Lattice QCD Calculation of x-dependent Meson Distribution Amplitudes at Physical Pion Mass with Threshold Logarithm Resummation

We present a lattice 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 MS̄ 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 x∈[x₀,1-x₀] with x₀=0.25 for pion and x₀=0.2 for kaon with systematics 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.