Toward an advanced phenomenology of $\pi N$ transition distribution amplitudes

TL;DR

This paper develops a flexible model for $ N$ transition distribution amplitudes, analyzing their impact on observables in exclusive pion production processes and emphasizing the need for future experimental constraints.

Contribution

It introduces a novel, adaptable modeling approach for $ N$ TDAs that aligns with theoretical constraints and explores their influence on measurable asymmetries.

Findings

Model sensitivity to different assumptions analyzed

Predictions for unpolarized and polarized cross-sections provided

Guidance for future experiments in backward kinematics offered

Abstract

We introduce a new approach to modeling transition distribution amplitudes (TDAs) for the processes $e p \to e n \pi^+$ and $e p \to e p \pi^0$. The modeling is flexible, constrained by sparsely available experimental data, and satisfies theoretical requirements, including reduction to nucleon distribution amplitudes in the appropriate limit. We study the sensitivity of observable predictions to various modeling assumptions. We discuss unpolarized cross-sections, as well as the three non-vanishing polarization observables at leading twist, namely, the single transverse target spin asymmetry and the two double spin asymmetries that occur with a polarized lepton beam on either a longitudinally or transversely polarized target. The analysis is complemented by a simple Monte Carlo study to provide guidance for exploring exclusive processes in the so-called backward kinematics. Our work aims to highlight the importance of future measurements to better constrain TDAs and to support upcoming experimental proposals.