New physics in $b\to s{\mu }^{+}{\mu }^{-}$: Distinguishing models through $CP$-violating effects

At present, there are several measurements of $B$ decays that exhibit discrepancies with the predictions of the SM, and suggest the presence of new physics (NP) in $b\to s{\mu }^{+}{\mu }^{-}$ transitions. Many NP models have been proposed as explanations. These involve the tree-level exchange of a leptoquark (LQ) or a flavor-changing $Z^{\prime }$ boson. In this paper we examine whether it is possible to distinguish the various models via $CP$-violating effects in $B\to K^{(*)}{\mu }^{+}{\mu }^{-}$. Using fits to the data, we find the following results. Of all possible LQ models, only three can explain the data, and these are all equivalent as far as $b\to s{\mu }^{+}{\mu }^{-}$ processes are concerned. In this single LQ model, the weak phase of the coupling can be large, leading to some sizable $CP$ asymmetries in $B\to K^{(*)}{\mu }^{+}{\mu }^{-}$. There is a spectrum of $Z^{\prime }$ models; the key parameter is $g_L^{\mu \mu }$, which describes the strength of the $Z^{\prime }$ coupling to ${\mu }^{+}{\mu }^{-}$. If $g_L^{\mu \mu }$ is small (large), the constraints from $B_s^0-{\overline{B}}_s^0$ mixing are stringent (weak), leading to a small (large) value of the NP weak phase, and corresponding small (large) $CP$ asymmetries. We therefore find that the measurement of $CP$-violating asymmetries in $B\to K^{(*)}{\mu }^{+}{\mu }^{-}$ can indeed distinguish among NP $b\to s{\mu }^{+}{\mu }^{-}$ models.

Figure 1

Allowed regions in the Re(WC)-Im(WC) plane for the four model-independent scenarios I–IV. See Table 1 for definitions of Re(WC) and Im(WC) in each of the four scenarios.

Figure 2

Predictions of the $CP$ asymmetries $A_7$, $A_8$ and $A_9$ at the $2\sigma$ level for the four model-independent scenarios I–IV.

Figure 3

Predictions of the LQ model [solutions (A) and (B)] and the $Z^{\prime }$ model with $g_L^{\mu \mu }=0.1$, 0.5, 1.0 for the $CP$ asymmetries $A_3–A_9$ in $B^0\to K^{*0}{\mu }^{+}{\mu }^{-}$ and $A_{CP}$ in $B\to K{\mu }^{+}{\mu }^{-}$. In the models, the real and imaginary parts of the couplings are allowed to vary by $\pm 2\sigma$.