Generalized parton correlation functions for a spin-1/2 hadron

TL;DR

This work extends the GPCF framework to spin-1/2 hadrons, establishing a complete parameterization of the fully unintegrated, off-diagonal quark-quark correlator and showing how GTMDs universally act as mother distributions for GPDs and TMDs. It provides a comprehensive twist-by-twist classification of GTMDs and derives explicit connections to GPDs and TMDs through well-defined projections, while demonstrating that model-independent nontrivial GPD–TMD relations do not exist. The analysis uses symmetry constraints (parity, hermiticity, time-reversal) and explores both general properties and a scalar diquark model to illustrate the vanishing of T-odd GTMDs at leading order. The results clarify the limits of model-dependent relations and offer a robust framework for interpreting two-parton structure in hard exclusive and semi-inclusive processes.

Abstract

The fully unintegrated, off-diagonal quark-quark correlator for a spin-1/2 hadron is parameterized in terms of so-called generalized parton correlation functions. Such objects, in particular, can be considered as mother distributions of generalized parton distributions on the one hand and transverse momentum dependent parton distributions on the other. Therefore, our study provides new, model-independent insights into the recently proposed nontrivial relations between generalized and transverse momentum dependent parton distributions. We find that none of these relations can be promoted to a model-independent status. As a by-product we obtain the first complete classification of generalized parton distributions beyond leading twist. The present paper is a natural extension of our previous corresponding analysis for spin-0 hadrons.