Nucleon isovector couplings in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>f</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math> 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 (${M}_{\ensuremath{\pi}}=135\text{ }\text{ }\mathrm{MeV}$) 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 $\mathcal{O}(a)$ improved Wilson quark action and Iwasaki gauge action on $(10.9\text{ }\text{ }\mathrm{fm}{)}^{4}$ and $(5.5\text{ }\text{ }\mathrm{fm}{)}^{4}$ lattices, where the finite-size effect on the nucleon mass was not shown at the level of 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 $(10.9\text{ }\text{ }\mathrm{fm}{)}^{4}$ 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 $\mathrm{RI}/{\mathrm{SMOM}}_{({\ensuremath{\gamma}}_{\ensuremath{\mu}})}$ 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 the matching procedure between the $\mathrm{RI}/{\mathrm{SMOM}}_{({\ensuremath{\gamma}}_{\ensuremath{\mu}})}$ and $\overline{\mathrm{MS}}$ schemes with the help of perturbation theory, and then obtain ${g}_{S}=0.927(83{)}_{\mathrm{stat}}(22{)}_{\mathrm{syst}}$ and ${g}_{T}=1.036(6{)}_{\mathrm{stat}}(20{)}_{\mathrm{syst}}$.

Topics & Concepts