Nucleon isovector couplings in Nf = 2 + 1 lattice QCD at the physical point

Abstract

We present results for the scalar and tensor isovector-couplings ($g_S$ and $g_T$) of the nucleon measured at the physical point ($M_{\pi }=135$ MeV) with a single lattice spacing of $0.085\mathrm{fm}$ in 2+1 flavor QCD. Our calculations are carried out with two ensembles of gauge configurations generated by the PACS Collaboration with nonperturbatively $\mathcal{O}(a)$ improved Wilson quark action and Iwasaki gauge action on $(10.9\mathrm{fm}{)}^4$ and $(5.5\mathrm{fm}{)}^4$ lattices, where the finite-size effect on the nucleon mass was not shown at the level of the statistical precision less than 0.5%. We compute the nucleon three-point correlation functions in the vector, axial, scalar, and tensor channels. We confirm that our previous result of the nucleon axial coupling on the large spatial volume of $(10.9\mathrm{fm}{)}^4$ has no finite-size effect at the level of the statistical precision of 1.9%. For the renormalization, we first renormalize $g_S$ and $g_T$ nonperturbatively using the RI/SMOM${}_{({\gamma }_{\mu })}$ scheme, a variant of Rome-Southampton RI/MOM scheme with reduced systematic errors, as the intermediate scheme. We evaluate our final results at the renormalization scale of 2 GeV in the $\overline{\mathrm{MS}}$ scheme through matching procedure between the RI/SMOM${}_{({\gamma }_{\mu })}$ and $\overline{\mathrm{MS}}$ schemes with the help of perturbation theory, and then obtain $g_S=0.927(71{)}_{\mathrm{stat}}(22{)}_{\mathrm{syst}}$ and $g_T=1.036(6{)}_{\mathrm{stat}}(20{)}_{\mathrm{syst}}$.

arXiv comment52 pages, 11 figures

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