Updating bounds on the low-energy constants of Chiral Perturbation Theory from exact bounds on amplitudes

Abstract: Chiral perturbation theory is an efficient effective theory to describe meson-meson scattering at low energy. An effective theory naturally introduces low energy constants and they are used, for example, to solve the ultraviolet divergences. The aim of this master thesis is to focus on meson-meson scattering to find some theoretical bounds on the coupling constants, based mainly on arguments from analyticity and unitarity. In this work, new bounds have been derived for the two and three flavours cases, at p4. Next, properties of the general N flavours case have been studied and applied to the four flavours case. The contribution of the p6 lagrangian has also been considered to estimate the error in our calculations. Finally, upon all the calculated constraints, one might want to keep only the necessary ones. When the number of coupling constants is high, it is a problematic issue. A way to treat this problem has been developed.