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  1. The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up toQ24.3GeV2and the nucleon up toQ21GeV2. The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from250to540MeV, including the unitary point340MeV. We calculate the radius of the glue trace anomaly for the pion and the nucleon from thezexpansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion’s form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit.

    <supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec> </div> <a href='#' class='show open-abstract' style='margin-left:10px;'>more »</a> <a href='#' class='hide close-abstract' style='margin-left:10px;'>« less</a> <div class="actions" style="padding-left:10px;"> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10471084-connected-disconnected-sea-partons-from-ct18-parametrization-pdfs" itemprop="url"> <span class='span-link' itemprop="name">Connected and disconnected sea partons from the CT18 parametrization of PDFs</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.106.096008" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevD.106.096008  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Hou, Tie-Jiun</span> <span class="sep">; </span><span class="author" itemprop="author">Yan, Mengshi</span> <span class="sep">; </span><span class="author" itemprop="author">Liang, Jian</span> <span class="sep">; </span><span class="author" itemprop="author">Liu, Keh-Fei</span> <span class="sep">; </span><span class="author" itemprop="author">Yuan, C.-P.</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2022-11-01">November 2022</time> , Physical Review D) </span> </div> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.106.096008" target="_blank" title="Link to document DOI" data-ostiid="10471084"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10199836-nucleon-isovector-tensor-charge-from-lattice-qcd-using-chiral-fermions" itemprop="url"> <span class='span-link' itemprop="name">Nucleon isovector tensor charge from lattice QCD using chiral fermions</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.101.094501" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevD.101.094501  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Horkel, Derek</span> <span class="sep">; </span><span class="author" itemprop="author">Bi, Yujiang</span> <span class="sep">; </span><span class="author" itemprop="author">Constantinou, Martha</span> <span class="sep">; </span><span class="author" itemprop="author">Draper, Terrence</span> <span class="sep">; </span><span class="author" itemprop="author">Liang, Jian</span> <span class="sep">; </span><span class="author" itemprop="author">Liu, Keh-Fei</span> <span class="sep">; </span><span class="author" itemprop="author">Liu, Zhaofeng</span> <span class="sep">; </span><span class="author" itemprop="author">Yang, Yi-Bo</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2020-05-01">May 2020</time> , Physical Review D) </span> </div> <span class="editors"> <span class="editor" itemprop="editor">null</span> (Ed.) </span> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.101.094501" target="_blank" title="Link to document DOI" data-ostiid="10199836"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10338748-parton-distributions-lattice-qcd-calculations-toward-structure" itemprop="url"> <span class='span-link' itemprop="name">Parton distributions and lattice-QCD calculations: Toward 3D structure</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1016/j.ppnp.2021.103908" target="_blank" title="Link to document DOI">https://doi.org/10.1016/j.ppnp.2021.103908  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Constantinou, Martha</span> <span class="sep">; 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</span><span class="author" itemprop="author">Richards, David G.</span> <span class="sep">; </span><span class="author" itemprop="author">Detmold, William</span> <span class="sep">; </span><span class="author" itemprop="author">Gupta, Rajan</span> <span class="sep">; </span><span class="author" itemprop="author">Lin, Huey-Wen</span> <span class="sep">; </span><span class="author" itemprop="author">Liu, Keh-Fei</span> <span class="sep">; </span><span class="author" itemprop="author">Meyer, Aaron S.</span> <span class="sep">; </span><span class="author" itemprop="author">Sufian, Raza</span> <span class="sep">; </span><span class="author" itemprop="author">Syritsyn, Sergey</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2019-11-01">November 2019</time> , The European Physical Journal A) </span> </div> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1140/epja/i2019-12916-x" target="_blank" title="Link to document DOI" data-ostiid="10165579"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10093086-gluon-quasi-parton-distribution-functions-from-lattice-qcd" itemprop="url"> <span class='span-link' itemprop="name">Gluon Quasi-Parton-Distribution Functions from Lattice QCD</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevLett.121.242001" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevLett.121.242001  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Fan, Zhou-You</span> <span class="sep">; </span><span class="author" itemprop="author">Yang, Yi-Bo</span> <span class="sep">; </span><span class="author" itemprop="author">Anthony, Adam</span> <span class="sep">; </span><span class="author" itemprop="author">Lin, Huey-Wen</span> <span class="sep">; </span><span class="author" itemprop="author">Liu, Keh-Fei</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2018-12-01">December 2018</time> , Physical Review Letters) </span> </div> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevLett.121.242001" target="_blank" title="Link to document DOI" data-ostiid="10093086"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10087220-nonperturbatively-renormalized-glue-momentum-fraction-physical-pion-mass-from-lattice-qcd" itemprop="url"> <span class='span-link' itemprop="name">Nonperturbatively renormalized