Positivity constraints on the low-energy constants of the chiral pion-nucleon Lagrangian

Abstract

Positivity constraints on the pion-nucleon scattering amplitude are derived in this article with the help of general S-matrix arguments, such as analyticity, crossing symmetry and unitarity, in the upper part of Mandelstam triangle, R. Scanning inside the region R, the most stringent bounds on the chiral low energy constants of the pion-nucleon Lagrangian are determined. When just considering the central values of the fit results from covariant baryon chiral perturbation theory using extended-on-mass-shell scheme, it is found that these bounds are well respected numerically both at O(p^3) and O(p^4) level. Nevertheless, when taking the errors into account, only the O(p^4) bounds are obeyed in the full error interval, while the bounds on O(p^3) fits are slightly violated. If one disregards loop contributions, the bounds always fail in certain regions of R. Thus, at a given chiral order these terms are not numerically negligible and one needs to consider all possible contributions, i.e., both tree-level and loop diagrams. We have provided the constraints for special points in R where the bounds are nearly optimal in terms of just a few chiral couplings, which can be easily implemented and employed to constrain future analyses. Some issues about calculations with an explicit Delta(1232) resonance are also discussed.

15 pages, 13 eps figures, 2 tables

References in corpus (10)

• Electromagnetic excitation of the Delta(1232)-resonance
• Improved description of the $\pi N$-scattering phenomenology in covariant baryon chiral perturbation theory
• Analyses of pion-nucleon elastic scattering amplitudes up to $O(p^4)$ in extended-on-mass-shell subtraction scheme
• Roy-Steiner equations for pion-nucleon scattering
• Dispersion Relation Bounds for pi pi Scattering
• πN scattering in relativistic baryon chiral perturbation theory revisited
• Universal Bounds for SU(3) Low Energy Constants
• Unitarity Constraints on effective interaction in $\pi N$ scattering
• The Froissart--Martin Bound for $\pi \pi$ Scattering in QCD
• Pion-nucleon elastic scattering amplitude within covariant baryon chiral perturbation theory up to $O(p^4)$ level

Cited by in corpus (6)

• Softness and Amplitudes' Positivity for Spinning Particles
• Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings
• Generalized positivity bounds on chiral perturbation theory
• Aspects of the low-energy constants in the chiral Lagrangian for charmed mesons
• Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes
• Meson-baryon effective chiral Lagrangians at order $p^4$