Abstract
We present results from a lattice QCD study of nucleon matrix elements at vanishing 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 $M_\pi\approx200$MeV. Several source-sink separations (typically ~1.0fm to ~1.5fm) 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. Renormalization has been performed non-perturbatively using the Rome-Southampton method for all but the finest lattice spacing for which an extrapolation has been used. Physical results are quoted in the $\overline{MS}$ scheme at a scale of $\mu=2$GeV and 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 $g_A^{u-d}=1.242(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+00}{-31})_\text{sys}$, $g_S^{u-d}=1.13(11)_\text{stat}(\genfrac{}{}{0pt}{2}{+07}{-06})_\text{sys}$ and $g_T^{u-d}=0.965(38)_\text{stat}(\genfrac{}{}{0pt}{2}{+13}{-41})_\text{sys}$, 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 $\langle x\rangle_{u-d}=0.180(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+14}{-06})_\text{sys}$, $\langle x\rangle_{\Delta u-\Delta d}=0.221(25)_\text{stat}(\genfrac{}{}{0pt}{2}{+10}{-00})_\text{sys}$ and $\langle x\rangle_{\delta u-\delta d}=0.212(32)_\text{stat}(\genfrac{}{}{0pt}{2}{+20}{-10})_\text{sys}$, respectively.
Highlights
Nucleon matrix elements carry information on the internal structure and properties of nucleons, which can be related to a large variety of physical processes
For the nucleon isovector axial, scalar, and tensor charges we find physical values of guA−d 1⁄4 1.242ð25Þstatðþ−3010Þsys, gSu−d 1⁄4 1.13ð11Þstatðþ−0067Þsys and gTu−d 1⁄4 0.965ð38Þstatðþ−4113Þsys, respectively, where individual systematic errors in each direction from the chiral, continuum, and finite-size extrapolation have been added in quadrature
II we present the setup for our lattice calculations, including an overview of the ensembles, operators and matrix elements, technical details on the calculation of two-point and three-point functions, as well as a discussion of the renormalization required to obtain physical results
Summary
Nucleon matrix elements carry information on the internal structure and properties of nucleons, which can be related to a large variety of physical processes. The scalar and tensor charges, which can contribute to the β decay of the nucleon through nonstandard couplings outside the Standard Model (SM) [19] and are important for interpreting the results of dark matter searches [20], are much less well determined from phenomenology In this case lattice QCD can provide crucial input to searches for beyond the Standard Model (BSM) physics. For twist-2 operator insertions, as required for, e.g., the isovector average quark momentum fraction and the second moments of helicity and transversity PDFs, again lattice QCD can be used to compute the relevant matrix elements, which are typically less well determined than the ones related to local operators. We present physical results for the isovector axial, scalar, and tensor charge of the nucleon, its average quark momentum fraction, and the isovector moments for the helicity and transversity PDFs from isovector twist-2 operator insertions. Additional technical details related to renormalization have been moved to an Appendix
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