Precision control in lattice calculation of x-dependent pion distribution amplitude
Jack Holligan, Xiangdong Ji, Huey-Wen Lin, Yushan Su, Rui Zhang
Abstract
We present a new Bjorken x -dependence analysis of a previous lattice quantum chromodynamics data for the pion distribution amplitude from MILC configurations with three lattice spacing a = 0.06 , 0.09 , 0.12 fm. A leading renormalon resummation in renormalization as well as the perturbative matching kernel in the framework of large momentum expansion generates the power accuracy of the matching to the light-cone amplitude. Meanwhile, a small momentum log resummation is implemented for both the quark momentum x P z and the antiquark momentum ( 1 − x ) P z inside a meson of boost momentum P z up to 1.72 GeV along the z direction, allowing us to have more accurate determination of the x -dependence in the middle range. Finally, we use the complementarity between the short-distance factorization and the large momentum expansion to constrain the endpoint regions x ∼ 0 , 1 , thus obtaining the full-range x -dependence of the amplitude.