Two-Meson Form Factors in Unitarized Chiral Perturbation Theory

TL;DR

This paper develops a detailed method to calculate two-meson form factors using unitarized chiral perturbation theory combined with dispersion relations, providing new insights into tensor form factors and their applications in low-energy physics.

Contribution

It introduces a systematic approach to compute two-meson form factors, including tensor form factors, within unitarized chiral perturbation theory, updating and expanding previous results.

Findings

Form factors are computed with improved accuracy.

Tensor form factors are systematically studied for the first time.

Applications to B and tau decays are discussed.

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 $\tau\rightarrow\pi^{-}\pi^{0}\nu_{\tau}$, in searches for physics beyond the Standard Model.