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

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.

References in corpus (10)

• Chiral effective field theory and nuclear forces
• Improved chiral nucleon-nucleon potential up to next-to-next-to-next-to-leading order
• Extended Partial-Wave Analysis of piN Scattering Data
• Chiral Perturbation Theory and Baryon Properties
• Peripheral nucleon-nucleon scattering at fifth order of chiral perturbation theory
• Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering
• Chiral perturbation theory
• Analyses of pion-nucleon elastic scattering amplitudes up to $O(p^4)$ in extended-on-mass-shell subtraction scheme
• Isospin breaking in the pion-nucleon scattering lengths
• The reaction pi N -> pi pi N in chiral effective field theory with explicit Delta(1232) degrees of freedom

Cited by in corpus (28)

• Local chiral potentials and the structure of light nuclei
• Reconciling threshold and subthreshold expansions for pion-nucleon scattering
• Extracting the sigma-term from low-energy pion-nucleon scattering
• Towards high-order calculations of three-nucleon scattering in chiral effective field theory
• Few- and many-nucleon systems with semilocal coordinate-space regularized chiral nucleon-nucleon forces
• Atomic nuclei from quantum Monte Carlo calculations with chiral EFT interactions
• Local nucleon-nucleon and three-nucleon interactions within chiral effective field theory
• Nuclear Forces for Precision Nuclear Physics -- a collection of perspectives
• Cross-channel constraints on resonant antikaon-nucleon scattering
• Three-nucleon force in chiral EFT with explicit $\Delta (1232)$ degrees of freedom: Longest-range contributions at fourth order
• Weak pion production off the nucleon in covariant chiral perturbation theory
• Elastic and inelastic pion-nucleon scattering to fourth order in chiral perturbation theory
• New Insights on Low Energy $\pi N$ Scattering Amplitudes
• Meson-baryon scattering to one-loop order in heavy baryon chiral perturbation theory
• Pion photoproduction off nucleons in covariant chiral perturbation theory
• Meson-baryon scattering up to the next-to-next-to-leading order in covariant baryon chiral perturbation theory
• Applying the Density Matrix Expansion with Coordinate-Space Chiral Interactions
• Three-body forces and Efimov physics in nuclei and atoms
• Consistency between SU(3) and SU(2) chiral perturbation theory for the nucleon mass
• The reaction $\pi N\to \omega N$ in a dynamical coupled-channel approach
• New Insights on Low Energy $\pi N$ Scattering Amplitudes: Comprehensive Analyses at $\mathcal{O}(p^3)$ Level
• Threshold pion electro- and photoproduction off nucleons in covariant chiral perturbation theory
• Nucleon polarizabilities in covariant baryon chiral perturbation theory with explicit $\Delta$ degrees of freedom
• Light-quark mass dependence of the nucleon axial charge and pion-nucleon scattering phenomenology
• How does the $S_{11}$ $N^{\ast }(890)$ state emerge from a naive $K$ matrix fit?
• Radiative pion photoproduction in covariant chiral perturbation theory
• On the Existence of $N^{\ast }(890)$ Resonance in $S_{11}$ Channel of $\pi N$ Scatterings
• Calculation of the axial-vector coupling constant $g_A$ to two loops in covariant chiral perturbation theory