J-F Arguin, S Argyropoulos, J-H Arling, AJ Armbruster, O Arnaez, H Arnold, ZP Arrubarrena Tame, G Artoni, H Asada, K Asai, S Asai, NA Asbah, K Assamagan, R Astalos, S Atashi, RJ Atkin, M Atkinson, NB Atlay, H Atmani, PA Atmasiddha, K Augsten, S Auricchio, AD Auriol, VA Austrup, G Avolio, K Axiotis, G Azuelos, D Babal, H Bachacou, K Bachas, A Bachiu, F Backman, A Badea, P Bagnaia, M Bahmani, AJ Bailey, VR Bailey, JT Baines, L Baines, C Bakalis, OK Baker, E Bakos</div></div><div class="gs_scl"><div class="gsc_oci_field">Publication date</div><div class="gsc_oci_value">2024/3/25</div></div><div class="gs_scl"><div class="gsc_oci_field">Journal</div><div class="gsc_oci_value">The European Physical Journal C</div></div><div class="gs_scl"><div class="gsc_oci_field">Volume</div><div class="gsc_oci_value">84</div></div><div class="gs_scl"><div class="gsc_oci_field">Issue</div><div class="gsc_oci_value">3</div></div><div class="gs_scl"><div class="gsc_oci_field">Pages</div><div class="gsc_oci_value">315</div></div><div class="gs_scl"><div class="gsc_oci_field">Publisher</div><div class="gsc_oci_value">Springer Berlin Heidelberg</div></div><div class="gs_scl"><div class="gsc_oci_field">Description</div><div class="gsc_oci_value" id="gsc_oci_descr"><div class="gsh_small"><div class="gsh_csp">This paper presents for the first time a precise measurement of the production properties of the <i>Z</i> boson in the full phase space of the decay leptons. This is in contrast to the many previous precise unfolded measurements performed in the fiducial phase space of the decay leptons. The measurement is obtained from proton–proton collision data collected by the ATLAS experiment in 2012 at <svg class="gs_fsvg" aria-label="s=8" width="44px" height="15px" style="vertical-align:-3px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 11.16499)"><g><g><g><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 0.00000, -717.49945)" d="M 719 -1954 L 311 -1057 L 190 -1149 Q 184 -1155 176 -1155 Q 167 -1155 157 -1146 T 147 -1126 Q 147 -1116 156 -1110 L 399 -926 Q 405 -920 414 -920 Q 427 -920 434 -934 L 801 -1741 L 1671 63 Q 1681 82 1706 82 Q 1723 82 1735 70 T 1747 41 Q 1747 31 1745 27 L 793 -1948 Q 780 -1966 760 -1966 H 737 Q 727 -1966 719 -1954 Z "/><g transform="translate(833.33002, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 178 125 Q 233 31 399 31 Q 471 31 536 55 T 643 129 T 686 248 Q 686 301 648 335 T 555 381 L 444 403 Q 368 422 319 474 T 270 600 Q 270 691 319 761 T 450 868 T 618 905 Q 711 905 784 860 T 858 729 Q 858 682 831 646 T 758 610 Q 731 610 711 627 T 692 672 Q 692 696 705 718 T 741 754 T 788 768 Q 770 812 720 832 T 614 852 Q 562 852 510 831 T 426 769 T 395 674 Q 395 637 421 609 T 485 569 L 604 545 Q 661 533 708 502 T 783 425 T 811 319 Q 811 243 768 169 T 664 51 Q 555 -23 397 -23 Q 288 -23 197 27 T 106 176 Q 106 232 138 273 T 227 315 Q 260 315 282 295 T 305 242 Q 305 195 270 160 T 