⟨x⟩ and ⟨x2⟩ of the pion PDF from lattice QCD with Nf=2+1+1 dynamical quark flavors

M Oehm,C Urbach,C Alexandrou,S Zafeiropoulos,F Steffens,K Jansen,M Constantinou,G Koutsou,B Kostrzewa

doi:10.1103/physrevd.99.014508

Abstract

Using Nf=2+1+1 lattice QCD, we determine the fermionic connected contributions to the second and third moment of the pion PDF. Based on gauge configurations from the European Twisted Mass Collaboration, chiral and continuum extrapolations are performed using pion masses in the range of 230 to 500 MeV and three values of the lattice spacing. Finite volume effects are investigated using different volumes. In order to avoid mixing under renormalisation for the third moment, we use an operator with two non-zero spatial components of momentum. Momenta are injected using twisted boundary conditions. Our final values read $\langle x\rangle=0.2075(106)$ and $\langle x^2\rangle=0.163(33)$, determined at 2 GeV in the $\overline{MS}$-scheme and with systematic and statistical uncertainties summend in quadrature.

Highlights

In quantum chromodynamics (QCD), the pion represents the Goldstone boson of spontaneously broken chiral symmetry and is the lightest hadronic state in the spectrum
In order to avoid mixing under renormalization for the second moment, we use an operator with two nonzero spatial components of momentum
In this work we present a multicomponent effort in the aforementioned direction, with a variety of improvements compared to the studies available in the literature, in terms of the ensembles employed and level of control over systematic uncertainties in the computed moments

Summary

Introduction

In quantum chromodynamics (QCD), the pion represents the Goldstone boson of spontaneously broken chiral symmetry and is the lightest hadronic state in the spectrum. As such it is of deep importance both for the long range part of the nucleon-nucleon interaction and for the inner structure of the nucleon. In the latter case, it is widely recognized that the pion is responsible for most, if not for all, of the excess of dover uantiquarks in the proton sea [1,2,3,4].

Results

Discussion

Conclusion