Nucleon Momentum Fraction, Helicity and Transversity from 2+1-flavor Lattice QCD

Abstract

High statistics results for 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 are presented using seven ensembles of gauge configurations generated by the JLab/W&M/LANL/MIT collaborations using $2+1$-flavors of dynamical Wilson-clover quarks. Attention is given to understanding and controlling the contributions of excited states. 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. The main variation is with $M_{\pi }$, whose magnitude depends on the mass gap of the first excited state used in the analysis. Our final results, in the $\overline{\mathrm{MS}}$ scheme at 2 GeV, are $⟨x{⟩}_{u-d}=0.160(16)(20)$, $⟨x{⟩}_{\Delta u-\Delta d}=0.192(13)(20)$ and $⟨x{⟩}_{\delta u-\delta d}=0.215(17)(20)$, 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 other recent lattice calculations and phenomenological global fit values.

Comments: 28 pages, 11 figures, 12 tables. arXiv admin note: text overlap with arXiv:2005.13779