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<p>In this work, we present a lattice QCD calculation of the Mellin moments of the twist-2 axial-vector generalized parton distribution (GPD), <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>H</mi> <mo stretchy="true">~</mo> </mover> <mfenced close=")" open="(" separators=",,"> <mi>x</mi> <mi>ξ</mi> <mi>t</mi> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \overset{\sim }{H}\left(x,\xi, t\right) \)</EquationSource> </InlineEquation>, at zero skewness, <i>ξ</i>, with multiple values of the momentum transfer, <i>t</i>. Our analysis employs the short-distance factorization framework on ratio-scheme renormalized quasi-GPD matrix elements. The calculations are based on an <i>N</i><sub><i>f</i></sub> = 2 + 1 + 1 twisted mass fermions ensemble with clover improvement, a lattice spacing of <i>a</i> = 0<i>.</i>093 fm, and a pion mass of <i>m</i><sub><i>π</i></sub> = 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 <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mover accent="true"> <mi>H</mi> <mo stretchy="true">~</mo> </mover> </math></EquationSource> <EquationSource Format="TEX">\( \overset{\sim }{H} \)</EquationSource> </InlineEquation> 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.</p>

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

  • 期刊论文

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  • 发表日期：

    2025年1月28日

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  • Shohini Bhattacharya,
  • Krzysztof Cichy,
  • Martha Constantinou,
  • Xiang Gao,
  • Andreas Metz,
  • Joshua Miller,
  • Swagato Mukherjee,
  • Peter Petreczky,
  • Fernanda Steffens,
  • Yong Zhao

摘要

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 \( \overset{\sim }{H}\left(x,\xi, t\right) \) , 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 Nf = 2 + 1 + 1 twisted mass fermions ensemble with clover improvement, a lattice spacing of a = 0.093 fm, and a pion mass of mπ = 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.