Towards nucleon structure function moments and parton momentum fractions from lattice QCD

Abstract

We calculate the lowest even isovector moment of the $F_2$ structure function in $2+1$-flavour lattice QCD with varying quark masses corresponding to $m_{\pi }\approx [410,360,300]\mathrm{MeV}$, at a fixed volume of $V=48^3\times 96$ and coupling $\beta =5.65$ ($a=0.068(3)\mathrm{fm}$). We directly compute the physical Compton amplitude using the Feynman-Hellmann approach and extract moments of the physical structure function. We report on the quark-mass dependence of the lowest isovector moment and estimate its value at the physical quark-mass point with $\sim 10\%$ uncertainty at fixed $Q^2$. By analysing the $Q^2$ dependence of the moments at the $SU(3)$ symmetric point ($m_{\pi }\approx 410\mathrm{MeV}$), we separate the leading- and higher-twist contributions and estimate the parton momentum fraction, $⟨x{⟩}_{u-d}$, which agrees with existing results.

Comments: 14 pages, 4 figues. Contribution to the the XVIth Quark Confinement and the Hadron Spectrum Conference (QCHSC24) 19-24 August, 2024 Cairns Convention Centre, Cairns, Queensland, Australia