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 π = 135 MeV) with a single lattice spacing of 0.085 fm in 2+1 flavor QCD. Our calculations are carried out with two ensembles of gauge configurations generated by the PACS Collaboration with nonperturbatively O(a) improved Wilson quark action and Iwasaki gauge action on (10.9 fm) 4 and (5.5 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 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 (γµ) 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 MS scheme through matching procedure between the RI/SMOM (γµ) and MS schemes with the help of perturbation theory, and then obtain g S = 0.927(71) stat (22) syst and g T = 1.036( 6) stat (20) syst .G /2nG . The positivity of α requires the condition of 3w 2 G < 2n G in our parameter set.