The $K\pi$ form factors from Analyticity and Unitarity

TL;DR

This paper uses analyticity and unitarity principles, combined with theoretical and experimental data, to constrain the shape and zero locations of $K o\pi$ form factors relevant for semileptonic decays.

Contribution

It provides new bounds on the shape parameters of $K o\pi$ form factors using a comprehensive approach integrating multiple theoretical and experimental inputs.

Findings

Derived bounds on scalar and vector form factor shape parameters.

Identified regions where the form factors cannot have zeros.

Established constraints on the form factors' analytic structure.

Abstract

Analyticity and unitarity techniques are employed to obtain bounds on the shape parameters of the scalar and vector form factors of semileptonic $K_{l3}$ decays. For this purpose we use vector and scalar correlators evaluated in pQCD, a low energy theorem for scalar form factor, lattice results for the ratio of kaon and pion decay constants, chiral perturbation theory calculations for the scalar form factor at the Callan-Treiman point and experimental information on the phase and modulus of $K\pi $ form factors up to an energy $\tin=1 {\rm GeV}^2$. We further derive regions on the real axis and in the complex-energy plane where the form factors cannot have zeros.