Analyticity constraints on the strangeness changing vector current and applications to τ→K πντ and τ→K ππντ

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 flavor symmetry breaking parameter, imposing boundary conditions at t=0 from chiral and flavor symmetries and at t ->infinity from QCD. We apply the results to the tau -> K pi nu(tau) and tau -> K pi pi nu(tau) amplitudes and compare the former to recent high statistics results from B factories.