$B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$ Decay in the Aligned Two-Higgs-Doublet Model

Abstract

In the aligned two-Higgs-doublet model, we perform a complete one-loop computation of the short-distance Wilson coefficients $C_{7,9,10}^{(\prime )}$, which are the most relevant ones for $b\to s{\ell }^{+}{\ell }^{-}$ transitions. It is found that, when the model parameter $\left|{\varsigma }_u\right|$ is much smaller than $\left|{\varsigma }_d\right|$, the charged-scalar contributes mainly to chirality-flipped $C_{9,10}^{\prime }$, with the corresponding effects being proportional to ${\left|{\varsigma }_d\right|}^2$. Numerically, the charged-scalar effects fit into two categories: (A) $C_{7,9,10}^{{\mathrm{H}}^{\pm }}$ are sizable, but $C_{9,10}^{\prime {\mathrm{H}}^{\pm }}\simeq 0$, corresponding to the (large $\left|{\varsigma }_u\right|$, small $\left|{\varsigma }_d\right|$) region; (B) $C_7^{{\mathrm{H}}^{\pm }}$ and $C_{9,10}^{\prime {\mathrm{H}}^{\pm }}$ are sizable, but $C_{9,10}^{{\mathrm{H}}^{\pm }}\simeq 0$, corresponding to the (small $\left|{\varsigma }_u\right|$, large $\left|{\varsigma }_d\right|$) region. Taking into account phenomenological constraints from the inclusive radiative decay $B\to X_s\gamma$, as well as the latest model-independent global analysis of $b\to s{\ell }^{+}{\ell }^{-}$ data, we obtain the much restricted parameter space of the model. We then study the impact of the allowed model parameters on the angular observables $P_2$ and $P_5^{\prime }$ of $B^0\to K^{\ast 0}{\mu }^{+}{\mu }^{-}$ decay, and find that $P_5^{\prime }$ could be increased significantly to be consistent with the experimental data in case B.

34 pages, 8 figures, 2 tables; More references and discussions added, final version published in the journal

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