Moments of axial-vector GPD from lattice QCD: quark helicity, orbital angular momentum, and spin-orbit correlation

A bstract In this work, we present a lattice QCD calculation of the Mellin moments of the twist-2 axial-vector generalized parton distribution (GPD), $$ \overset{\sim }{H}\left(x,\xi, t\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>~</mml:mo> </mml:mover> <mml:mfenced> <mml:mi>x</mml:mi> <mml:mi>ξ</mml:mi> <mml:mi>t</mml:mi> </mml:mfenced> </mml:math> , 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 $$ \overset{\sim }{H} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mover> <mml:mi>H</mml:mi> <mml:mo>~</mml:mo> </mml:mover> </mml:math> 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.