Complete definition of $N \rightarrow \Delta$ transition generalized parton distributions

TL;DR

This paper provides a comprehensive and corrected definition of the leading-twist chiral-even generalized parton distributions for nucleon to Delta transitions, addressing previous deficiencies and including new structures supported by multiple analyses.

Contribution

It systematically derives complete sets of independent structures for the transition GPDs, correcting previous definitions and including additional terms supported by multiple theoretical approaches.

Findings

Identified and corrected deficiencies in previous GPD definitions.

Derived complete sets of covariant structures for transition matrix elements.

Confirmed the new structures through light-front and partial-wave analyses.

Abstract

We revisit the definition of the leading-twist chiral-even generalized parton distributions (GPDs) for $N \to \Delta$ baryon transitions. We identify and address deficiencies in previous definitions of the transition GPDs inspired by the transition form factors of the vector and axial-vector currents. Through systematic analysis of all possible covariant structures, respecting discrete symmetries and the baryon spinor equations of motion, we derive complete sets of independent structures for the transition matrix elements of the vector and axial-vector partonic operators. They contain additional structures proportional to the light-cone vector, corresponding to transition GPDs of vanishing first moment, which were not included in previous parametrizations. Their presence is confirmed independently by the light-front multipole expansion and the cross-channel SO(3) partial-wave analysis of the transition matrix elements. Our analysis provides a complete definition of the $N \to \Delta$ transition GPDs for use in theoretical and phenomenological studies.