Proton mass decomposition

Yi-Bo Yang,Keh-Fei Liu,Ying Chen,Jian Liang,Terrence Draper,M Della Morte,P Fritzsch,E Gámiz Sánchez,C Pena Ruano

doi:10.1051/epjconf/201817514002

Abstract

We report the results on the proton mass decomposition and also on the related quark and glue momentum fractions. The results are based on overlap valence fermions on four ensembles of Nf = 2 + 1 DWF configurations with three lattice spacings and volumes, and several pion masses including the physical pion mass. With 1-loop pertur-bative calculation and proper normalization of the glue operator, we find that the u, d, and s quark masses contribute 9(2)% to the proton mass. The quark energy and glue field energy contribute 31(5)% and 37(5)% respectively in the MS scheme at µ = 2 GeV. The trace anomaly gives the remaining 23(1)% contribution. The u, d, s and glue momentum fractions in the MS scheme are consistent with the global analysis at µ = 2 GeV.

Highlights

The Higgs boson provides the source of quark masses
It would be better to use the conserved energy-momentum tensor (EMT) on the lattice to avoid the need for normalization and attempts to construct such a conserved EMT on the lattice have been made perturbatively and non-perturbatively [3] and recently by Suzuki [4, 5] with gradient flow at finite lattice spacing
We will calculate the renormalized quark and glue momentum fractions in the proton on four lattice ensembles and interpolate the results to the physical pion mass with a global fit including finite lattice spacing and volume corrections

Summary

Introduction

The Higgs boson provides the source of quark masses. But how it is related to the proton mass and the mass of nuclei and atoms is another question. It would be better to use the conserved energy-momentum tensor (EMT) on the lattice to avoid the need for normalization and attempts to construct such a conserved EMT on the lattice have been made perturbatively and non-perturbatively [3] and recently by Suzuki [4, 5] with gradient flow at finite lattice spacing. We will discuss the normalization, renormalization, and mixing of x q and x g later In this proceeding, we will calculate the renormalized quark and glue momentum fractions in the proton on four lattice ensembles and interpolate the results to the physical pion mass with a global fit including finite lattice spacing and volume corrections. We will combine the previous Hm result [6] to obtain the full decomposition of the proton mass

Numerical setup

Results

Summary