188 125 H 178 Z "/><line transform="translate(0.00000, -717.49945)" x1="0" x2="468.78000" y1="0" y2="0" style="stroke-width:40.00000"/></g></g><g transform="translate(1302.10999, 0.00000)"><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 277.77780, 0.00000)" d="M 154 272 Q 137 272 126 285 T 115 313 Q 115 330 126 342 T 154 354 H 1440 Q 1455 354 1466 342 T 1477 313 Q 1477 298 1466 285 T 1440 272 H 154 Z M 154 670 Q 137 670 126 682 T 115 711 Q 115 726 126 739 T 154 752 H 1440 Q 1455 752 1466 739 T 1477 711 Q 1477 694 1466 682 T 1440 670 H 154 Z "/></g><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 2635.44580, 0.00000)" d="M 86 311 Q 86 434 167 528 T 375 686 L 299 735 Q 229 781 185 857 T 141 1018 Q 141 1116 192 1195 T 329 1319 T 512 1364 Q 603 1364 687 1327 T 826 1221 T 881 1057 Q 881 988 848 929 T 759 823 T 639 743 L 756 668 Q 837 615 886 529 T 936 348 Q 936 237 876 146 T 719 5 T 512 -45 Q 406 -45 307 -2 T 147 122 T 86 311 Z M 197 311 Q 197 230 241 163 T 359 58 T 512 20 Q 631 20 728 89 T 825 274 Q 825 313 809 351 T 766 421 T 705 473 L 430 651 Q 366 617 312 565 T 228 448 T 197 311 Z M 338 936 L 586 776 Q 672 826 727 897 T 782 1057 Q 782 1126 743 1183 T 643 1273 T 510 1305 Q 448 1305 385 1281 T 281 1209 T 240 1098 Q 240 1002 338 936 Z "/></g></g></g></svg> TeV at the LHC and corresponding to an integrated luminosity of 20.2 fb<svg class="gs_fsvg" aria-label="-1" width="14px" height="12px" style="vertical-align:0px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 11.58769)"><g><g><g><g transform="translate(0.00000, -362.89200)"><path transform="scale(0.34180, -0.34180)" d="M 268 461 Q 248 464 234 477 T 221 512 Q 221 554 268 561 H 1559 Q 1606 554 1606 512 Q 1606 491 1592 477 T 1559 461 H 268 Z "/><path transform="matrix(0.34180, 0.00000, 0.00000, -0.34180, 624.98102, 0.00000)" d="M 233 0 V 82 Q 516 82 516 143 V 1202 Q 401 1147 219 1147 V 1229 Q 341 1229 447 1258 T 629 1360 H 666 Q 685 1355 690 1335 V 143 Q 690 82 973 82 V 0 H 233 Z "/></g></g></g></g></g></svg>. The results, based on a total of 15.3 million <i>Z</i>-boson decays to electron and muon pairs, extend and improve a previous measurement of the full set of angular coefficients describing <i>Z</i>-boson decay. The double-differential cross-section distributions in <i>Z</i>-boson transverse momentum <svg class="gs_fsvg" aria-label="pT" width="16px" height="9px" style="vertical-align:-3px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 6.18800)"><g><g><g><path transform="scale(0.48828, -0.48828)" d="M -51 -397 Q -70 -397 -70 -371 Q -63 -326 -43 -326 Q 21 -326 46 -315 T 86 -256 L 317 666 Q 332 704 332 764 Q 332 852 272 852 Q 208 852 177 775 T 117 582 Q 117 569 100 569 H 76 Q 71 569 65 576 T 59 590 Q 81 679 101 741 T 165 854 T 274 905 Q 344 905 397 865 T 465 758 Q 521 823 589 864 T 729 905 Q 815 905 878 859 T 974 738 T 1006 578 Q 1006 446 938 305 T 755 70 T 508 -23 Q 448 -23 399 11 T 324 100 L 231 -264 