Power corrections to quasidistribution amplitudes of a heavy meson

Abstract

It has been recently demonstrated that light cone distribution amplitudes (LCDAs) for a heavy meson, defined in the heavy quark limit, can be extracted by simulating quasidistribution amplitudes on the lattice with a large meson momentum <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:msup> <a:mi>P</a:mi> <a:mi>z</a:mi> </a:msup> </a:math> . This extraction involves a two-step procedure. In the first step, the quasidistribution amplitudes are matched onto the QCD LCDAs in the large <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:msup> <c:mi>P</c:mi> <c:mi>z</c:mi> </c:msup> </c:math> limit. In the second step, the QCD LCDAs are matched onto the desired LCDAs defined in heavy quark effective theory. In this work, we present the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:msubsup> <e:mi>m</e:mi> <e:mi>H</e:mi> <e:mrow> <e:mn>2</e:mn> <e:mi>n</e:mi> </e:mrow> </e:msubsup> <e:mo>/</e:mo> <e:mo stretchy="false">(</e:mo> <e:msup> <e:mi>P</e:mi> <e:mi>z</e:mi> </e:msup> <e:msup> <e:mo stretchy="false">)</e:mo> <e:mrow> <e:mn>2</e:mn> <e:mi>n</e:mi> </e:mrow> </e:msup> </e:math> and <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"> <i:msubsup> <i:mi mathvariant="normal">Λ</i:mi> <i:mi>QCD</i:mi> <i:mn>2</i:mn> </i:msubsup> <i:mo>/</i:mo> <i:mo stretchy="false">(</i:mo> <i:mi>x</i:mi> <i:msup> <i:mi>P</i:mi> <i:mi>z</i:mi> </i:msup> <i:msup> <i:mo stretchy="false">)</i:mo> <i:mn>2</i:mn> </i:msup> </i:math> and <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msubsup> <n:mi mathvariant="normal">Λ</n:mi> <n:mi>QCD</n:mi> <n:mn>2</n:mn> </n:msubsup> <n:mo>/</n:mo> <n:mo stretchy="false">(</n:mo> <n:mo stretchy="false">(</n:mo> <n:mn>1</n:mn> <n:mo>−</n:mo> <n:mi>x</n:mi> <n:mo stretchy="false">)</n:mo> <n:msup> <n:mi>P</n:mi> <n:mi>z</n:mi> </n:msup> <n:msup> <n:mo stretchy="false">)</n:mo> <n:mn>2</n:mn> </n:msup> </n:math> corrections in the first step with <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:msub> <u:mi>m</u:mi> <u:mi>H</u:mi> </u:msub> </u:math> being the heavy meson mass and <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"> <w:mi>x</w:mi> </w:math> being the momentum fraction of the light quark. To account for <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"> <y:msubsup> <y:mi>m</y:mi> <y:mi>H</y:mi> <y:mrow> <y:mn>2</y:mn> <y:mi>n</y:mi> </y:mrow> </y:msubsup> <y:mo>/</y:mo> <y:mo stretchy="false">(</y:mo> <y:msup> <y:mi>P</y:mi> <y:mi>z</y:mi> </y:msup> <y:msup> <y:mo stretchy="false">)</y:mo> <y:mrow> <y:mn>2</y:mn> <y:mi>n</y:mi> </y:mrow> </y:msup> </y:math> corrections, we employ two methods: the moment relation that can provide mass corrections to all orders, and a leading-twist projector that gives the leading-order mass corrections. For the <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"> <cb:msubsup> <cb:mi mathvariant="normal">Λ</cb:mi> <cb:mi>QCD</cb:mi> <cb:mn>2</cb:mn> </cb:msubsup> <cb:mo>/</cb:mo> <cb:mo stretchy="false">(</cb:mo> <cb:msup> <cb:mi>P</cb:mi> <cb:mi>z</cb:mi> </cb:msup> <cb:msup> <cb:mo stretchy="false">)</cb:mo> <cb:mn>2</cb:mn> </cb:msup> </cb:math> corrections, we employ a renormalon model that addresses the renormalon ambiguity stemming from the divergence of the perturbative series. We adopt two parametrizations for QCD LCDAs to conduct a numerical analysis. The results suggest that these corrections are typically smaller than 20% in the region <hb:math xmlns:hb="http://www.w3.org/1998/Math/MathML" display="inline"> <hb:mn>0.2</hb:mn> <hb:mo>&lt;</hb:mo> <hb:mi>x</hb:mi> <hb:mo>&lt;</hb:mo> <hb:mn>0.8</hb:mn> </hb:math> , and should be included in a precision analysis. These findings will serve as a valuable guide for future studies on heavy meson LCDAs, particularly in the context of lattice QCD, where accounting for such corrections is crucial for improving the accuracy and reliability of the results. Published by the American Physical Society 2024

Topics & Concepts