Generalized transverse momentum dependent parton distributions of the nucleon

TL;DR

This paper formulates the most general quark-quark correlator for the nucleon (GTMDs) and shows how GTMDs subsume GPDs and TMDs as limiting cases. It provides a complete all-twist parameterization of nucleon GTMDs, and from this, the full all-twist parameterizations of GPDs and TMDs, detailing parity, hermiticity, and time-reversal constraints. The authors derive explicit expressions linking GPDs (H,E) and TMDs (f1,f1T^⊥) to GTMD components, and demonstrate that there are 64 GTMDs split into T-even and T-odd parts, with 32 real functions surviving in the GPD/TMD limits. By comparing the mother distributions, they establish that no general, model-independent GPD–TMD relations exist, since proposed relations cannot hold universally due to different underlying GTMD structures.

Abstract

We present first results from our analysis of the most general quark-quark correlator of the nucleon, which can be parameterized in terms of so-called generalized transverse momentum dependent parton distributions. These results include the first complete parameterization of the nucleon GPDs and TMDs to all twists as well as new results on possible nontrivial relations between them.