Complete flavor decomposition of the spin and momentum fraction of the proton using lattice QCD simulations at physical pion mass

Abstract

We evaluate the gluon and quark contributions to the spin of the proton using an ensemble of gauge configurations generated at physical pion mass. We compute all valence and sea quark contributions to high accuracy. We perform a nonperturbative renormalization for both quark and gluon matrix elements. We find that the contribution of the up, down, strange, and charm quarks to the proton intrinsic spin is $\frac{1}{2}{\ensuremath{\sum}}_{q=u,d,s,c}\mathrm{\ensuremath{\Delta}}{\mathrm{\ensuremath{\Sigma}}}^{{q}^{+}}=0.191(15)$ and to the total spin ${\ensuremath{\sum}}_{q=u,d,s,c}{J}^{{q}^{+}}=0.285(45)(10)$. The gluon contribution to the spin is ${J}^{g}=0.187(46)(10)$ yielding $J={J}^{q}+{J}^{g}=0.473(71)(14)$ confirming the spin sum. The momentum fraction carried by quarks in the proton is found to be 0.618(60) and by gluons 0.427(92), the sum of which gives 1.045(118) confirming the momentum sum rule. All scale and scheme dependent quantities are given in the $\overline{\mathrm{MS}}$ scheme at 2 GeV.