Accessing proton GPDs in asymmetric frames: Numerical implementation

TL;DR

This paper introduces a numerical method using an asymmetric frame to efficiently extract proton GPDs across multiple momentum transfers from a single calculation, reducing computational costs.

Contribution

The novel Lorentz-covariant parametrization and asymmetric frame approach enable simultaneous GPD extraction at various momentum transfers, improving efficiency over traditional symmetric frame methods.

Findings

Successfully implemented the method on a twisted mass fermion ensemble.

Able to extract GPDs at multiple momentum transfers from one calculation.

Demonstrated feasibility with a proton unpolarized GPDs calculation.

Abstract

In this work, we present a numerical investigation of a novel Lorentz-covariant parametrization to extract $x$-dependent GPDs using off-forward matrix elements of momentum-boosted hadrons coupled to non-local operators. The novelty of the method is the implementation of an asymmetric frame for the momentum transfer between the initial and final hadron state and the parametrization of the matrix elements into Lorentz-invariant amplitudes. The amplitudes can then be related to the standard light-cone GPDs. GPDs are defined in the symmetric frame, which requires a separate calculation for each value of the momentum transfer, increasing the computational cost significantly. The proposed method is powerful, as one can extract the GPDs at multiple values of the momentum transfer at the computational cost of a single value. For this proof-of-concept calculation, we use one ensemble of $N_f=2+1+1$ twisted mass fermions and a clover improvement with a pion mass of 260 MeV to calculate the proton unpolarized GPDs.