Q 226 -294 225 -299 Q 225 -326 360 -326 Q 381 -326 381 -352 Q 374 -379 369 -388 T 346 -397 H -51 Z M 510 31 Q 581 31 642 89 T 741 221 Q 769 276 793 355 T 836 525 T 854 668 Q 854 715 841 756 T 800 824 T 725 852 Q 650 852 583 798 T 463 666 V 659 L 350 207 Q 364 134 404 82 T 510 31 Z "/><g transform="translate(503.10999, 150.00000)"><path transform="scale(0.34180, -0.34180)" d="M 434 0 V 82 Q 536 82 634 92 T 733 143 V 1255 Q 733 1297 707 1307 T 627 1317 H 522 Q 434 1317 371 1303 T 262 1243 Q 222 1204 204 1122 T 176 920 H 98 L 141 1399 H 1526 L 1569 920 H 1491 Q 1480 1041 1463 1122 T 1405 1243 Q 1358 1290 1296 1303 T 1145 1317 H 1042 Q 988 1317 962 1307 T 936 1255 V 143 Q 936 103 1034 92 T 1235 82 V 0 H 434 Z "/></g></g></g></g></g></svg> and rapidity <svg class="gs_fsvg" aria-label="y" width="8px" height="9px" style="vertical-align:-3px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 6.18800)"><g><path transform="scale(0.48828, -0.48828)" d="M 172 -293 Q 215 -367 322 -367 Q 419 -367 490 -299 T 604 -135 T 672 63 Q 581 -23 475 -23 Q 394 -23 337 5 T 248 88 T 217 223 Q 217 290 235 360 T 285 517 T 342 668 Q 369 743 369 791 Q 369 852 324 852 Q 243 852 190 768 T 113 582 Q 109 569 96 569 H 72 Q 55 569 55 588 V 594 Q 88 716 156 810 T 328 905 Q 401 905 451 857 T 502 735 Q 502 697 485 655 Q 476 630 444 546 T 395 407 T 367 299 T 356 193 Q 356 125 385 78 T 477 31 Q 604 31 705 186 L 860 817 Q 867 844 892 863 T 946 883 Q 971 883 989 867 T 1008 825 Q 1008 813 1006 809 L 803 -6 Q 776 -111 704 -207 T 530 -362 T 319 -420 Q 266 -420 214 -400 T 130 -338 T 98 -242 Q 98 -186 131 -145 T 219 -104 Q 252 -104 274 -125 T 297 -178 Q 297 -225 262 -260 T 180 -295 Q 178 -294 176 -294 T 172 -293 Z "/></g></g></svg> are measured in the pole region, defined as <svg class="gs_fsvg" aria-label="80<mℓℓ<100" width="94px" height="13px" style="vertical-align:-1px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 11.97969)"><g><g><g><path transform="scale(0.48828, -0.48828)" d="M 86 311 Q 86 434 167 528 T 375 686 L 299 735 Q 229 781 185 857 T 141 1018 Q 141 1116 192 1195 T 329 1319 T 512 1364 Q 603 1364 687 1327 T 826 1221 T 881 1057 Q 881 988 848 929 T 759 823 T 639 743 L 756 668 Q 837 615 886 529 T 936 348 Q 936 237 876 146 T 719 5 T 512 -45 Q 406 -45 307 -2 T 147 122 T 86 311 Z M 197 311 Q 197 230 241 163 T 359 58 T 512 20 Q 631 20 728 89 T 825 274 Q 825 313 809 351 T 766 421 T 705 473 L 430 651 Q 366 617 312 565 T 228 448 T 197 311 Z M 338 936 L 586 776 Q 672 826 727 897 T 782 1057 Q 782 1126 743 1183 T 643 1273 T 510 1305 Q 448 1305 385 1281 T 281 1209 T 240 1098 Q 240 1002 338 936 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 500.00000, 0.00000)" d="M 512 -45 Q 261 -45 170 161 T 80 653 Q 80 831 112 988 T 241 1254 T 512 1364 Q 647 1364 733 1298 T 864 1127 T 925 903 T 942 653 Q 942 477 909 323 T 782 62 T 512 -45 Z M 512 8 Q 626 8 682 125 T 751 384 T 764 686 Q 764 840 751 970 T 682 1205 T 512 1311 