Unified explanation of the anomalies in semileptonic $B$ decays and the $W$ mass

The discrepancies between the measurements of rare (semi)leptonic $B$ decays and the corresponding Standard Model predictions point convincingly toward the existence of new physics for which a heavy neutral gauge boson ($Z^{\prime }$) is a prime candidate. However, the effect of the mixing of the $Z^{\prime }$ with the SM $Z$, even though it cannot be avoided by any symmetry, is usually assumed to be small and thus neglected in phenomenological analyses. In this paper we point out that a mixing of the naturally expected size leads to lepton flavor universal contributions, providing a very good fit to $B$ data. Furthermore, the global electroweak fit is affected by $Z-Z^{\prime }$ mixing where the tension in the $W$ mass, recently confirmed and strengthened by the CDF measurement, prefers a nonzero value of it. We find that a $Z^{\prime }$ boson with a mass between $\approx 1–5\mathrm{TeV}$ can provide a unified explanations of the $B$ anomalies and the $W$ mass. This strongly suggest that the breaking of the new gauge symmetry giving raise to the $Z^{\prime }$ boson is linked to electroweak symmetry breaking with intriguing consequences for model building.

Figure 1

Preferred $1\sigma$, $2\sigma$ and $3\sigma$ regions in the $({\mathcal{C}}_{9\mu }^{\mathrm{V}},{\mathcal{C}}_{10}^{\mathrm{U}}=-k{\mathcal{C}}_9^{\mathrm{U}})$ plane for the scenario discussed in the paper, including all available $b\to s{\ell }^{+}{\ell }^{-}$ data and using the most updated version of ACDMN code [14]. Note that the SM case corresponds to the (0,0) point.

Figure 2

Global fit to EW data, neutrino trident production, LEP bounds on 4-lepton contact interactions and $\tau \to \mu \nu \nu$ data with vectorial flavor diagonal couplings $g_{ii}^L=g_{ii}^R=g_i^V$. Here we marginalized over the $Z-Z^{\prime }$ mixing angle $\xi$. The 68% and 95% confidence level regions are shown for a $Z^{\prime }$ mass of 2 TeV. Note that a preference for the $L_{\mu }-L_{\tau }$ scenario emerges.

Figure 3

Global fit EW precision observables, neutrino trident production, LEP bounds on 4-lepton contact interactions and $\tau \to \mu \nu \nu$ data (orange) and $b\to s{\ell }^{+}{\ell }^{-}$ data (blue) in the $g^{\prime }$—$\sin \xi$ plane for $m_{Z^{\prime }}=2\mathrm{TeV}$ and $m_{Z^{\prime }}=3\mathrm{TeV}$. One can see that both regions overlap nicely and that a nonzero value of the mixing angle is preferred.