New Physics in $B$ decays

While the LHC did not observe direct evidence for physics beyond the standard model, indirect hints for new physics were uncovered in the flavour sector in the decays $B\to K^*μ^+μ^-$, $B\to Kμ^+μ^-/B\to Ke^+e^-$, $B_s\toϕμ^+μ^-$, $B\to D^{(*)}τν$ and $h\toτ^\pmμ^\mp$. Each observable deviates from the SM predictions at the $2-3\,σ$ level only, but combining all $b\to sμ^+μ^-$ data via a global fit, one finds $4-5\,σ$ difference for NP compared to the SM and combining $B\to D^{*}τν$ with $B\to Dτν$ one obtains $3.9\,σ$. While $B\to D^{(*)}τν$ and $h\toτμ$ can be naturally explained by an extended Higgs sector, the $b\to sμ^+μ^-$ anomalies point at a $Z'$ gauge boson. However, it is also possible to explain $B\to D^{(*)}τν$ and $b\to sμ^+μ^-$ simultaneously with leptoquarks while their effect in $h\toτ^\pmμ^\mp$ is far too small to account for current data. Combining a 2HDM with a gauged $L_μ-L_τ$ symmetry allows for explaining the $b\to sμ^+μ^-$ anomalies in combination with $h\toτ^\pmμ^\mp$, predicting interesting correlations with $τ\to3μ$. In the light of these deviations from the SM we also discuss the possibilities of observing lepton flavour violating $B$ decays (e.g. $B\to K^{(*)}τ^\pmμ^\mp$ and $B_s\toτ^\pmμ^\mp$).

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