Baryon Chiral Perturbation Theory in Manifestly Lorentz Invariant Form

TL;DR

This paper introduces a Lorentz-invariant approach to baryon chiral perturbation theory that maintains explicit symmetry and provides a consistent low-energy expansion, overcoming convergence issues near threshold regions.

Contribution

The authors develop a method that preserves Lorentz and chiral invariance throughout the low energy expansion, improving convergence near thresholds compared to traditional approaches.

Findings

The new method yields a coherent low energy representation.

Application to nucleon mass and scalar form factor demonstrates effectiveness.

The approach maintains explicit Lorentz and chiral invariance.

Abstract

We show that in the presence of massive particles such as nucleons, the standard low energy expansion in powers of meson momenta and light quark masses in general only converges in part of the low energy region. The expansion of the scalar form factor $\sigma(t)$, for instance, breaks down in the vicinity of $t=4M_\pi^2$. In the language of heavy baryon chiral perturbation theory, the proper behaviour in the threshold region only results if the multiple internal line insertions generated by relativistic kinematics are summed up to all orders. We propose a method that yields a coherent representation throughout the low energy region while keeping Lorentz and chiral invariance explicit at all stages. The method is illustrated with a calculation of the nucleon mass and of the scalar form factor to order $p^4$.