New Physics in $b\to s{\mu }^{+}{\mu }^{-}$: 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 $b\to s{\mu }^{+}{\mu }^{-}$ 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 $B\to K^{(\ast )}{\mu }^{+}{\mu }^{-}$. 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 $B\to K^{(\ast )}{\mu }^{+}{\mu }^{-}$. 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 $B_s^0$-${\bar{B}}_s^0$ 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 $B\to K^{(\ast )}{\mu }^{+}{\mu }^{-}$ can indeed distinguish among NP $b\to s{\mu }^{+}{\mu }^{-}$ models

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