Baryon chiral perturbation theory extended beyond the low-energy region

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.

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

“…An extension of the range of applicability of chiral effective field theory (EFT) beyond the low-energy region has been also suggested in the recent work of ref. [22].…”

The width of the Roper resonance in baryon chiral perturbation theory

“…To calculate the full decay width of the Roper resonance we use the following standard values of the parameters [33] M π = 139 MeV, m N = 939 MeV, m ∆ = 1210 MeV, Γ ∆ = 100 MeV, m R = 1365 MeV, F π = 92.2 MeV, (26) in Eqs. (15) and (23)…”

Pion-nucleon scattering with explicit Delta resonance

“…the low-energy region is done in Ref. [18]. Contributions to the scattering amplitudes obtained in those works possess the correct power counting and correct analytic properties.…”