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 Bs→ π+π−ℓ+ℓ− and the τ lepton decay τ → π−π0ντ, in searches for physics beyond the Standard Model.
Highlights
The study of multi-meson systems is an interesting problem as they are universal in various physical processes
We fit to the following data sets using the MINUIT function minimization and error analysis package [83,84,85]: the ππ scattering phase shifts are taken from the dispersive analysis compiled in ref. [70];1 the data for the inelasiticity η00 are taken from the analysis of ref. [81]; the ππ → KKdata are from refs. [79, 80]; the Kπ phase shifts are taken from refs. [71,72,73,74,75,76,77,78]; the data for the πη invariant mass distribution are taken from ref. [82], and the background is extracted from the corresponding curve in that reference
The coefficients C3r6 and C3r7 vanish in the large-Nc limit, where Nc refers to the number of colors in the quantum chromodynamics (QCD) Lagrangian, while other nonzero coefficients are collected in table 2
Summary
The study of multi-meson systems is an interesting problem as they are universal in various physical processes An example of this is the B → K∗(→ Kπ)μ+μ− decay that is induced by the flavor-changing neutral current. Recent experimental studies have led to some hints for moderate deviations from the SM [1,2,3] Note that this process is a four-body decay since the K∗ meson is reconstructed from the Kπ final state. The next-to-leading-order (NLO) ChPT calculation for the ππ scalar form factor was firstly given in ref. The two-meson vector form factors for Kπ were first derived in ChPT [28], while it was mostly obtained by fitting to the data of semi-leptonic τ decays in refs.
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