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 ${ \cal O}(a)$ improved Wilson quark action and Iwasaki gauge action on $(10.9\ { \rm fm})^4$ and $(5.5\ { \rm fm})^4$ 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 $(10.9\ { \rm fm})^4$ 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 $\overline{ \rm MS}$ scheme through matching procedure between the RI/SMOM$_{ (\gamma_\mu)}$ and $\overline{ \rm MS}$ schemes with the help of perturbation theory, and then obtain $g_S=0.927(71)_{ \rm stat}(22)_{ \rm syst}$ and $g_T=1.036(6)_{ \rm stat}(20)_{ \rm syst}$.
Categories: hep-lat