Virtual photons to fourth order CHPT with nucleons

TL;DR

This paper explores the calculation of isospin violation effects in chiral perturbation theory (CHPT) with nucleons, emphasizing the importance of including all non-isospin symmetric sources for accurate results.

Contribution

It provides a comprehensive framework for calculating isospin violation effects in CHPT, including electromagnetic interactions and quark mass differences.

Findings

Electromagnetic contributions significantly affect the pion nucleon sigma term.

Quark mass differences influence S-wave pion nucleon scattering length.

All non-isospin symmetric sources must be included for correct isospin violation size.

Abstract

I discuss the whole mechanism to calculate isospin violation effects in the framework of CHPT. In order to get the correct size of isospin violation one has to include all non-isospin symmetric sources like the electromagnetic interaction, the quark mass difference ($\pi_0 - \eta$ mixing), explicit photon loops. As examples I discuss the electromagnetic contributions to the pion nucleon sigma term and to the S-wave pion nucleon scattering length.