glue momentum fraction at the physical pion mass from lattice QCD</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.98.074506" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevD.98.074506  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Yang, Yi-Bo</span> <span class="sep">; </span><span class="author" itemprop="author">Gong, Ming</span> <span class="sep">; </span><span class="author" itemprop="author">Liang, Jian</span> <span class="sep">; </span><span class="author" itemprop="author">Lin, Huey-Wen</span> <span class="sep">; </span><span class="author" itemprop="author">Liu, Keh-Fei</span> <span class="sep">; </span><span class="author" itemprop="author">Pefkou, Dimitra</span> <span class="sep">; </span><span class="author" itemprop="author">Shanahan, Phiala</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2018-10-01">October 2018</time> , Physical Review D) </span> </div> <div class="actions" style="padding-left:10px;"> <span class="reader-count"> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.98.074506" target="_blank" title="Link to document DOI" data-ostiid="10087220"> Full Text Available <span class="fas fa-external-link-alt"></span> </a> </span> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10047783-sea-quarks-contribution-nucleon-magnetic-moment-charge-radius-physical-point" itemprop="url"> <span class='span-link' itemprop="name">Sea quarks contribution to the nucleon magnetic moment and charge radius at the physical point</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.96.114504" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevD.96.114504  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Sufian, Raza Sabbir</span> <span class="sep">; </span><span class="author" itemprop="author">Yang, Yi-Bo</span> <span class="sep">; </span><span class="author" itemprop="author">Liang, Jian</span> <span class="sep">; </span><span class="author" itemprop="author">Draper, Terrence</span> <span class="sep">; </span><span class="author" itemprop="author">Liu, Keh-Fei</span> <span class="sep">; </span><span class="author" itemprop="author">χQCD Collaboration</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2017-12-01">December 2017</time> , Physical Review D) </span> </div> <div class="actions" style="padding-left:10px;"> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10039325-lattice-calculation-nucleon-isovector-axial-charge-improved-currents" itemprop="url"> <span class='span-link' itemprop="name">Lattice calculation of nucleon isovector axial charge with improved currents</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.96.034519" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevD.96.034519  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Liang, Jian</span> <span class="sep">; </span><span class="author" itemprop="author">Yang, Yi-Bo</span> <span class="sep">; </span><span class="author" itemprop="author">Liu, Keh-Fei</span> <span class="sep">; </span><span class="author" itemprop="author">Alexandru, Andrei</span> <span class="sep">; </span><span class="author" itemprop="author">Draper, Terrence</span> <span class="sep">; </span><span class="author" itemprop="author">Sufian, Raza Sabbir</span> <span class="sep">; </span><span class="author" itemprop="author">χQCD Collaboration</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2017-08-01">August 2017</time> , Physical Review D) </span> </div> <div class="actions" style="padding-left:10px;"> </div> </div><div class="clearfix"></div> </div> </li> <li> <div class="article item document" itemscope itemtype="http://schema.org/TechArticle"> <div class="item-info"> <div class="title"> <a href="https://par.nsf.gov/biblio/10050798-strange-charm-quark-spins-from-anomalous-ward-identity" itemprop="url"> <span class='span-link' itemprop="name">Strange and charm quark spins from the anomalous Ward identity</span> </a> </div> <div> <strong> <a class="misc external-link" href="https://doi.org/10.1103/PhysRevD.95.114509" target="_blank" title="Link to document DOI">https://doi.org/10.1103/PhysRevD.95.114509  <span class="fas fa-external-link-alt"></span></a> </strong> </div> <div class="metadata"> <span class="authors"> <span class="author" itemprop="author">Gong, Ming</span> <span class="sep">; </span><span class="author" itemprop="author">Yang, Yi-Bo</span> <span class="sep">; </span><span class="author" itemprop="author">Liang, Jian</span> <span class="sep">; </span><span class="author" itemprop="author">Alexandru, Andrei</span> <span class="sep">; </span><span class="author" itemprop="author">Draper, Terrence</span> <span class="sep">; </span><span class="author" itemprop="author">Liu, Keh-Fei</span> <span class="sep">; </span><span class="author" itemprop="author">χQCD Collaboration</span> </span> <span class="year">( <time itemprop="datePublished" datetime="2017-06-01">June 2017</time> , Physical Review D) </span> </div> <div class="actions" style="padding-left:10px;"> </div> </div><div class="clearfix"></div> </div> </li> </ol> <div id="pagination-lower" style=""> <div class="pull-right" style="line-height: 30px;"> <div class="btn-group pagination nomargin"> <a href="#" class="btn btn-sm btn-default noborderradius" disabled="disabled">«<span class="hidden-xs"> Prev</span></a> <a class="dropdown-toggle btn btn-sm btn-default paging-dropdown hidden-xs noborderradius" href="#" data-toggle="dropdown"><span class="caret"></span><span class="sr-only">Select page number</span></a> <div class="dropdown-menu pull-right paging-slider-dropdown" style="padding: 15px;"> <small> <div class="text-muted" style="line-height:20px;"><label for="pagination-sel-sptag-2">Go to page: <span class="paging-target">1</span> of <span class="paging-max">2</span></label></div> <div> <table> <tr> <td valign="top"> <input id="pagination-sel-sptag-2" data-range="" value="1" min="1" max="2" name="pagination-sel" type="range" class="pagination-sel noborderradius" style="height:26px;padding:0px;margin-right:5px; 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