Improving the phenomenology ofKl3form factors with analyticity and unitarity

Abstract

The shape of the vector and scalar ${K}_{\ensuremath{\ell}3}$ 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 ${K}_{\ensuremath{\ell}3}$ data analyses and provide theoretical underpinning for recent phenomenological dispersive representations for the form factors.