A consistent model for \pi N transition distribution amplitudes and backward pion electroproduction

TL;DR

This paper develops a comprehensive model for  N transition distribution amplitudes (TDAs), applying it to backward pion electroproduction to improve understanding of nucleon-to-meson transitions in QCD.

Contribution

It introduces a spectral representation framework for  N TDAs using quadruple distributions and a factorized Ansatz, incorporating the soft-pion theorem and nucleon exchange contributions.

Findings

Updated estimates of unpolarized cross sections in backward pion electroproduction.

Predicted sizable transverse target single spin asymmetry in the valence region.

Model sensitivity to phenomenological inputs of  N TDAs.

Abstract

The extension of the concept of generalized parton distributions leads to the introduction of baryon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of the nonlocal three quark operator between a nucleon and a meson state. We present a general framework for modelling nucleon to pion ($\pi N$) TDAs. Our main tool is the spectral representation for \pi N TDAs in terms of quadruple distributions. We propose a factorized Ansatz for quadruple distributions with input from the soft-pion theorem for \pi N TDAs. The spectral representation is complemented with a D-term like contribution from the nucleon exchange in the cross channel. We then study backward pion electroproduction in the QCD collinear factorization approach in which the non-perturbative part of the amplitude involves \pi N TDAs. Within our two component model for \pi N TDAs we update previous leading-twist estimates of the unpolarized cross section. Finally, we compute the transverse target single spin asymmetry as a function of skewness. We find it to be sizable in the valence region and sensitive to the phenomenological input of our \pi N TDA model.