Moments of axial-vector GPD from lattice QCD: quark helicity, orbital angular momentum, and spin-orbit correlation - Shohini Bhattacharya; Krzysztof Cichy; Martha Constantinou; Xiang Gao; Andreas Metz; Joshua Miller; Swagato Mukherjee; Peter Petreczky; Fernanda Steffens; Yong Zhao (Journal of High Energy Physics)
Abstract In this work, we present a lattice QCD calculation of the Mellin moments of the twist-2 axial-vector generalized parton distribution (GPD), H ~ x ξ t $$ \overset{\sim }{H}\left(x,ξ, t\right) $$ , at zero skewness, ξ, with multiple values of the momentum transfer, t. Our analysis employs the short-distance factorization framework on ratio-scheme renormalized quasi-GPD matrix elements. The calculations are based on an N f = 2 + 1 + 1 twisted mass fermions ensemble with clover improvement, a lattice spacing of a = 0.093 fm, and a pion mass of m π = 260 MeV. We consider both the iso-vector and iso-scalar cases, utilizing next-to-leading-order perturbative matching while omitting the disconnected contributions and gluon mixing in the iso-scalar case. For the first time, we determine the Mellin moments of H ~ $$ \overset{\sim }{H} $$ up to the fifth order. From these moments, we discuss the quark helicity and orbital angular momentum contributions to the nucleon spin, as well as the spin-orbit correlations of the quarks. Additionally, we perform a Fourier transform over the momentum transfer, which allows us to explore the spin structure in the impact-parameter space.