New Physics in $b \rightarrow s \mu^+ \mu^-$: 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 $Z'$ 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 sizeable CP asymmetries in $B \to K^{(*)} \mu^+ \mu^-$. There is a spectrum of $Z'$ models; the key parameter is $g_L^{\mu\mu}$, which describes the strength of the $Z'$ coupling to $\mu^+\mu^-$. If $g_L^{\mu\mu}$ is small (large), the constraints from $B^0_s$-${\bar B}^0_s$ 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