Lepton-flavour violating $B$ decays in generic $Z'$ models

Crivellin, Andreas; Rosiek, Janusz; Nierste, Ulrich; Matias, Joaquim; Hofer, Lars; Pokorski, Stefan

doi:10.1103/PhysRevD.92.054013

Article
Report number	arXiv:1504.07928 ; CERN-PH-TH-2015-091
Title	Lepton-flavour violating $B$ decays in generic $Z'$ models
Author(s)	Crivellin, Andreas (CERN) ; Hofer, Lars (Barcelona, Autonoma U.) ; Matias, Joaquim (Barcelona, Autonoma U.) ; Nierste, Ulrich (KIT, Karlsruhe, TTP) ; Pokorski, Stefan (Warsaw U.) ; Rosiek, Janusz (Warsaw U.)
Publication	2015
Imprint	29 Apr 2015
Number of pages	10
Note	7 pages, 4 figures, constraints from B->Knunu added, typos corrected
In:	Phys. Rev. D 92 (2015) 054013
DOI	10.1103/PhysRevD.92.054013
Subject category	Particle Physics - Phenomenology
Abstract	LHCb has reported deviations from the SM expectations in $B\to K^* \mu^+\mu^-$ angular observables, in $B_s\to\phi\mu^+\mu^-$ and in ratio $R(K)=Br[B\to K \mu^+\mu^-]/Br[B\to K e^+e^-]$. For all three decays, a heavy neutral gauge boson mediating $b\to s\mu^+\mu^-$ transitions is a prime candidate for an explanation. As $R(K)$ measures violation of lepton-flavour universality, it is interesting to examine the possibility that also lepton flavour is violated. In this article, we investigate the perspectives to discover the lepton-flavour violating modes $B\to K^{()}\tau^\pm\mu^\mp$, $B_s\to \tau^\pm\mu^\mp$ and $B\to K^{()} \mu^\pm e^\mp$, $B_s\to \mu^\pm e^\mp$. For this purpose we consider a simplified model in which new-physics effects originate from an additional neutral gauge boson ($Z^\prime$) with generic couplings to quarks and leptons. The constraints from $\tau\to3\mu$, $\tau\to\mu\nu\bar{\nu}$, $\mu\to e\gamma$, $g_\mu-2$, neutrino trident production, $Z\to\ell^+\ell^{\prime-}$, semi-leptonic $b\to s\mu^+\mu^-$ decays and $B_s$--$\overline{B}_s$ mixing are examined. Taking into account these limits, we determine upper bounds on the decay rates of $B\to K^{()}\tau^\pm\mu^\mp$, $B_s\to \tau^\pm\mu^\mp$, $B\to K^{()}\mu^\pm e^\mp$ and $B_s\to \mu^\pm e^\mp$ as a function of fine-tuning in $B_s$--$\overline{B}_s$ mixing. We find that for a significant degree of fine-tuning the effect in all considered decays with $\tau\mu$ final states can be sizable (leading to branching ratios of the order of $\times 10^{-6}$). For $\mu e$ final states, $B_s\to \mu^\pm e^\mp$ is strongly suppressed and only $B\to K^{(*)} \mu^\pm e^\mp$ can be relevant (of the order of $\times 10^{-7}$). However, this is only possible in a region of the parameter space disfavoured by the current LHCb data on $b\to s\mu^+\mu^-$ transitions.
Copyright/License	arXiv nonexclusive-distrib. 1.0 preprint: © 2015-2024 CERN (License: CC-BY-4.0) publication: © 2015-2024 The Author(s) (License: CC-BY-3.0)

$Feynman diagrams illustrating the steps 1-4 of our analysis (see text). The diagrams display the dominant $Z^\prime$ constribution to $\overline{B}_s-B_s$ mixing, $\overline{B}\to \overline{K}^{(*)}\mu^+\mu^-$, $\overline{B}_s\to\phi\mu^+\mu^-$, $\tau\to 3\mu$, $\tau\to\mu\nu\bar{\nu}$ and $\overline{B}\to\overline{K}^{(*)}\tau^+\mu^-$.$ $Left: Allowed regions in the $\Gamma^{V}_{\mu\mu}- \Gamma^{V}_{\mu\tau}$ plane from $\tau\to\mu\nu\bar{\nu}$ (at $3\,\sigma$ level) for $\Gamma^{V}_{\tau\tau}=0$ (blue), $\Gamma^{V}_{\tau\tau}=-2$ (yellow), $\Gamma^{V}_{\tau\tau}=2$ (green), $\tau\to3\mu$ (red) and $a_{\mu}$ (light gray) for $m_{Z^\prime}=1\,{\rm TeV}$. The $1\,\sigma$ region allowed from NTP lies between the magenta dashed lines. Although NP effects move $a_\mu$ to the right direction, it cannot be explained within our model and we do not impose it as a constraint later on in our analysis. \newline Right: Allowed regions in the $\Gamma^{L}_{\mu\mu} - \Gamma^{L}_{\mu\tau}$ plane: from $\tau\to\mu\nu\bar{\nu}$ for $\Gamma^{L}_{\tau\tau}=0$ (blue), $\Gamma^{L}_{\tau\tau}=-2$ (yellow), $\Gamma^{L}_{\tau\tau}=2$ (green), $\tau\to3\mu$ (red) for $m_{Z^\prime}=1\,{\rm TeV}$. The contour lines denote the shift in $a_{\mu}$ in units of $10^{-10}$. For regions compatible with $\tau\to\mu\nu\bar{\nu}$, the NP effects in $a_\mu$ are rather small. Therefore, we do not impose it as a constraint later on. Bounds from NTP lie outside the plotted range and are not shown.$ $Allowed $2\,\sigma$ regions in the $\Gamma^{V}_{\mu\mu}-\Gamma^{V}_{\mu\tau}$ plane from $\tau\to\mu\nu\bar{\nu}$ for $\Gamma^{V}_{\tau\tau}=0$ (blue), $\Gamma^{V}_{\tau\tau}=-2$ (yellow), $\Gamma^{V}_{\tau\tau}=2$ (green), $\tau\to3\mu$ (red) and $a_{\mu}$ (light grey) for $m_{Z^\prime}=1\,{\rm TeV}$. The dependence of the bounds on the Z' mass is only logarithmic. Although NP effects move $a_\mu$ to the right direction, it cannot be explained within our model and we do not impose it as a constraint later on in our analysis.$ Show more plots

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