Q 396 1311 340 1205 T 271 969 T 258 686 Q 258 572 263 471 T 293 262 T 370 81 T 512 8 Z "/></g><g transform="translate(1000.00000, 0.00000)"><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 277.77780, 0.00000)" d="M 190 477 Q 170 486 170 512 Q 170 538 197 551 L 1366 1102 Q 1374 1106 1380 1106 Q 1398 1106 1409 1093 T 1421 1065 Q 1421 1040 1397 1026 L 307 512 L 1403 -6 Q 1421 -12 1421 -41 Q 1421 -57 1409 -70 T 1380 -82 Q 1374 -82 1366 -78 L 190 477 Z "/></g><g transform="translate(2333.33569, 0.00000)"><g><path transform="scale(0.48828, -0.48828)" d="M 158 35 Q 158 47 160 53 L 313 664 Q 328 721 328 764 Q 328 852 268 852 Q 204 852 173 775 T 113 582 Q 113 576 107 572 T 96 569 H 72 Q 65 569 60 576 T 55 590 Q 77 679 97 741 T 161 854 T 270 905 Q 347 905 406 856 T 465 733 Q 526 813 608 859 T 782 905 Q 879 905 949 855 T 1020 715 Q 1083 804 1167 854 T 1352 905 Q 1458 905 1522 847 T 1587 684 Q 1587 600 1549 481 T 1456 215 Q 1427 144 1427 92 Q 1427 31 1475 31 Q 1555 31 1608 117 T 1683 301 Q 1689 313 1700 313 H 1724 Q 1732 313 1737 307 T 1743 295 Q 1743 293 1741 289 Q 1713 173 1643 75 T 1470 -23 Q 1398 -23 1347 26 T 1296 147 Q 1296 183 1313 227 Q 1371 381 1409 502 T 1448 715 Q 1448 772 1425 812 T 1348 852 Q 1236 852 1154 783 T 1012 602 Q 1008 582 1006 571 L 874 45 Q 867 17 842 -3 T 788 -23 Q 764 -23 745 -7 T 727 35 Q 727 47 729 53 L 860 575 Q 881 659 881 715 Q 881 772 857 812 T 778 852 Q 703 852 640 819 T 530 731 T 444 602 L 305 45 Q 298 17 273 -3 T 219 -23 Q 194 -23 176 -7 T 158 35 Z "/><g transform="translate(878.00000, -362.89200)"><path transform="scale(0.34180, -0.34180)" d="M 84 143 Q 75 143 69 148 T 59 159 T 47 176 Q 45 178 45 188 Q 45 196 77 226 T 169 310 T 233 367 Q 233 381 232 390 T 231 410 Q 231 659 356 969 Q 396 1068 456 1175 T 598 1362 T 764 1442 Q 835 1442 867 1391 T 899 1266 Q 899 1153 850 1030 T 727 799 T 565 593 T 379 401 Q 375 337 375 307 Q 375 206 402 121 T 508 37 Q 557 37 607 61 T 695 114 T 775 177 T 825 213 Q 832 213 837 210 T 847 201 T 856 190 T 862 180 Q 864 176 864 168 Q 864 155 856 150 Q 765 68 680 19 T 504 -29 Q 425 -29 370 15 T 286 129 T 244 274 Q 234 266 195 231 T 124 170 T 84 143 Z M 397 522 Q 478 603 551 690 T 686 874 T 786 1076 T 825 1278 Q 825 1376 760 1376 Q 682 1376 606 1211 T 477 854 T 397 522 Z "/><path transform="matrix(0.34180, 0.00000, 0.00000, -0.34180, 334.71899, 0.00000)" d="M 84 143 Q 75 143 69 148 T 59 159 T 47 176 Q 45 178 45 188 Q 45 196 77 226 T 169 310 T 233 367 Q 233 381 232 390 T 231 410 Q 231 659 356 969 Q 396 1068 456 1175 T 598 1362 T 764 1442 Q 835 1442 867 1391 T 899 1266 Q 899 1153 850 1030 T 727 799 T 565 593 T 379 401 Q 375 337 375 307 Q 375 206 402 121 T 508 37 Q 557 37 607 61 T 695 114 T 775 177 T 825 213 Q 832 213 837 210 T 847 201 T 856 190 T 862 180 Q 864 176 864 168 Q 864 155 856 150 Q 765 68 680 19 T 504 -29 Q 425 -29 370 15 T 286 129 T 244 274 Q 234 266 195 231 T 124 170 T 84 143 Z M 397 522 Q 478 603 551 690 T 686 