Lattice QCD calculation of x-dependent meson distribution amplitudes at physical pion mass with threshold logarithm resummation

We present a lattice quantum chromodynamics (QCD) calculation of the x-dependent pion and kaon distribution amplitudes (DA) in the framework of large momentum effective theory. This calculation is performed on a fine lattice of a=0.076 fm 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 MS¯ 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 xâ[x0,1-x0] with x0=0.25 for pion and x0=0.2 for kaon with theoretical systematic errors under control. The kaon DA is shown to be slighted skewed, and narrower than pion DA. Although the x-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.