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Positivity constraints on the pion-nucleon scattering amplitude are derivedin this article with the help of general S-matrix arguments, such asanalyticity, crossing symmetry and unitarity, in the upper part of Mandelstamtriangle, R. Scanning inside the region R, the most stringent bounds on thechiral low energy constants of the pion-nucleon Lagrangian are determined. Whenjust considering the central values of the fit results from covariant baryonchiral perturbation theory using extended-on-mass-shell scheme, it is foundthat 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) fitsare slightly violated. If one disregards loop contributions, the bounds alwaysfail in certain regions of R. Thus, at a given chiral order these terms are notnumerically negligible and one needs to consider all possible contributions,i.e., both tree-level and loop diagrams. We have provided the constraints forspecial points in R where the bounds are nearly optimal in terms of just a fewchiral couplings, which can be easily implemented and employed to constrainfuture analyses. Some issues about calculations with an explicit Delta(1232)resonance are also discussed.

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