$B\to S$ Transition Form Factors in the PQCD approach

Abstract

Under two different scenarios for the light scalar mesons, we investigate the transition form factors of $B(B_s)$ mesons decay into a scalar meson in the perturbative QCD approach. In the large recoiling region, the form factors are dominated by the short-distance dynamics and can be calculated using perturbation theory. We adopt the dipole parametrization to recast the $q^2$ dependence of the form factors. Since the decay constants defined by the scalar current are large, our predictions on the $B\to S$ form factors are much larger than the $B\to P$ transitions, especially in the second scenario. Contributions from various light-cone distribution amplitudes (LCDAs) are elaborated and we find that the twist-3 LCDAs provide more than a half contributions to the form factors. The two terms of the twist-2 LCDAs give destructive contributions in the first scenario while they give constructive contributions in the second scenario. With the form factors, we also predict the decay width and branching ratios of the semileptonic $B\to Sl\bar{\nu }$ and $B\to S{l}^{+}{l}^{-}$ decays. The branching ratios of $B\to Sl\bar{\nu }$ channels are found to have the order of $10^{-4}$ while those of $B\to S{l}^{+}{l}^{-}$ have the order of $10^{-7}$. These predictions can be tested by the future experiments.

20 pages, 31 figures

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