Precision Control in Lattice Calculation of $x$-dependent Pion Distribution Amplitude

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 $x\sim 0,1$, thus obtaining the full-range $x$-dependence of the amplitude.

arXiv commentUpdate to the published version in NPB

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