Positivity constraints on LECs of $\chi$PT lagrangian at $\text{cO}(p^6)$ level

Abstract

Positivity constraints on the LECs of $\text{cO}(p^6)$ $\chi$PT lagrangian are discussed. We demonstrate that the constraints are automatically satisfied inside the Mandelstam triangle for $\pi \pi$ scatterings, when $N_C$ is large. Numerical tests are made in the $N_C=3$ case, and it is found that these constraints are also well respected.

Comments: 9 pages with 2 eps figures