Proton momentum and angular momentum decompositions with overlap fermions

TL;DR

This paper calculates the proton's momentum and angular momentum decompositions using overlap fermions on a near-physical lattice, providing detailed fractions for quarks and gluons with nonperturbative renormalization.

Contribution

It presents a comprehensive nonperturbative determination of proton momentum and angular momentum fractions with overlap fermions, including renormalization and mixing effects, near physical pion mass.

Findings

Quark and gluon momentum fractions sum to 1.

Quark total angular momentum is approximately 0.54.

Quark spin and orbital angular momentum fractions are quantified.

Abstract

We present a calculation of the proton momentum and angular momentum decompositions using overlap fermions on a $2+1$-flavor RBC/UKQCD domain-wall lattice at 0.143 fm with a pion mass of 171 MeV which is close to the physical one. A complete determination of the momentum and angular momentum fractions carried by up, down, strange and glue inside the proton has been done with valence pion masses varying from 171 to 391 MeV. We have utilized fast Fourier transform on the stochastic-sandwich method for connected-insertion parts and the cluster-decomposition error reduction technique for disconnected-insertion parts has been used to reduce statistical errors. The full nonperturbative renormalization and mixing between the quark and glue operators are carried out. The final results are normalized with the momentum and angular momentum sum rules and reported at the physical valence pion mass at ${\overline{\rm {MS}}}\, (\mu = 2\ {\rm{GeV}})$. The renormalized momentum fractions for the quarks and glue are $\langle x \rangle^q = 0.491(20)(23)$ and $\langle x \rangle^g = 0.509(20)(23)$, respectively, and the renormalized total angular momentum fractions for quarks and glue are $2 J^q = 0.539(22)(44)$ and $2 J^g = 0.461(22)(44)$, respectively. The quark spin fraction is $\Sigma = 0.405(25)(37)$ from our previous work and the quark orbital angular momentum fraction is deduced from $2 L^q = 2 J^q - \Sigma$ to be $0.134(22)(44)$.