  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.

High Energy Physics - Phenomenology