$B^0\to K^{\ast 0}μ^+μ^-$ 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 $\left|ς_u\right|$ is much smaller than $\left|ς_d\right|$, the charged-scalar contributes mainly to chirality-flipped $C_{9,10}^\prime$, with the corresponding effects being proportional to $\left|ς_d\right|^2$. Numerically, the charged-scalar effects fit into two categories: (A) $C_{7,9,10}^\mathrm{H^\pm}$ are sizable, but $C_{9,10}^{\prime\mathrm{H^\pm}}\simeq0$, corresponding to the (large $\left|ς_u\right|$, small $\left|ς_d\right|$) region; (B) $C_7^\mathrm{H^\pm}$ and $C_{9,10}^{\prime\mathrm{H^\pm}}$ are sizable, but $C_{9,10}^\mathrm{H^\pm}\simeq0$, corresponding to the (small $\left|ς_u\right|$, large $\left|ς_d\right|$) region. Taking into account phenomenological constraints from the inclusive radiative decay $B\to X_sγ$, 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 $P_5'$ of $B^0\to K^{\ast 0}μ^+μ^-$ decay, and find that $P_5'$ could be increased significantly to be consistent with the experimental data in case B.