Generalized parton correlation functions for a spin-0 hadron

TL;DR

The paper develops a comprehensive framework for the two-parton structure of a spin-0 hadron by introducing generalized parton correlation functions (GPCFs) as the most general fully unintegrated quark–quark correlators. These GPCFs yield generalized transverse momentum dependent distributions (GTMDs) upon light-cone projections and, in limit cases, reduce to GPDs and TMDs, establishing GPCFs and GTMDs as the mother distributions for these objects. A complete classification of GPDs beyond leading twist is achieved, and the work analyzes model-independent relations between GPDs and TMDs, finding only three trivial, non-contradicted relations and arguing that nontrivial relations are generally model-dependent. The study provides insights into the role of Wilson lines, the complex nature of GTMDs, and lays groundwork for future explorations of nucleon targets and gluon GTMDs in hard exclusive processes.

Abstract

The fully unintegrated, off-diagonal quark-quark correlator for a spin-0 hadron is parameterized in terms of so-called generalized parton correlation functions. Such objects are of relevance for the phenomenology of certain hard exclusive reactions. In particular, they can be considered as {\it 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. As a by-product we obtain the first complete classification of generalized parton distributions beyond leading twist.