874 T 786 1076 T 825 1278 Q 825 1376 760 1376 Q 682 1376 606 1211 T 477 854 T 397 522 Z "/></g></g></g><g transform="translate(3880.77368, 0.00000)"><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 277.77780, 0.00000)" d="M 190 477 Q 170 486 170 512 Q 170 538 197 551 L 1366 1102 Q 1374 1106 1380 1106 Q 1398 1106 1409 1093 T 1421 1065 Q 1421 1040 1397 1026 L 307 512 L 1403 -6 Q 1421 -12 1421 -41 Q 1421 -57 1409 -70 T 1380 -82 Q 1374 -82 1366 -78 L 190 477 Z "/></g><g transform="translate(5214.10938, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 190 0 V 72 Q 446 72 446 137 V 1212 Q 340 1161 178 1161 V 1233 Q 429 1233 557 1364 H 586 Q 593 1364 599 1358 T 606 1346 V 137 Q 606 72 862 72 V 0 H 190 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 500.00000, 0.00000)" d="M 512 -45 Q 261 -45 170 161 T 80 653 Q 80 831 112 988 T 241 1254 T 512 1364 Q 647 1364 733 1298 T 864 1127 T 925 903 T 942 653 Q 942 477 909 323 T 782 62 T 512 -45 Z M 512 8 Q 626 8 682 125 T 751 384 T 764 686 Q 764 840 751 970 T 682 1205 T 512 1311 Q 396 1311 340 1205 T 271 969 T 258 686 Q 258 572 263 471 T 293 262 T 370 81 T 512 8 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 1000.00000, 0.00000)" d="M 512 -45 Q 261 -45 170 161 T 80 653 Q 80 831 112 988 T 241 1254 T 512 1364 Q 647 1364 733 1298 T 864 1127 T 925 903 T 942 653 Q 942 477 909 323 T 782 62 T 512 -45 Z M 512 8 Q 626 8 682 125 T 751 384 T 764 686 Q 764 840 751 970 T 682 1205 T 512 1311 Q 396 1311 340 1205 T 271 969 T 258 686 Q 258 572 263 471 T 293 262 T 370 81 T 512 8 Z "/></g></g></g></g></svg> GeV, over the range <svg class="gs_fsvg" aria-label="|y|<3.6" width="55px" height="14px" style="vertical-align:-4px;"><g transform="matrix(0.01400, 0.00000, 0.00000, 0.01400, 0.00000, 10.50000)"><g><g><g><path transform="scale(0.48828, -0.48828)" d="M 244 -475 V 1499 Q 244 1515 256 1525 T 285 1536 Q 300 1536 313 1525 T 326 1499 V -475 Q 326 -491 313 -502 T 285 -512 Q 268 -512 256 -502 T 244 -475 Z "/></g><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 277.78000, 0.00000)" d="M 172 -293 Q 215 -367 322 -367 Q 419 -367 490 -299 T 604 -135 T 672 63 Q 581 -23 475 -23 Q 394 -23 337 5 T 248 88 T 217 223 Q 217 290 235 360 T 285 517 T 342 668 Q 369 743 369 791 Q 369 852 324 852 Q 243 852 190 768 T 113 582 Q 109 569 96 569 H 72 Q 55 569 55 588 V 594 Q 88 716 156 810 T 328 905 Q 401 905 451 857 T 502 735 Q 502 697 485 655 Q 476 630 444 546 T 395 407 T 367 299 T 356 193 Q 356 125 385 78 T 477 31 Q 604 31 705 186 L 860 817 Q 867 844 892 863 T 946 883 Q 971 883 989 867 T 1008 825 Q 1008 813 1006 809 L 803 -6 Q 776 -111 704 -207 T 530 -362 T 319 -420 Q 266 -420 214 -400 T 130 -338 T 98 -242 Q 98 -186 131 -145 T 219 -104 Q 252 -104 274 -125 T 297 -178 Q 297 -225 262 -260 T 180 -295 Q 178 -294 176 -294 T 172 -293 Z "/><g transform="translate(803.93903, 0.00000)"><g transform="translate(111.11111, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 