Elastic pion-nucleon scattering in chiral perturbation theory: A fresh look

TL;DR

This paper analyzes elastic pion-nucleon scattering using chiral perturbation theory up to fourth order, employing both heavy-baryon and covariant approaches, and demonstrates that including the Δ-resonance extends the theory's applicability.

Contribution

It provides a detailed renormalization scheme for low-energy constants and shows that explicit Δ-resonance inclusion improves the effective field theory's range.

Findings

Explicit Δ-resonance inclusion extends applicability.

Predicted phase shifts agree with Roy-Steiner analysis.

Reliable extraction of low-energy constants from data.

Abstract

Elastic pion-nucleon scattering is analyzed in the framework of chiral perturbation theory up to fourth order within the heavy-baryon expansion and a covariant approach based on an extended on-mass-shell renormalization scheme. We discuss in detail the renormalization of the various low-energy constants and provide explicit expressions for the relevant $\beta$-functions and the finite subtractions of the power-counting breaking terms within the covariant formulation. To estimate the theoretical uncertainty from the truncation of the chiral expansion, we employ an approach which has been successfully applied in the most recent analysis of the nuclear forces. This allows us to reliably extract the relevant low-energy constants from the available scattering data at low energy. The obtained results provide a clear evidence that the breakdown scale of the chiral expansion for this reaction is related to the $\Delta$-resonance. The explicit inclusion of the leading contributions of the $\Delta$-isobar is demonstrated to substantially increase the range of applicability of the effective field theory. The resulting predictions for the phase shifts are in an excellent agreement with the ones from the recent Roy-Steiner-equation analysis of pion-nucleon scattering.