Light cone distribution amplitude for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:math> baryon from lattice QCD
Min-Huan Chu, Haoyang Bai, Jun Hua, Jian Liang, Xiangdong Ji, Andreas Schäfer, Yushan Su, Wei Wang, Xiaonu Xiong, Yi-Bo Yang, Jun Zeng, Jian-Hui Zhang, Qi-An Zhang
Abstract
We calculate the leading-twist light cone distribution amplitudes of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi mathvariant="normal">Λ</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>u</a:mi> <a:mi>d</a:mi> <a:mi>s</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> baryon using lattice QCD methods within the framework of large-momentum effective theory. Our numerical computations are carried out with <f:math xmlns:f="http://www.w3.org/1998/Math/MathML" display="inline"> <f:msub> <f:mi>N</f:mi> <f:mi>f</f:mi> </f:msub> <f:mo>=</f:mo> <f:mn>2</f:mn> <f:mo>+</f:mo> <f:mn>1</f:mn> </f:math> stout smeared clover fermions and a Symanzik gauge action on a lattice with spacing <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"> <h:mi>a</h:mi> <h:mo>=</h:mo> <h:mn>0.077</h:mn> <h:mtext> </h:mtext> <h:mtext> </h:mtext> <h:mi>fm</h:mi> </h:math> and a pion mass of 303 MeV. To approach the large-momentum region, we simulate the equal-time correlations with the hadron momentum <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:msup> <j:mrow> <j:mi>P</j:mi> </j:mrow> <j:mrow> <j:mi>z</j:mi> </j:mrow> </j:msup> <j:mo>=</j:mo> <j:mo stretchy="false">{</j:mo> <j:mn>2.52</j:mn> <j:mo>,</j:mo> <j:mn>3.02</j:mn> <j:mo>,</j:mo> <j:mn>3.52</j:mn> <j:mo stretchy="false">}</j:mo> <j:mtext> </j:mtext> <j:mtext> </j:mtext> <j:mi>GeV</j:mi> </j:mrow> </j:math> . We investigate the analytic properties of the baryon quasidistribution amplitude in coordinate space and validate them through our lattice calculations. After renormalization and extrapolation, we present results for the three-dimensional distribution in momentum fractions of the two light quarks. Based on these findings, we briefly discuss the phenomenological impact on weak decays of <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"> <n:msub> <n:mi mathvariant="normal">Λ</n:mi> <n:mi>b</n:mi> </n:msub> </n:math> and outline potential systematic uncertainties that can be improved in the future. This work lays the theoretical foundation for accessing baryon light cone distribution amplitudes from lattice QCD.