Eur. Phys. J. C (2014) 74: 2763
https://doi.org/10.1140/epjc/s10052-014-2763-0

Regular Article - Theoretical Physics

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

¹ Departamento de Física Teórica and Instituto de Física Teórica, IFT-UAM/CSIC Universidad Autónoma de Madrid, Cantoblanco, Madrid, Spain
² Institute for Advanced Simulation, Institut für Kernphysik and Jülich Center for Hadron Physics, Forschungszentrum Jülich, 52425 , Jülich, Germany
³ Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing, 100871, People’s Republic of China
⁴ Collaborative Innovation Center of Quantum Matter, Beijing, People’s Republic of China

^* e-mail: juanj.sanz@uam.es

Received: 16 December 2013
Accepted: 29 January 2014
Published online: 5 March 2014

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 the Mandelstam triangle, . Scanning inside the region , 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 the extended-on-mass-shell scheme, it is found that these bounds are well respected numerically both at the and the level. Nevertheless, when taking the errors into account, only the bounds are obeyed in the full error interval, while the bounds on the fits are slightly violated. If one disregards the loop contributions, the bounds always fail in certain regions of . 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 where the bounds are nearly optimal in terms of just a few chiral couplings, which can easily be implemented and employed to constrain future analyses. Some issues concerned with calculations with an explicit resonance are also discussed.