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

TL;DR

This study calculates the distribution of momentum between quarks and gluons in the pion and kaon using lattice QCD with physical quark masses, providing the first continuum extrapolation at the physical pion mass.

Contribution

It presents the first continuum limit results for quark and gluon momentum fractions in the pion and kaon directly at the physical pion mass.

Findings

Quark momentum fraction in pion: 0.575(79)

Quark momentum fraction in kaon: 0.683(50)

Gluon momentum fraction in pion: 0.402(53)

Abstract

We present results on 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 with physical quark masses. We perform, for the first time, a continuum extrapolation directly at the physical pion. We find that the total momentum fraction carried by quarks is $\langle x \rangle_{q, R}^{\pi}= 0.575(79)$ and $\langle x \rangle_{q,R}^{K} = 0.683(50)$ and by gluons $\langle x \rangle_{g, R}^{\pi}=0.402(53)$ and $\langle x \rangle_{g, R}^{K}=0.422(67)$ 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 verify the momentum sum, finding 0.984(89) for the pion and 1.13(11) for the kaon.