Valence parton distribution function of pion from fine lattice

Abstract

We present a lattice QCD study of the valence parton distribution inside the pion within the framework of Large Momentum Effective Theory. We use a mixed action approach with 1-HYP smeared valence Wilson clover quarks on $2+1$ flavor HISQ sea with the valence quark mass tuned to 300 MeV pion mass. We use $4{8}^{3}\ifmmode\times\else\texttimes\fi{}64$ lattice at a fine lattice spacing $a=0.06\text{ }\text{ }\mathrm{fm}$ for this computation. We renormalize the quasi parton distribution function matrix element in the nonperturbative regularization independent momentum subtraction (RI-MOM) scheme. As a byproduct, we test the validity of a 1-loop matching procedure by comparing the RI-MOM renormalized quasi parton distribution function matrix element with off-shell quark external states as computed in the continuum 1-loop perturbation theory with the lattice results at $a=0.04$ and 0.06 fm. By applying the RI-MOM to $\overline{\mathrm{MS}}$ one-loop matching, implemented through a fit to phenomenologically motivated parton distribution functions, we obtain the valence parton distribution function of pion.