New Physics in $b \rightarrow s μ^+ μ^-$: Distinguishing Models through CP-Violating Effects

Abstract

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 $b \to s μ^+ μ^-$ 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 $B \to K^{(*)} μ^+ μ^-$. 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 $b \to s μ^+ μ^-$ processes are concerned. In this single LQ model, the weak phase of the coupling can be large, leading to some sizeable CP asymmetries in $B \to K^{(*)} μ^+ μ^-$. There is a spectrum of $Z'$ models; the key parameter is $g_L^{μμ}$, which describes the strength of the $Z'$ coupling to $μ^+μ^-$. If $g_L^{μμ}$ 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 $B \to K^{(*)} μ^+ μ^-$ can indeed distinguish among NP $b \to s μ^+ μ^-$ models

23 pages, 3 figures; references updated; published in Physical Review D