High statistics results for the isovector momentum fraction, $langle x rangle_{u-d}$, helicity moment, $langle x rangle_{Delta u-Delta d}$, and the transversity moment, $langle xrangle_{delta u-delta d}$, 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 $overline{rm MS}$ scheme at 2 GeV, are $langle x rangle_{u-d} = 0.160(16)(20)$, $langle x rangle_{Delta u-Delta d} = 0.192(13)(20)$ and $langle x rangle_{delta u-delta d} = 0.215(17)(20)$, 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.
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