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Perturbative results for the matrix elements of the vector current and the role of different infrared regulators

Alessio Carmelo Alvaro, Ignacio Castelli, Cédric Lorcé, Andreas Metz, Barbara Pasquini, Simone Rodini

TL;DR

This work analyzes twist-2 unpolarized quark GPDs for a gluon target in QCD, using two infrared regulators—the quark mass and dimensional regularization—to study the forward limit and off-forward contributions of the nonlocal vector current. The matrix elements decompose into two GPDs, $H_1^q$ (helicity-conserving) and $H_2^q$ (helicity-flip), with angular-momentum conservation forcing $H_2^q \to 0$ in the forward limit while $H_1^q \to f_1^q$. The authors present one-loop results with a nonzero quark mass and with dimensional regularization, showing that a well-defined forward limit requires an IR regulator beyond $\Delta^2$, and demonstrating consistency with forward kinematics and prior axial-current results. The analysis reinforces the expected IR-regulator dependence of the forward limit, connects to known quark-gluon evolution kernels, and has implications for DVCS and related processes where gluon helicity flips play a role.

Abstract

We investigate the twist-2 unpolarized generalized parton distributions (GPDs) of quarks for an on-shell gluon target in quantum chromodynamics. These GPDs parametrize the leading-twist matrix elements of the nonlocal light-like flavor-singlet vector current. We compute them at one-loop accuracy in perturbation theory using a quark mass and dimensional regularization as infrared regulators. In particular, we discuss the limit of vanishing momentum transfer. The present work extends our previous related study on the axial current.

Perturbative results for the matrix elements of the vector current and the role of different infrared regulators

TL;DR

This work analyzes twist-2 unpolarized quark GPDs for a gluon target in QCD, using two infrared regulators—the quark mass and dimensional regularization—to study the forward limit and off-forward contributions of the nonlocal vector current. The matrix elements decompose into two GPDs, (helicity-conserving) and (helicity-flip), with angular-momentum conservation forcing in the forward limit while . The authors present one-loop results with a nonzero quark mass and with dimensional regularization, showing that a well-defined forward limit requires an IR regulator beyond , and demonstrating consistency with forward kinematics and prior axial-current results. The analysis reinforces the expected IR-regulator dependence of the forward limit, connects to known quark-gluon evolution kernels, and has implications for DVCS and related processes where gluon helicity flips play a role.

Abstract

We investigate the twist-2 unpolarized generalized parton distributions (GPDs) of quarks for an on-shell gluon target in quantum chromodynamics. These GPDs parametrize the leading-twist matrix elements of the nonlocal light-like flavor-singlet vector current. We compute them at one-loop accuracy in perturbation theory using a quark mass and dimensional regularization as infrared regulators. In particular, we discuss the limit of vanishing momentum transfer. The present work extends our previous related study on the axial current.
Paper Structure (6 sections, 27 equations, 1 figure)

This paper contains 6 sections, 27 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Unpolarized parton distributions
  3. One-loop results with a massive quark
  4. One-loop results in dimensional regularization
  5. Conclusions
  6. One-loop results for a massive quark in $n$ dimensions

Figures (1)

  • Figure 1: Lowest-order diagram contributing to the PDF in the positive-$x$ region and to the GPDs in the positive DGLAP region ($\xi\!\le\! x\!\le\! 1$) and the ERBL region ($-\,\xi \!<\! x \!< \!\xi$). A second diagram with reversed arrows is not shown. It contributes to the negative-$x$ region of the PDF and to the ERBL and negative DGLAP regions for the GPDs.