244 -475 V 1499 Q 244 1515 256 1525 T 285 1536 Q 300 1536 313 1525 T 326 1499 V -475 Q 326 -491 313 -502 T 285 -512 Q 268 -512 256 -502 T 244 -475 Z "/></g></g><g transform="translate(1303.94128, 0.00000)"><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 277.77780, 0.00000)" d="M 190 477 Q 170 486 170 512 Q 170 538 197 551 L 1366 1102 Q 1374 1106 1380 1106 Q 1398 1106 1409 1093 T 1421 1065 Q 1421 1040 1397 1026 L 307 512 L 1403 -6 Q 1421 -12 1421 -41 Q 1421 -57 1409 -70 T 1380 -82 Q 1374 -82 1366 -78 L 190 477 Z "/></g><g transform="translate(2637.27686, 0.00000)"><path transform="scale(0.48828, -0.48828)" d="M 195 158 Q 243 88 324 54 T 498 20 Q 617 20 667 121 T 717 352 Q 717 410 706 468 T 671 576 T 602 656 T 496 686 H 360 Q 342 686 342 705 V 723 Q 342 739 360 739 L 473 748 Q 545 748 592 802 T 662 933 T 684 1081 Q 684 1179 638 1242 T 498 1305 Q 420 1305 349 1275 T 236 1186 Q 240 1187 243 1187 T 250 1188 Q 296 1188 327 1156 T 358 1079 Q 358 1035 327 1003 T 250 971 Q 205 971 173 1003 T 141 1079 Q 141 1167 194 1232 T 330 1330 T 498 1364 Q 560 1364 629 1345 T 754 1292 T 845 1204 T 881 1081 Q 881 995 842 922 T 737 796 T 590 717 Q 679 700 759 650 T 887 522 T 936 354 Q 936 241 874 149 T 711 6 T 498 -45 Q 402 -45 305 -9 T 147 101 T 86 276 Q 86 327 120 361 T 205 395 Q 238 395 265 379 T 308 336 T 324 276 Q 324 226 289 192 T 205 158 H 195 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 500.00000, 0.00000)" d="M 172 113 Q 172 159 206 192 T 285 225 Q 313 225 340 210 T 382 168 T 397 113 Q 397 68 364 34 T 285 0 Q 240 0 206 34 T 172 113 Z "/><path transform="matrix(0.48828, 0.00000, 0.00000, -0.48828, 777.78003, 0.00000)" d="M 512 -45 Q 385 -45 300 22 T 168 197 T 104 423 T 86 662 Q 86 824 149 987 T 334 1257 T 625 1364 Q 695 1364 755 1337 T 850 1259 T 885 1135 Q 885 1093 856 1064 T 786 1036 Q 746 1036 717 1065 T 688 1135 Q 688 1175 717 1204 T 786 1233 H 797 Q 771 1270 723 1287 T 625 1305 Q 563 1305 510 1278 T 416 1205 T 346 1103 T 302 977 T 283 844 T 279 688 Q 315 772 381 825 T 530 879 Q 621 879 696 842 T 825 739 T 907 590 T 936 420 Q 936 300 882 191 T 732 19 T 512 -45 Z M 512 20 Q 591 20 639 56 T 709 151 T 737 271 T 743 420 Q 743 536 732 618 T 672 762 T 522 825 Q 439 825 385 769 T 307 627 T 283 463 Q 283 436 285 422 Q 285 419 284 417 T 283 412 Q 283 324 301 234 T 370 82 T 512 20 Z "/></g></g></g></g></svg>. The total uncertainty of the normalised cross-section measurements in the peak region of the …</div></div></div></div><div class="gs_scl"><div class="gsc_oci_field">Total citations</div><div class="gsc_oci_value"><div style="margin-bottom:1em"><a href="https://scholar.google.com/scholar?oi=bibs&hl=en&cites=8242135921645934326,13596319634241718286&as_sdt=5">Cited by 8</a></div><div id="gsc_oci_graph_wrapper"><div id="gsc_oci_graph" style="width:63px;"><div id="gsc_oci_graph_x"></div><div id="gsc_oci_graph_bars"><span class="gsc_oci_g_t" style="left:0px">2023</span><span