Pion Valence Quark Distribution at Physical Pion mass of $N_f=2+1+1$ Lattice QCD

TL;DR

This paper presents a high-precision lattice QCD calculation of the pion valence quark distribution at physical pion mass using LaMET, with advanced error handling and two-loop matching to improve accuracy.

Contribution

It introduces improved systematic error control and two-loop perturbative matching in lattice QCD calculations of the pion PDF at physical pion mass.

Findings

Compatible PDFs between different renormalization schemes.

Systematics reduced with RGR and LRR methods.

Results at $=2.0$ GeV are consistent and precise.

Abstract

We present a state-of-the-art calculation of the unpolarized pion valence-quark distribution in the framework of large-momentum effective theory (LaMET) with improved handling of systematic errors as well as two-loop perturbative matching. We use lattice ensembles generated by the MILC collaboration at lattice spacing $a\approx 0.09$~fm, lattice volume $64^3\times 96$, $N_f=2+1+1$ flavors of highly-improved staggered quarks and a physical pion mass. The LaMET matrix elements are calculated with pions boosted to momentum $P_z\approx 1.72$~GeV with high-statistics of $O(10^6)$ measurements. We study the pion PDF in both hybrid-ratio and hybrid-regularization-independent momentum subtraction (hybrid-RI/MOM) schemes and also compare the systematic errors with and without the addition of leading-renormalon resummation (LRR) and renormalization-group resummation (RGR) in both the renormalization and lightcone matching. The final lightcone PDF results are presented in the modified minimal-subtraction scheme at renormalization scale $\mu=2.0$~GeV. We show that the $x$-dependent PDFs are compatible between the hybrid-ratio and hybrid-RI/MOM renormalization with the same improvements. We also show that systematics are greatly reduced by the simultaneous inclusion of RGR and LRR and that these methods are necessary if improved precision is to be reached with higher-order terms in renormalization and matching.