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We study the resonant contributions in the process $\bar{B}^0\to K^-\pi^+\mu^+\mu^-$ with the $K^-\pi^+$ invariant mass square $m_{K\pi}^2\in [1,5] {\rm GeV}^2$. Width effects of the involved strange mesons, $K^*(1410),K_0^*(1430), K_2^*(1430), K^*(1680), K_3^*(1780)$ and $K_4^*(2045)$, areincorporated. In terms of the helicity amplitudes, we derive a compact form forthe full angular distributions, through which the branching ratios,forward-backward asymmetries and polarizations are attained. We propose thatthe uncertainties in the $B\to K^*_J$ form factors can be pinned down by themeasurements of a set of SU(3)-related processes. Using results from the largeenergy limit, we derive the dependence of branching fractions on the$m_{K\pi}$, and find that the $K^*_2(1430)$ resonance has a clear signature, inparticular, in the transverse polarizations.

Analysis of $B\to K^*_J (\to K \pi) \mu^+\mu^-$ in the higher kaon resonance region