\pi N transition distribution amplitudes: Their symmetries and constraints from chiral dynamics

TL;DR

This paper explores the symmetries and constraints of  transition distribution amplitudes (TDAs) for baryon-to-meson transitions, deriving their properties from QCD symmetries and modeling them with resonance exchanges.

Contribution

It provides a comprehensive analysis of   TDAs, establishing their symmetry properties, deriving soft pion theorems, and proposing a resonance exchange model.

Findings

Identified eight independent    TDAs based on symmetry constraints.

Derived soft pion theorems linking   TDAs to chiral symmetry.

Constructed a resonance exchange model including N and elta(1232) contributions.

Abstract

Baryon to meson transition distribution amplitudes (TDAs) extend the concept of generalized parton distributions. Baryon to meson TDAs appear as building blocks in the collinear factorized description of amplitudes for a class of hard exclusive reactions, prominent examples of which being hard exclusive meson electroproduction off a nucleon in the backward region and baryon-antibaryon annihilation into a meson and a lepton pair. We study the general properties of these objects following from the underlying symmetries of QCD. In particular, the Lorentz symmetry results in the polynomiality property of the Mellin moments in longitudinal momentum fractions. We present a detailed account of the isotopic and permutation symmetry properties of nucleon to pion (\pi N) TDAs. This restricts the number of independent leading twist \pi N TDAs to eight functions, providing description of all isotopic channels. Using chiral symmetry and the crossing relation between \pi N TDAs and \pi N generalized distribution amplitudes we establish soft pion theorems for \pi N TDAs, which determine the magnitude of \pi N TDAs. Finally, we build a simple resonance exchange model for \pi N TDAs considering N and \Delta(1232) exchange contributions into the isospin-1/2 and isospin-3/2 \pi N TDAs.