Quark and gluon momentum fractions in the pion and in the kaon

TL;DR

This study provides the first direct continuum-extrapolated determination of quark and gluon momentum fractions in the pion and kaon at physical quark masses, confirming the momentum sum rule within uncertainties.

Contribution

It offers the first physical-point, continuum-limit calculation of the momentum decomposition in pion and kaon using $N_f=2+1+1$ Wilson twisted-mass fermions.

Findings

Quark momentum fraction in pion: 0.532(56)

Quark momentum fraction in kaon: 0.618(32)

Gluon momentum fraction in pion: 0.388(49)

Abstract

We present the full decomposition of the momentum fraction carried by quarks and gluons in the pion and the kaon. We employ three gauge ensembles generated with $N_f=2+1+1$ Wilson twisted-mass clover-improved fermions at the physical quark masses. For both mesons we perform a continuum extrapolation directly at the physical pion mass, which allows us to determine for the first time the momentum decomposition at the physical point. We find that the total momentum fraction carried by quarks is 0.532(56) and 0.618(32) and by gluons 0.388(49) and 0.408(61) in the pion and in the kaon, respectively, in the $\overline{\mathrm{MS}}$ scheme and at the renormalization scale of 2 GeV. Having computed both the quark and gluon contributions in the continuum limit, we find that the momentum sum is 0.926(68) for the pion and 1.046(90) for the kaon, verifying the momentum sum rule.