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 >(Delta u-Delta d), and the transversity moment, < x >(delta u-delta d), 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. The final results are obtained using a simultaneous fit in the lattice spacing a, pion mass M-pi and the finite volume parameter M pi 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) over bar scheme at 2 GeV, are < x >(u-d) = 0.155(17)(20), < x >(Delta u-Delta d) = 0.183(14)(20) and < x >(delta u-delta d) = 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.