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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 $a=0.076\mathrm{fm}$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 $\overline{\mathrm{MS}}$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 $x\in [x_0,1-x_0]$with $x_0=0.25$for pion and $x_0=0.2$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. Published by the American Physical Society2024