Analyticity constraints on the strangeness changing vector current and applications to $\tau\to K\pi \nu_\tau$, $\tau\to K\pi\pi \nu_\tau$

TL;DR

This paper uses analyticity and experimental scattering data to determine strangeness-changing vector current form factors, applying them to tau decays and comparing with recent experimental results.

Contribution

It provides a model-independent determination of form factors for strangeness-changing currents using analyticity and scattering data, with applications to tau decay processes.

Findings

Form factors are fully determined up to a symmetry-breaking parameter.

Results agree with recent high-statistics tau decay data.

The approach incorporates phase-shift measurements and inelastic scattering details.

Abstract

We discuss matrix elements of the strangeness changing vector current using their relation, due to analyticity, with $\pi K$ scattering in the $P$-wave. We take into account experimental phase-shift measurements in the elastic channel as well as results, obtained by the LASS collaboration, on the details of inelastic scattering, which show the dominance of two quasi two-body channels at medium energies.The associated form factors are shown to be completely determined, up to one flavour symmetry breaking parameter, imposing boundary conditions at $t=0$ from chiral and flavour symmetries and at $t\to\infty$ from QCD. We apply the results to the $\tau\to K\pi \nu_\tau$ and $\tau\to K\pi\pi \nu_\tau$ amplitudes and compare the former to recent high statistics results from B factories.