Photoproduction of neutral pions

TL;DR

This paper develops a nonrelativistic effective field theory to accurately describe the photoproduction of neutral pions on protons, capturing the effects of pion and nucleon mass differences and providing detailed amplitude calculations.

Contribution

It introduces a rigorous effective field theory framework with a consistent power counting scheme for neutral pion photoproduction, including one-loop amplitude expressions.

Findings

Derived expressions for S- and P-wave multipole amplitudes at one loop

Analyzed the phase relation between electric multipole and pi^0 p scattering

Identified a pronounced cusp effect due to mass differences

Abstract

The pion and nucleon mass differences generate a very pronounced cusp in the photoproduction reaction of a single neutral pion on the proton. A nonrelativistic effective field theory to describe this reaction is constructed. The approach is rigorous in the sense that it is an effective field theory with a consistent power counting scheme. Expressions for the S- and P-wave multipole amplitudes at one loop are given. The relation of the phase of the electric multipole E_0+ to the phase of the S-wave of pi^0 p --> pi^0 p scattering is discussed.