Baryon chiral perturbation theory extended beyond the low-energy region

TL;DR

This paper extends baryon chiral perturbation theory to higher energies at small scattering angles by re-arranging the effective Lagrangian and introducing a sliding scale with complex couplings, broadening its applicability.

Contribution

It generalizes the extended on-mass-shell scheme for baryon chiral perturbation theory by allowing expansion around kinematic points beyond the threshold with complex couplings.

Findings

Applicable to higher energies at small angles

Introduces complex-valued renormalized couplings

Expands the physical amplitudes beyond the threshold

Abstract

We consider an extension of the one-nucleon sector of baryon chiral perturbation theory beyond the low-energy region. The applicability of this approach for higher energies is restricted to small scattering angles, i.e. the kinematical region, where the quark structure of hadrons cannot be resolved. The main idea is to re-arrange the low-energy effective Lagrangian according to a new power counting and to exploit the freedom of the choice of the renormalization condition for loop diagrams. We generalize the extended on-mass-shell scheme for the one-nucleon sector of baryon chiral perturbation theory by choosing a sliding scale, that is we expand the physical amplitudes around kinematical points beyond the threshold. This requires the introduction of complex-valued renormalized coupling constants which can be either extracted from experimental data, or calculated using the renormalization group evolution of coupling constants fixed in threshold region.