K pi vector form factor constrained by tau ---> K pi nu_tau and K_l3 decays

Abstract

Dispersive representations of the Kpi vector and scalar form factors are used to fit the spectrum of tau ---> K pi nu_tau obtained by the Belle collaboration incorporating constraints from results for K_l3 decays. The slope and curvature of the vector form factor are obtained directly from the data through the use of a three-times-subtracted dispersion relation. We find ${\lambda }_{+}^{\prime }=(25.49\pm 0.31)\times 10^{-3}$ and ${\lambda }_{+}"=(12.22\pm 0.14)\times 10^{-4}$. From the pole position on the second Riemann sheet the mass and width of the $K^{\ast }(892{)}^{\pm }$ are found to be $m_{K^{\ast }(892{)}^{\pm }}=892.0\pm 0.5$~MeV and ${\Gamma }_{K^{\ast }(892{)}^{\pm }}=46.5\pm 1.1$~MeV. The phase-space integrals needed for K_l3 decays are calculated as well. Furthermore, the Kpi isospin-1/2 P-wave threshold parameters are derived from the phase of the vector form factor. For the scattering length and the effective range we find respectively $a_1^{1/2}=(0.166\pm 0.004)m_{\pi }^{-3}$ and $b_1^{1/2}=(0.258\pm 0.009)m_{\pi }^{-5}$.

22 pages, 4 figures

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