Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks

Abstract

Traditionally, lattice QCD computations of generalized parton distributions (GPDs) have been carried out in a symmetric frame, where the transferred momentum is symmetrically distributed between the incoming and outgoing hadrons. However, such frames are inconvenient since they require a separate calculation for each value of the momentum transfer, increasing significantly the computational cost. In this work, by focusing on the quasi-distribution approach, we lay the foundation for faster and more effective lattice QCD calculations of GPDs exploiting asymmetric frames, with freedom in the transferred momentum distribution. An important ingredient of our approach is the Lorentz covariant parameterization of the matrix elements in terms of Lorentz-invariant amplitudes, which allows one to relate matrix elements in different frames. We also use this amplitude approach to propose a new definition of quasi-GPDs that is frame-independent and, more importantly, may lead to smaller power corrections in the matching relations to the light-cone GPDs. We demonstrate the efficacy of the formalism through numerical calculations using one ensemble of $N_f$=2+1+1 twisted mass fermions with a clover improvement. The value of the light-quark masses lead to a pion mass of about 260 MeV. Concentrating on the proton, and limiting ourselves to a vanishing longitudinal momentum transfer to the target, we extract the invariant amplitudes from matrix element calculations in both the symmetric and asymmetric frame, and obtain results for the twist-2 light-cone GPDs for unpolarized quarks, that is, $H$ and $E$.

39 pages, 19 figures, matches with published version

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• Towards Unpolarized GPDs from Pseudo-Distributions
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• Systematic Improvement of $x$-dependent Unpolarized Nucleon Generalized Parton Distribution in Lattice-QCD Calculation
• Moments of Axial-Vector GPD from Lattice QCD: Quark Helicity, Orbital Angular Momentum, and Spin-Orbit Correlation
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• Hadronic structure on the light-front VI. Generalized parton distributions of unpolarized hadrons
• Mapping Parton Distributions of Hadrons with Lattice QCD
• String-based axial and helicity-flip GPDs: a comparison to lattice QCD
• Nucleon Structure from Basis Light-Front Quantization : Status and Prospects
• Large-Momentum Effective Theory's Asymptotic Extrapolation vs the Inverse Problem
• Unified and optimal frame choice for generalized parton distributions
• Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Unpolarized Quarks at Nonzero Skewness