Lattice QCD calculation of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>x</mml:mi> </mml:math> -dependent meson distribution amplitudes at physical pion mass with threshold logarithm resummation
Ian C. Cloët, Xiang Gao, Swagato Mukherjee, Sergey Syritsyn, Nikhil Karthik, Péter Petreczky, Rui Zhang, Yong Zhao
Abstract
We present a lattice quantum chromodynamics (QCD) calculation of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>x</a:mi> </a:math> -dependent pion and kaon distribution amplitudes (DA) in the framework of large momentum effective theory. This calculation is performed on a fine lattice of <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>a</c:mi> <c:mo>=</c:mo> <c:mn>0.076</c:mn> <c:mtext> </c:mtext> <c:mtext> </c:mtext> <c:mi>fm</c:mi> </c:math> at physical pion mass, with the pion boosted to 1.8 GeV and kaon boosted to 2.3 GeV. We renormalize the matrix elements in the hybrid scheme and match to <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mover accent="true"> <e:mi>MS</e:mi> <e:mo stretchy="true">¯</e:mo> </e:mover> </e:math> with a subtraction of the leading renormalon in the Wilson-line mass. The perturbative matching is improved by resumming the large logarithms related to the small quark and gluon momenta in the soft-gluon limit. After resummation, we demonstrate that we are able to calculate a range of <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:mi>x</i:mi> <i:mo>∈</i:mo> <i:mo stretchy="false">[</i:mo> <i:msub> <i:mi>x</i:mi> <i:mn>0</i:mn> </i:msub> <i:mo>,</i:mo> <i:mn>1</i:mn> <i:mo>−</i:mo> <i:msub> <i:mi>x</i:mi> <i:mn>0</i:mn> </i:msub> <i:mo stretchy="false">]</i:mo> </i:math> with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:msub> <m:mi>x</m:mi> <m:mn>0</m:mn> </m:msub> <m:mo>=</m:mo> <m:mn>0.25</m:mn> </m:math> for pion and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"> <o:msub> <o:mi>x</o:mi> <o:mn>0</o:mn> </o:msub> <o:mo>=</o:mo> <o:mn>0.2</o:mn> </o:math> for kaon with theoretical systematic errors under control. The kaon DA is shown to be slighted skewed, and narrower than pion DA. Although the <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"> <q:mi>x</q:mi> </q:math> -dependence cannot be direct calculated beyond these ranges, we estimate higher moments of the pion and kaon DAs by complementing our calculation with short-distance factorization. Published by the American Physical Society 2024