Virtual photons in baryon chiral perturbation theory

TL;DR

This paper develops a comprehensive chiral perturbation theory framework including virtual photons, analyzing electromagnetic and isospin-violating effects on nucleon properties and scattering, with implications for precision hadronic physics.

Contribution

It constructs the complete relativistic and heavy baryon chiral Lagrangian with virtual photons up to fourth order, detailing electromagnetic and isospin-breaking effects on nucleon observables.

Findings

Electromagnetic contributions to nucleon self-energy and mass are quantified.

Electromagnetic effects on the Cheng-Dashen point shift can reach 2 MeV.

Corrections to Weinberg's scattering length prediction are minimal.

Abstract

We construct the general Lagrangian for relativistic and heavy baryon chiral perturbation theory with virtual photons to fourth order. We work out the electromagnetic and strong isospin violating contributions to the nucleon self-energy, the nucleon mass and the scalar form factor of the nucleon. Electromagnetic effects for the shift to the Cheng-Dashen point can be as large as 2 MeV. We also discuss the corrections to Weinberg's prediction for the scattering length difference $a(\pi^0 p) - a(\pi^0 n)$ and show that they are small.