Derivation of O(q^4) Effective Pion-Nucleon Lagrangian Within Heavy Baryon Chiral Perturbation Theory

TL;DR

This paper systematically derives the complete set of O(q^4) terms in the Heavy Baryon Chiral Perturbation Theory Lagrangian for nucleons, ensuring linear independence and applying it to pion double charge exchange processes.

Contribution

It provides the first comprehensive list of O(q^4) terms in HBChPT, including off-shell and on-shell reductions, using algebraic identities and reparameterization invariance.

Findings

Complete O(q^4) HBChPT Lagrangian terms derived.

Application to pion double charge exchange analyzed.

Ensures linear independence of low energy constants.

Abstract

We construct a complete list of O(q^4) terms directly within Heavy Baryon Chiral Perturbation Theory (HBChPT) in the absence of external fields and assuming isospin symmetry. In addition to a phase rule recently developed (NPA646, 343, '99), a variety of algebraic identities and reparameterization invariance, are used to ensure linear independence of the terms and their low energy coupling constants. We first construct O(q^4) terms terms for off-shell nucleons, and then perform the on-shell reduction, again within HBChPT. We discuss an application of the O(q^4) terms to the evaluation of the O(q^4) operator insertions in the "contact graph" of pion double charge exchange.