Pion and kaon distribution amplitudes in the continuum limit

Rui Zhang,Jiunn-Wei Chen,Carson Honkala,Huey-Wen Lin

doi:10.1103/physrevd.102.094519

Abstract

We present a lattice-QCD calculation of the pion, kaon and $\eta_s$ distribution amplitudes using large-momentum effective theory (LaMET). Our calculation is carried out using three ensembles with 2+1+1 flavors of highly improved staggered quarks (HISQ), generated by MILC collaboration, at 310 MeV pion mass with 0.06, 0.09 and 0.12 fm lattice spacings. We use clover fermion action for the valence quarks and tune the quark mass to match the lightest light and strange masses in the sea. The resulting lattice matrix elements are nonperturbatively renormalized in regularization-independent momentum-subtraction (RI/MOM) scheme and extrapolated to the continuum. We use two approaches to extract the $x$-dependence of the meson distribution amplitudes: 1) we fit the renormalized matrix elements in coordinate space to an assumed distribution form through a one-loop matching kernel; 2) we use a machine-learning algorithm trained on pseudo lattice-QCD data to make predictions on the lattice data. We found the results are consistent between these methods with the latter method giving a less smooth shape. Both approaches suggest that as the quark mass increases, the distribution amplitude becomes narrower. Our pion distribution amplitude has broader distribution than predicted by light-front constituent-quark model, and the moments of our pion distributions agree with previous lattice-QCD results using the operator production expansion.

Highlights

Meson distribution amplitudes (DAs) φM hold the key to understanding how light-quark hadron masses emerge from QCD, an important topic of study at a future electron-ion collider [1]
We extend our previous work on the kaon distribution amplitude from a single a12m310 lattice [84] to three lattice ensembles with different lattice spacings and extrapolate the results to continuum
The nonperturbative renormalization (NPR) factors Zðz; μR; pRz ; aÞ are calculated by implementing the condition that

Summary

INTRODUCTION

Meson distribution amplitudes (DAs) φM hold the key to understanding how light-quark hadron masses emerge from QCD, an important topic of study at a future electron-ion collider [1]. This is largely due to the omission of the long-range tail of the spatial correlator, which is cut off by the finite size of the lattice To fix this problem, we would need larger hadron momentum instead of a larger lattice volume, because the long-range correlations of the matrix elements (MEs) increase the undesired mixing with higher-twist operators. Reference [46] argued that the matrix element of the twist-4 operator is set by the scale a; its suppression factor compared with twist-2 is Oð1=ðPzaÞ2Þ instead of OðΛ2QCD=P2zÞ with the hadron momentum Pz. the twist-4 contribution that needs to be subtracted from the quasidistribution operator can be written as equal-time correlators with two more mass dimensions than the original quasidistribution operator [24].

LATTICE SETUP

Nonperturbative renormalization

Continuum extrapolation

Quasi-DA matrix elements to light cone DA

Machine learning predictions for light cone DAs

SUMMARY AND OUTLOOK