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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.

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 regions in the $\Gamma^{L}_{sb}/M_{Z^\prime}- \Gamma^{R}_{sb}/M_{Z^\prime}$ plane from $B_s$-$\overline{B}_s$ mixing (blue), and from the $C^{\mu\mu}_9-C^{(\prime)\mu\mu}_9$ fit of Ref.~\cite{Altmannshofer:2014rta} to $B\to K^*\mu^+\mu^-$, $B_s\to\phi\mu^+\mu^-$ and $R(k)$, with $\Gamma^V_{\mu\mu}=\pm 1$ (red), $\Gamma_{\mu\mu}^V=\pm 0.5$ (orange) and $\Gamma^V_{\mu\mu}=\pm0.3$ (yellow). Note that the allowed regions with positive (negative) $ \Gamma^{L}_{sb}$ correspond to positive (negative) $\Gamma^V_{\mu\mu}$.

Maximal value of ${\rm Br}[B\to K^*\tau^\pm\mu^\mp]$ (red), ${\rm Br}[B\to K\tau^\pm\mu^\mp]$ (blue) and ${\rm Br}[B_s\to \tau^\pm\mu^\mp]$ (green) in scenario 1 as a function of $C_9^{\mu\mu}$ for a fine-tuning of $X_{B_s}=100$ (solid lines) and $X_{B_s}=20$ (dashed lines). The bounds are shown for $m_{Z'}=1$ TeV but their dependence on the Z' mass is only logarithmic.

Maximal value of ${\rm Br}[B\to K^*\tau^\pm\mu^\mp]$ (red), ${\rm Br}[B\to K\tau^\pm\mu^\mp]$ (blue) and ${\rm Br}[B_s\to \tau^\pm\mu^\mp]$ (green) in scenario 1 as a function of $C_9^{\mu\mu}$ for a fine-tuning of $X_{B_s}=100$ (solid lines) and $X_{B_s}=20$ (dashed lines). The bounds are shown for $m_{Z'}=1$ TeV but their dependence on the Z' mass is only logarithmic.

Left: Maximal value of ${\rm Br}[B\to K^*\tau^\pm\mu^\mp]$ (red), ${\rm Br}[B\to K\tau^\pm\mu^\mp]$ (blue) and ${\rm Br}[B_s\to \tau^\pm\mu^\mp]$ (green) in scenario 1 as a function of $C_9^{\mu\mu}$ for a fine-tuning of $X_{B_s}=100$ (solid lines) and $X_{B_s}=20$ (dashed lines). Right: Same as the left plot for scenario 2. The white area represents the $2\,\sigma$-allowed range for $C_9^{\mu\mu}$ from the fits of Ref.~\cite{Altmannshofer:2014rta, Altmannshofer:2015sma}.

Left: Maximal value of ${\rm Br}[B\to K^*\tau^\pm\mu^\mp]$ (red), ${\rm Br}[B\to K\tau^\pm\mu^\mp]$ (blue) and ${\rm Br}[B_s\to \tau^\pm\mu^\mp]$ (green) in scenario 1 as a function of $C_9^{\mu\mu}$ for a fine-tuning of $X_{B_s}=100$ (solid lines) and $X_{B_s}=20$ (dashed lines). Right: Same as the left plot for scenario 2. The white area represents the $2\,\sigma$-allowed range for $C_9^{\mu\mu}$ from the fits of Ref.~\cite{Altmannshofer:2014rta, Altmannshofer:2015sma}.

Maximal value of ${\rm Br}[B\to K^*e^\pm\mu^\mp]$ (red), ${\rm Br}[B\to K e^\pm\mu^\mp]$ (blue) and ${\rm Br}[B_s\to e^\pm\mu^\mp]$ (green) in scenario 1 as a function of $C_9^{\mu\mu}$ for a fine-tuning of $X_{B_s}=100$ (solid lines) and $X_{B_s}=20$ (dashed lines). Note that the limit on ${\rm Br}[B_s\to e^\pm\mu^\mp]$ is so stringent that it cannot be resolved in the plot. The white area represents the $2\,\sigma$-allowed range for $C_9^{\mu\mu}$ from the fits of Ref.~\cite{Altmannshofer:2014rta, Altmannshofer:2015sma}.