Improving the phenomenology of K_{l3} form factors with analyticity and unitarity

TL;DR

This paper develops a model-independent approach using analyticity and unitarity to improve the understanding of K_{l3} form factors, providing constraints and predictions useful for experimental data analysis.

Contribution

It introduces a novel method combining dispersion relations, soft-meson theorems, and experimental data to constrain K_{l3} form factors without relying on specific models.

Findings

Derived bounds on form factor coefficients in the semileptonic range.

Predicted regions in the complex plane where zeros are excluded.

Provided constraints on truncation errors in form factor parameterizations.

Abstract

The shape of the vector and scalar K_{l3} form factors is investigated by exploiting analyticity and unitarity in a model-independent formalism. The method uses as input dispersion relations for certain correlators computed in perturbative QCD in the deep Euclidean region, soft-meson theorems, and experimental information on the phase and modulus of the form factors along the elastic part of the unitarity cut. We derive constraints on the coefficients of the parameterizations valid in the semileptonic range and on the truncation error. The method also predicts low-energy domains in the complex $t$-plane where zeros of the form factors are excluded. The results are useful for K_{l3} data analyses and provide theoretical underpinning for recent phenomenological dispersive representations for the form factors.