Invariant Amplitudes for Pion Electroproduction

TL;DR

This paper evaluates invariant amplitudes for pion electroproduction using dispersion relations, compares them with low-energy theorems, and finds significant corrections due to finite pion mass, aligning with Chiral Perturbation Theory.

Contribution

It introduces a dispersive approach to compute invariant amplitudes for pion electroproduction and compares results with low-energy theorems and Chiral Perturbation Theory.

Findings

Large corrections to low-energy theorems due to finite pion mass

Dispersive approach agrees with Chiral Perturbation Theory

Provides detailed evaluation of invariant amplitudes

Abstract

The invariant amplitudes for pion electroproduction on the nucleon are evaluated by dispersion relations at constant t with MAID as input for the imaginary parts of these amplitudes. In the threshold region these amplitudes are confronted with the predictions of several low-energy theorems derived in the soft-pion limit. In general agreement with Chiral Perturbation Theory, the dispersive approach yields large corrections to these theorems because of the finite pion mass.