Nucleon isovector charges and twist-2 matrix elements with $N_f=2+1$ dynamical Wilson quarks

We present results from a lattice QCD study of nucleon matrix elements at zero momentum transfer for local and twist-2 isovector operator insertions. Computations are performed on gauge ensembles with non-perturbatively improved $N_f=2+1$ Wilson fermions, covering four values of the lattice spacing and pion masses down to $M_\pi \approx 200\,\mathrm{MeV}$. Several source-sink separations (typically $\sim 1.0\,\mathrm{fm}$ to $\sim 1.5\,\mathrm{fm}$) allow us to assess excited-state contamination. Results on individual ensembles are obtained from simultaneous two-state fits across all observables and all available source-sink separations with the energy gap as a common fit parameter. Physical results are obtained from a combined chiral, continuum and finite-size extrapolation. For the nucleon isovector axial, scalar and tensor charges we find physical values of $g_A^{u-d} = 1.242(25)_\mathrm{stat}(\genfrac{}{}{0pt}{2}{+00}{-31})_\mathrm{sys}$, $g_S^{u-d} = 1.13 (11)_\mathrm{stat}(\genfrac{}{}{0pt}{2}{+07}{-06})_\mathrm{sys}$ and $g_T^{u-d} = 0.965(38)_\mathrm{stat}(\genfrac{}{}{0pt}{2}{+13}{-41})_\mathrm{sys}$, respectively, where individual systematic errors in each direction from the chiral, continuum and finite-size extrapolation have been added in quadrature. Our final results for the isovector average quark momentum fraction and the isovector helicity and transversity moments are given by $\langle x\rangle_{u-d} = 0.180(25)_\mathrm{stat}(\genfrac{}{}{0pt}{2}{+14}{-06})_\mathrm{sys}$, $\langle x\rangle_{\Delta u-\Delta d} = 0.221(25)_\mathrm{stat}(\genfrac{}{}{0pt}{2}{+10}{-00})_\mathrm{sys}$ and $\langle x\rangle_{\delta u-\delta d} = 0.212(32)_\mathrm{stat}(\genfrac{}{}{0pt}{2}{+16}{-10})_\mathrm{sys}$, respectively.