Lepton flavor violation in a $Z^{\prime }$ model for the $b\to s$ anomalies

In recent years, several observables associated to semileptonic $b\to s$ processes have been found to depart from their predicted values in the Standard Model, including a few tantalizing hints of lepton flavor universality violation. In this work, we consider an existing model with a massive $Z^{\prime }$ boson that addresses the anomalies in $b\to s$ transitions and extend it with a nontrivial embedding of neutrino masses. We analyze lepton flavor–violating effects, induced by the nonuniversal interaction associated to the $b\to s$ anomalies and by the new physics associated to the neutrino mass generation, and determine the expected ranges for the most relevant observables.

Figure 1

Neutrino mass generation. We note that the model under discussion provides a specific ultraviolet completion to the dimension-8 operator ${\mathcal{O}}_{\nu }=\frac{1}{{\mathrm{\Lambda }}_{\nu }^5}\ell \ell HH\varphi \varphi S$ pointed out in Ref. [21].

Figure 2

Generation of ${\mathcal{O}}_9$ and ${\mathcal{O}}_{10}$. The mixing between the SM fermions and the VL ones induces semileptonic four-fermion interactions.

Figure 3

Correlation between $\mathrm{BR}(\tau \to 3\mu )$ and $\mathrm{BR}(B\to K\tau \mu )$ for three different sets of parameters. This figure has been obtained varying ${({\lambda }_L)}_{13}={({\lambda }_L)}_{22}$. The vertical dashed line corresponds to the Belle experimental bound $\mathrm{BR}(\tau \to 3\mu {)}_{\max }=2.1\times {10}^{-8}$ [61].

Figure 4

Behavior of the ratio $R_{\tau 3\mu }$ as a function of the gauge coupling $g_X$. Several model parameters have been randomly scanned over a wide range of numerical values; see the text for details. The tree-level expression in Eq. (29) and the complete numerical result including one-loop corrections can be very different for $g_X\gtrsim 0.4$.

Figure 5

Feynman diagrams relevant for the calculation of the $\tau \to 3\mu$ amplitude. On the left, the dominant tree-level contribution is shown, whereas the diagram on the right is one of the dominant one-loop contributions. We note that the one-loop diagram on the right should be accompanied by two diagrams with the $Z$ boson line attached to one of the external lepton legs.