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

We present results for the nucleon structure functions and form factors obtained from 2+1 flavor lattice QCD with physical light quark masses ($m_π=135$ 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 ${\mathscr{O}}(a)$ improved Wilson-clover quark action and Iwasaki gauge action at $β=1.82$ and $2.00$ corresponding to lattice spacings of $0.085$ fm and $0.064$ fm respectively. The lower moments of structure functions, $\langle x \rangle_{u-d}$ and $\langle x \rangle_{Δu - Δd}$ given by the twist-2 operators being properly renormalized, are evaluated in the $\overline{\rm MS}$ scheme at the renormalization scale of 2 GeV only at $β=1.82$, since the renormalization factors at $β=2.00$ 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 $\langle x \rangle_{u-d}/\langle x \rangle_{Δu -Δd}$, which are not renormalized in the continuum limit. These quantities thus can be directly compared with the experimental data without the renormalization.