Analyticity constraints on the strangeness changing vector current and applications to $\tau \to K\pi {\nu }_{\tau }$, $\tau \to K\pi \pi {\nu }_{\tau }$

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.

24 pages, 11 figures. v2: minor corrections and clarifications

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