Understand
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 $C_{9,10}^{\prime\mathrm{H^\pm}}\simeq0$, 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 $C_{9,10}^\mathrm{H^\pm}\simeq0$, 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.