The lower moments of nucleon structure functions in lattice QCD with physical quark masses

Abstract

We present results for the nucleon structure functions and form factors obtained from 2+1 flavor lattice QCD with physical light quark masses ($m_{\pi }=135$ MeV) in a large spatial extent of about 10 fm. Our calculations are performed with the PACS10 gauge configurations generated by the PACS Collaboration with the six stout-smeared $\mathcal{O}(a)$ improved Wilson-clover quark action and Iwasaki gauge action at $\beta =1.82$ and $2.00$ corresponding to lattice spacings of $0.085$ fm and $0.064$ fm respectively. The lower moments of structure functions, $⟨x{⟩}_{u-d}$ and $⟨x{⟩}_{\Delta u-\Delta d}$ given by the twist-2 operators being properly renormalized, are evaluated in the $\overline{\mathrm{MS}}$ scheme at the renormalization scale of 2 GeV only at $\beta =1.82$, since the renormalization factors at $\beta =2.00$ have not yet determined nonperturbatively in the RI/MOM scheme. Instead, at two lattice spacings, we evaluate appropriate ratios of $g_A/g_V$ and $⟨x{⟩}_{u-d}/⟨x{⟩}_{\Delta u-\Delta d}$, which are not renormalized in the continuum limit. These quantities thus can be directly compared with the experimental data without the renormalization.

Comments: 9 pages, 4 figures, , talk presented at the 38th International Symposium on Lattice Field Theory (Lattice 2021), 26-30 July, 2021, Zoom/Gather@Massachusetts Institute of Technology