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

TL;DR

This paper investigates positivity constraints on the low-energy constants of the $ ext{ChPT}$ Lagrangian at order $p^6$, showing they are naturally satisfied within the Mandelstam triangle for large $N_C$ and are respected at $N_C=3$.

Contribution

It demonstrates that positivity constraints are inherently satisfied in the large $N_C$ limit and are also respected numerically at the physical value $N_C=3$, providing insights into $ ext{ChPT}$ consistency.

Findings

Positivity constraints are automatically satisfied inside the Mandelstam triangle at large $N_C$.

Numerical tests show constraints are well respected at $N_C=3$.

The results support the consistency of $ ext{ChPT}$ LECs with positivity bounds.

Abstract

Positivity constraints on the LECs of $\cO(p^6)$ $\chi$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.