Dispersive representation and shape of the Kl3 form factors: robustness

TL;DR

This paper develops and tests a dispersive parametrization of the Kpi form factors, examining their robustness against various theoretical uncertainties and experimental data, to improve understanding of low-energy hadronic interactions.

Contribution

It introduces a twice subtracted dispersive parametrization for the vector Kpi form factor and analyzes its robustness, including effects of cut-off dependence, isospin breaking, and zeros.

Findings

The parametrization remains stable under various theoretical assumptions.

Constraints on zeros in form factors are derived from the Callan-Treiman theorem.

Comparison with tau decay data supports the robustness of the approach.

Abstract

An accurate low-energy dispersive parametrization of the scalar Kpi form factor was constructed some time ago in terms of a single parameter guided by the Callan-Treiman low-energy theorem. A similar twice subtracted dispersive parametrization for the vector Kpi form factor will be investigated here. The robustness of the parametrization of these two form factors will be studied in great detail. In particular the cut-off dependence, the isospin breaking effects and the possible, though not highly probable, presence of zeros in the form factors will be discussed. Interesting constraints in the latter case will be obtained from the soft-kaon analog of the Callan-Treiman theorem and a comparison with the recent tau --> K pi nu_tau data.