Generalized Parton Distributions from Lattice QCD with Asymmetric Momentum Transfer: Axial-vector case

TL;DR

This paper advances lattice QCD calculations of GPDs by using asymmetric frames and Lorentz covariant parameterizations, enabling more efficient and frame-independent computation of axial-vector GPDs with reduced corrections.

Contribution

It introduces a Lorentz covariant parameterization for axial-vector matrix elements and applies it to compute the axial-vector GPD $ ilde{H}$ in asymmetric frames, improving computational efficiency and frame independence.

Findings

Successful computation of axial-vector GPD $ ilde{H}$ at zero skewness.

Implementation of asymmetric frames for lattice QCD calculations.

Potential reduction of power corrections in GPD matching procedures.

Abstract

Recently, we made significant advancements in improving the computational efficiency of lattice QCD calculations for Generalized Parton Distributions (GPDs). This progress was achieved by adopting calculations of matrix elements in asymmetric frames, deviating from the computationally-expensive symmetric frame typically used, and allowing freedom in the choice for the distribution of the momentum transfer between the initial and final states. A crucial aspect of this approach involves the adoption of a Lorentz covariant parameterization for the matrix elements, introducing Lorentz-invariant amplitudes. This approach also allows us to propose an alternative definition of quasi-GPDs, ensuring frame independence and potentially reduce power corrections in matching to light-cone GPDs. In our previous work, we presented lattice QCD results for twist-2 unpolarized GPDs ($H$ and $E$) of quarks obtained from calculations performed in asymmetric frames at zero skewness. Building upon this work, we now introduce a novel Lorentz covariant parameterization for the axial-vector matrix elements. We employ this parameterization to compute the axial-vector GPD $\widetilde{H}$ at zero skewness, using an $N_f=2+1+1$ ensemble of twisted mass fermions with clover improvement. The light-quark masses employed in our calculations correspond to a pion mass of approximately 260 MeV.