Analysis of $B\to K_J^{\ast }(\to K\pi ){\mu }^{+}{\mu }^{-}$ in the higher kaon resonance region

Abstract

We study the resonant contributions in the process ${\bar{B}}^0\to K^{-}{\pi }^{+}{\mu }^{+}{\mu }^{-}$ with the $K^{-}{\pi }^{+}$ invariant mass square $m_{K\pi }^2\in [1,5]{\mathrm{GeV}}^2$. Width effects of the involved strange mesons, $K^{\ast }(1410),K_0^{\ast }(1430),K_2^{\ast }(1430),K^{\ast }(1680),K_3^{\ast }(1780)$ and $K_4^{\ast }(2045)$, are incorporated. In terms of the helicity amplitudes, we derive a compact form for the full angular distributions, through which the branching ratios, forward-backward asymmetries and polarizations are attained. We propose that the uncertainties in the $B\to K_J^{\ast }$ form factors can be pinned down by the measurements of a set of SU(3)-related processes. Using results from the large energy limit, we derive the dependence of branching fractions on the $m_{K\pi }$, and find that the $K_2^{\ast }(1430)$ resonance has a clear signature, in particular, in the transverse polarizations.

Comments: 12 pages, 5 figures, journal version