Explaining $b\to s{\ell }^{+}{\ell }^{-}$ and the Cabibbo angle anomaly with a vector triplet

The most statistically significant hints for new physics in the flavor sector are discrepancies between theory and experiment in $B$ decays to lepton pairs ($b\to s{\ell }^{+}{\ell }^{-}$) and a deficit in the unitarity constraints to the 1st row of the Cabibbo-Kobayashi-Maskawa matrix (the Cabibbo angle anomaly). We propose that these anomalies can be reconciled by a simplified model with massive gauge bosons transforming in the adjoint representation of $SU(2{)}_L$. After calculating the impact of this model on $B$ decays, observables testing charged current lepton flavor universality (LFU), electro-weak precision observables and LHC searches we perform a global fit to all available data. We find that our model can provide a consistent common explanation of both anomalies and that the fit to the data is more than $7\sigma$ better than the fit of the Standard Model. The model also predicts interesting correlations between LFU violation in the charged current and $b\to s{\ell }^{+}{\ell }^{-}$ data which can be tested experimentally in the near future.

Figure 1

Comparison of the different determinations of $V_{us}$ from kaon decays [111], tau decays [16] and superallowed beta decays [143] resulting in the CAA. For the latter, due to its smaller error, we will use the SGPR determination, which was recently confirmed by Ref. [134] in our numerical analysis. However, we confirmed that using CMS instead only has a minor impact on our results. The dashed lines indicate the posteriors for $V_{us}^{\mathcal{L}}$ in our NP fit extracted from the corresponding modes.

Figure 2

Global fit in the $g_{11}^{\ell }-g^q$, $g_{22}^{\ell }-g^q$ and $g_{33}^{\ell }-g^q$ planes for $M_X=10\mathrm{TeV}$. Even though we included the LHC measurements into our global fit, we display them as well as hatched regions to show their constraining power and to verify that treating as a hard cut would not change our results.

Figure 3

Global fit in the $g_{11}^{\ell }-g_{22}^{\ell }$ plane for $M_X=10\mathrm{TeV}$. One can see that the blue region from the $\mathrm{NO}bs\ell \ell$ data overlaps with the yellow one from the $b\to s{\ell }^{+}{\ell }^{-}$ data and $B_s-{\overline{B}}_s$ mixing at the 95% C.L. Note that the overlap between the $\mathrm{NO}bs\ell \ell$ region (which only mildly depends on $\sin {\alpha }_{Z{Z}^{\prime }}$) and the one from $b\to s\ell \ell$ is smaller when mixing is included. However, this does not mean that the agreement with the data is reduced. It is rather due to the fact that the three-dimensional scenario (including mixing) agrees better with the data and its best fit point is further away from the SM hypothesis.

Figure 4

Preferred regions (68%, 95%, 99% C.L.) of the two-dimensional ($C_9^{11}=-C_{10}^{11}$, $C_9^{22}=-C_{10}^{22}$) scenario (blue), and the three-dimensional scenario which includes $C_{10}^U$ (green).