Nucleon momentum fraction, helicity and transversity from 2+1-flavor lattice QCD

A detailed analysis of the systematic uncertainties in the calculation of the isovector momentum fraction, 〈 x 〉 u − d , helicity moment, 〈 x 〉 Δ u − Δ d , and the transversity moment, 〈 x 〉 δu − δd , of the nucleon is presented using high-statistics data on seven ensembles of gauge configurations generated by the JLab/W M/LANL/MIT collaborations using 2 + 1-flavors of dynamical Wilson-clover quarks. The much higher statistics have facilitated better control over all systematics compared to previous lattice calculations. The least understood systematic — excited-state contamination — is quantified by studying the variation of the results as a function of different estimates of the mass gap of the first excited state, obtained from two- and three-point correlation functions, and as a function of the pion mass M π . The final results are obtained using a simultaneous fit in the lattice spacing a , pion mass M π and the finite volume parameter M π L keeping leading order corrections. The data show no significant dependence on the lattice spacing and some evidence for finite-volume corrections. Our final results, in the MS scheme at 2 GeV, are 〈 x 〉 u − d = 0 . 155(17)(20), 〈 x 〉 Δ u − Δ d = 0 . 183(14)(20) and 〈 x 〉 δu − δd = 0 . 220(18)(20), where the first error is the overall analysis uncertainty assuming excited-state contributions have been removed, and the second is an additional systematic uncertainty due to possible residual excited-state contributions. These results are consistent with phenomenological global fit values.