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

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 $2\text{gev}$. We find ${\text{avgx}}_{u+d}=0.601(28)$, ${\text{avgx}}_s=0.059(13)$, ${\text{avgx}}_c=0.019(05)$, and ${\text{avgx}}_g=0.52(11)$ for the separate contributions, respectively, whose sum saturates the momentum sum rule.