Quark and gluon momentum fractions in the pion from $N_f=2+1+1$ lattice QCD

TL;DR

This paper presents the first full decomposition of the pion's momentum into quark and gluon contributions using lattice QCD with physical pion mass, providing detailed momentum fractions in the $ar{MS}$ scheme.

Contribution

It introduces a comprehensive lattice QCD calculation of the pion's momentum fractions, including gluons and all relevant quark flavors, at physical pion mass.

Findings

Quark momentum fraction $ar{x}_{u+d}=0.601(28)$

Strange quark momentum fraction $ar{x}_s=0.059(13)$

Gluon momentum fraction $ar{x}_g=0.52(11)$

Abstract

We perform the first full decomposition of the pion momentum into its gluon and quark contributions. We employ an ensemble generated by the Extended Twisted Mass Collaboration with $N_f=2 + 1 +1$ Wilson twisted mass clover fermions at maximal twist tuned to reproduce the physical pion mass. We present our results in the $\overline{\mathrm{MS}}$ scheme at $2\gev$. We find $\avgx_{u+d}=0.601(28)$, $\avgx_s=0.059(13)$, $\avgx_c=0.019(05)$, and $\avgx_g=0.52(11)$ for the separate contributions, respectively, whose sum saturates the momentum sum rule.