Expectations on $B\to (K_0^{\ast }(1430),K_2^{\ast }(1430))\varphi$ decays

Abstract

As the annihilation contributions play important roles in solving the puzzle of the small longitudinal polarizations in $B\to K^{\ast }\varphi$ decays, we examine the similar effects in the decays of $B\to K_{0,2}^{\ast }(1430)\varphi$. For the calculations on the annihilated contributions, we adopt that the form factors in $B\to K^{(\ast )}\varphi$ decays are parameters determined by the observed branching ratios (BRs), polarization fractions (PFs) and relative angles in experiments and we connect the parameters between $B\to K_{0(2)}^{\ast }\varphi$ and $B\to K^{(\ast )}\varphi$ by the ansatz of correlating $\la K^*_n(1430) ϕ| (V-A)_μ|0\ra$ to $\la K^{(*)} ϕ| (V-A)_μ|0\ra$. We find that the BR of $B_d\to K_0^{\ast 0}(1430)\varphi$ is $(3.69\pm 0.47)\times 10^{-6}$. By using the transition form factors of $B\to K_2^{\ast }(1430)$ in the light-front quark model (LFQM) and the 2nd version of Isgur-Scora-Grinstein-Wise (ISGW2), we show that BR of $B_d\to K_2^{\ast 0}(1430)\varphi$ is a broad allowed value and $(1.70\pm 0.80)\times 10^{-6}$, respectively. In terms of the recent BABAR's observations on BRs and PFs in $B_d\to K_2^{\ast 0}(1430)\varphi$, the results in the LFQM are found to be more favorable. In addition, due to the annihilation contributions to $B\to K_2^{\ast }\varphi$ and $B\to K^{\ast }\varphi$ being opposite in sign, we demonstrate that the longitudinal polarization of $B_d\to K_2^{\ast 0}(1430)\varphi$ is always O(1) with or without including the annihilation contributions.

20 pages, 4 figures, references added, version to appear in Phys. Rev. D

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