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Generalized parton distributions from lattice QCD with asymmetric momentum transfer: Tensor case

Shohini Bhattacharya1,2,*, Krzysztof Cichy3, Martha Constantinou4,†, Andreas Metz4, Joshua Miller4,‡, Peter Petreczky5, and Fernanda Steffens6

  • *Contact author: shohinib@uconn.edu
  • †Contact author: marthac@temple.edu
  • ‡Contact author: joshua.miller0007@temple.edu
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Phys. Rev. D 112, 114504 – Published 4 December, 2025

DOI: https://doi.org/10.1103/tlkb-ykgp

Abstract

The calculation of generalized parton distributions (GPDs) in lattice QCD was traditionally done by calculating matrix elements in the symmetric frame. Recent advancements have significantly reduced computational costs by calculating these matrix elements in the asymmetric frame, allowing us to choose the momentum transfer to be in either the initial or final states only. The theoretical methodology requires a new parametrization of the matrix element to obtain Lorentz-invariant amplitudes, which are then related to the GPDs. The formulation and implementation of this approach have already been established for the unpolarized and helicity GPDs. Building upon this idea, we extend this formulation to the four leading-twist quark transversity GPDs (HT, ET, H˜T, E˜T). We also present numerical results for zero skewness using an Nf=2+1+1 ensemble of twisted mass fermions with a clover improvement. The light quark masses employed in these calculations correspond to a pion mass of about 260 MeV. Furthermore, we include a comparison between the symmetric and asymmetric frame calculations to demonstrate frame independence of the Lorentz-invariant amplitudes. Analysis of the matrix elements in the asymmetric frame is performed at several values of the momentum transfer squared, −t, ranging from 0.17 to 2.29  GeV2.

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Phys. Rev. D 112, 114504– Published 4 December, 2025
  • Received 31 May 2025
  • Accepted 10 November 2025
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