Moments of nucleon isovector structure functions in $2+1+1$-flavor QCD

Abstract

We present results on the isovector momentum fraction, $⟨x{⟩}_{u-d}$, helicity moment, $⟨x{⟩}_{\Delta u-\Delta d}$, and the transversity moment, $⟨x{⟩}_{\delta u-\delta d}$, of the nucleon obtained using nine ensembles of gauge configurations generated by the MILC collaboration using $2+1+1$-flavors of dynamical highly improved staggered quarks (HISQ). The correlation functions are calculated using the Wilson-Clover action and the renormalization of the three operators is carried out nonperturbatively on the lattice in the RI${}^{\prime }$-MOM scheme. The data have been collected at lattice spacings $a\approx 0.15,0.12,0.09,$ and 0.06 fm and $M_{\pi }\approx 310,220$ and 135 MeV, which are used to obtain the physical values using a simultaneous chiral-continuum-finite-volume fit. The final results, in the $\overline{MS}$ scheme at 2 GeV, are $⟨x{⟩}_{u-d}=0.173(14)(07)$, $⟨x{⟩}_{\Delta u-\Delta d}=0.213(15)(22)$ and $⟨x{⟩}_{\delta u-\delta d}=0.208(19)(24)$, where the first error is the overall analysis uncertainty and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with other recent lattice calculations and phenomenological global fit values.

Comments: 18 pages, 8 figures. Final published version