New physics in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>b</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>s</mml:mi><mml:msup><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:mrow><mml:mi>μ</mml:mi></mml:mrow><mml:mrow><mml:mo>−</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math>: Distinguishing models through <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>C</mml:mi><mml:mi>P</mml:mi></mml:math>-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 $b\ensuremath{\rightarrow}s{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ transitions. Many NP models have been proposed as explanations. These involve the tree-level exchange of a leptoquark (LQ) or a flavor-changing ${Z}^{\ensuremath{'}}$ boson. In this paper we examine whether it is possible to distinguish the various models via $CP$-violating effects in $B\ensuremath{\rightarrow}{K}^{(*)}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. 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 $b\ensuremath{\rightarrow}s{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ processes are concerned. In this single LQ model, the weak phase of the coupling can be large, leading to some sizable $CP$ asymmetries in $B\ensuremath{\rightarrow}{K}^{(*)}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. There is a spectrum of ${Z}^{\ensuremath{'}}$ models; the key parameter is ${g}_{L}^{\ensuremath{\mu}\ensuremath{\mu}}$, which describes the strength of the ${Z}^{\ensuremath{'}}$ coupling to ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$. If ${g}_{L}^{\ensuremath{\mu}\ensuremath{\mu}}$ is small (large), the constraints from ${B}_{s}^{0}\ensuremath{-}{\overline{B}}_{s}^{0}$ 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 $B\ensuremath{\rightarrow}{K}^{(*)}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ can indeed distinguish among NP $b\ensuremath{\rightarrow}s{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ models.

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