Two-Meson Form Factors in Unitarized Chiral Perturbation Theory

Abstract

We present a comprehensive analysis of form factors for two light pseudoscalar mesons induced by scalar, vector, and tensor quark operators. The theoretical framework is based on a combination of unitarized chiral perturbation theory and dispersion relations. The low-energy constants in chiral perturbation theory are fixed by a global fit to the available data of the two-meson scattering phase shifts. Each form factor derived from unitarized chiral perturbation theory is improved by iteratively applying a dispersion relation. This study updates the existing results in the literature and explores those that have not been systematically studied previously, in particular the two-meson tensor form factors within unitarized chiral perturbation theory. We also discuss the applications of these form factors as mandatory inputs for low-energy phenomena, such as the semi-leptonic decays $B_s\to {\pi }^{+}{\pi }^{-}{\ell }^{+}{\ell }^{-}$ and the $\tau$ lepton decay $\tau \to {\pi }^{-}{\pi }^0{\nu }_{\tau }$, in searches for physics beyond the Standard Model.

Comments: 53 pages, 21 figures, 3 tables