Spectral distribution for the decay tau -> nu_tau K pi
  With the newly available data sets on hadronic tau decays from the B-factories BABAR and BELLE, and future data from BESIII, precise information on the decay distributions will soon become available. This calls for an improvement of the decay spectra also on the theoretical side. In this work, the distribution function for the decay tau -> nu_tau K pi will be presented with the relevant K pi vector and scalar form factors being calculated in the framework of the resonance chiral theory, also taking into account additional constraints from dispersion relations and short-distances. As a by-product the slope and curvature of the vector form factor F_+^{K pi}(s) are determined to be lambda_+^' = 25.6 10^{-3} and lambda_+^{''} = 1.31 10^{-3} respectively.   From our approach it appears that it should be possible to obtain information on the low lying scalar K_0^*(800) as well as the second vector K^*(1410) resonances from the tau decay data. In particular, the exclusive branching fraction of the scalar component is found to be B[tau -> nu_tau(K pi)_{S-wave}] = (3.88 +- 0.19) 10^{-4}. 
M. Jamin, A. Pich, J. Portoles