Expectations on $B\to (K^*_{0}(1430),K^*_{2}(1430))\phi$ decays

Abstract

As the annihilation contributions play important roles in solving the puzzle of the small longitudinal polarizations in $B\to K^* \phi$ decays, we examine the similar effects in the decays of $B\to K^*_{0,2}(1430) \phi$. For the calculations on the annihilated contributions, we adopt that the form factors in $B\to K^{(*)} \phi$ decays are parameters determined by the observed branching ratios (BRs), polarization fractions (PFs) and relative angles in experiments and we connect the parameters between $B\to K^*_{0(2)} \phi$ and $B\to K^{(*)}\phi$ by the ansatz of correlating $\la K^*_n(1430) \phi| (V-A)_{\mu}|0\ra$ to $\la K^{(*)} \phi| (V-A)_{\mu}|0\ra$. We find that the BR of $B_d\to K^{*0}_{0}(1430) \phi$ is $(3.69 \pm 0.47)\times 10^{-6}$. By using the transition form factors of $B\to K^*_2(1430)$ in the light-front quark model (LFQM) and the 2nd version of Isgur-Scora-Grinstein-Wise (ISGW2), we show that BR of $B_d\to K^{*0}_{2}(1430)\phi$ is a broad allowed value and $(1.70\pm0.80)\times 10^{-6}$, respectively. In terms of the recent BABAR's observations on BRs and PFs in $B_d\to K^{*0}_{2}(1430)\phi $, the results in the LFQM are found to be more favorable. In addition, due to the annihilation contributions to $B\to K^*_2\phi$ and $B\to K^*\phi$ being opposite in sign, we demonstrate that the longitudinal polarization of $B_d\to K^{*0}_2(1430) \phi$ is always O(1) with or without including the annihilation contributions.