class="gsc_oci_g_t" style="left:33px">2024</span><a href="https://scholar.google.com/scholar?oi=bibs&hl=en&cites=8242135921645934326,13596319634241718286&as_sdt=5&as_ylo=2023&as_yhi=2023" class="gsc_oci_g_a" style="left:5px;height:43px;top:14px;z-index:2"><span class="gsc_oci_g_al">3</span></a><a href="https://scholar.google.com/scholar?oi=bibs&hl=en&cites=8242135921645934326,13596319634241718286&as_sdt=5&as_ylo=2024&as_yhi=2024" class="gsc_oci_g_a" style="left:38px;height:57px;top:0px;z-index:1"><span class="gsc_oci_g_al">4</span></a></div></div></div></div></div><div class="gs_scl"><div class="gsc_oci_field">Scholar articles</div><div class="gsc_oci_value"><div class="gsc_oci_merged_snippet"><div><a href="/scholar?oi=bibs&cluster=8242135921645934326&btnI=1&hl=en">A precise measurement of the Z-boson double-differential transverse momentum and rapidity distributions in the full phase space of the decay leptons with the ATLAS experiment at s= 8 TeV</a></div><div>ATLAS Collaboration atlas. publications@ cern. ch… - The European Physical Journal C, 2024</div><div><a class="gsc_oms_link" href="https://scholar.google.com/scholar?oi=bibs&hl=en&cites=8242135921645934326&as_sdt=5">Cited by 8</a> <a class="gsc_oms_link" href="https://scholar.google.com/scholar?oi=bibs&hl=en&q=related:9lYxuPPyYXIJ:scholar.google.com/">Related articles</a> <a class="gsc_oms_link" href="https://scholar.google.com/scholar?oi=bibs&hl=en&cluster=8242135921645934326">All 29 versions</a> </div></div><div class="gsc_oci_merged_snippet"><div><a href="/scholar?oi=bibs&cluster=13596319634241718286&btnI=1&hl=en">A precise measurement of the Z-boson double-differential transverse momentum and rapidity distributions in the full phase space of the decay leptons with the ATLAS experiment at√ s= 8 TeV</a></div><div>A Collaboration - Eur. Phys. J. C, 2024</div><div><a class="gsc_oms_link" href="https://scholar.google.com/scholar?oi=bibs&hl=en&q=related:Doilw6vUr7wJ:scholar.google.com/">Related articles</a> <a class="gsc_oms_link" href="https://scholar.google.com/scholar?oi=bibs&hl=en&cluster=13596319634241718286">All 2 versions</a> </div></div></div></div></div></div></div></div><div id="gs_ftr_sp" role="presentation"></div><div id="gs_ftr" class="gs_md_rmb" role="contentinfo"><div id="gs_ftr_rt"><a href="//www.google.com/intl/en/policies/privacy/">Privacy</a><a href="//www.google.com/intl/en/policies/terms/">Terms</a><a href="javascript:void(0)" ontouchstart="gs_evt_dsp(event)" role="button" aria-controls="gs_ftr_mnu" aria-haspopup="true" class="gs_press gs_md_tb">Help</a></div><div id="gs_ftr_mnu" class="gs_md_d gs_md_ds gs_ttzi gs_md_ulr" role="menu" tabindex="-1"><a role="menuitem" href="/intl/en/scholar/about.html" tabindex="-1" class="gs_md_li">About Scholar</a><a role="menuitem" href="//support.google.com/websearch?p=scholar_dsa&hl=en" tabindex="-1" class="gs_md_li">Search help</a></div></div></div></body></html>