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Generalized parton distributions with helicity flip

M. Diehl

TL;DR

The paper classifies helicity-flip generalized parton distributions (GPDs) for a spin-1/2 target, showing that there are eight independent twist-2 GPDs in total: four for quarks ($H_T^q$, $\tilde{H}_T^q$, $E_T^q$, $\tilde{E}_T^q$) and four for gluons ($H_T^g$, $\tilde{H}_T^g$, $E_T^g$, $\tilde{E}_T^g$). It provides a helicity-based representation, clarifies the symmetry constraints from parity and time reversal (and why time reversal does not reduce the count in general, contrary to previous claims), and demonstrates that gluon helicity-flip distributions do not mix with quark distributions under evolution. The work also connects these distributions to deeply virtual Compton scattering, showing that gluon helicity-flip GPDs contribute to photon-helicity-flip amplitudes at leading order in $\alpha_s$ and could be accessed via angular observables such as a $\cos 3\varphi$ modulation. Overall, this establishes a richer spin structure in GPDs and highlights a potential new window into gluon dynamics in the nucleon.

Abstract

We show that for both quarks and gluons there are eight generalized parton distributions in the proton: four which conserve parton helicity and four which do not. We explain why time reversal invariance does not reduce this number from eight to six, as previously assumed in the literature.

Generalized parton distributions with helicity flip

TL;DR

The paper classifies helicity-flip generalized parton distributions (GPDs) for a spin-1/2 target, showing that there are eight independent twist-2 GPDs in total: four for quarks (, , , ) and four for gluons (, , , ). It provides a helicity-based representation, clarifies the symmetry constraints from parity and time reversal (and why time reversal does not reduce the count in general, contrary to previous claims), and demonstrates that gluon helicity-flip distributions do not mix with quark distributions under evolution. The work also connects these distributions to deeply virtual Compton scattering, showing that gluon helicity-flip GPDs contribute to photon-helicity-flip amplitudes at leading order in and could be accessed via angular observables such as a modulation. Overall, this establishes a richer spin structure in GPDs and highlights a potential new window into gluon dynamics in the nucleon.

Abstract

We show that for both quarks and gluons there are eight generalized parton distributions in the proton: four which conserve parton helicity and four which do not. We explain why time reversal invariance does not reduce this number from eight to six, as previously assumed in the literature.

Paper Structure

This paper contains 6 sections, 39 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Quark helicity flip distributions
  3. Helicity representation
  4. Gluon helicity flip distributions
  5. Compton scattering
  6. Summary

Figures (2)

  • Figure 1: Representation of a generalized parton distribution in the region $\xi<x<1$. The flow of plus-momentum is indicated by arrows, and the labels $\lambda$, $\lambda'$, $\mu$, $\mu'$ denote helicities. (a) shows the ordering of lines as "proton in, quark out, quark back in, proton out" that is common for parton distributions. (b) displays the order "proton in, quark in, quark out, proton out" appropriate for a scattering amplitude.
  • Figure 2: A Feynman diagram for the photon helicity flip amplitude in deeply virtual Compton scattering. The remaining diagrams are obtained by appropriate permutations of the photon and gluon lines. Greek letters label helicities, and the relevant combinations are $(\mu',\mu) = (1,-1)$ and $(\mu',\mu) = (-1,1)$.