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 $Bto K^*mu^+mu^-$, $Bto Kmu^+mu^-/Bto Ke^+e^-$, $B_stophimu^+mu^-$, $Bto D^{(*)}tau u$ and $htotau^pmmu^mp$. Each observable deviates from the SM predictions at the $2-3,sigma$ level only, but combining all $bto smu^+mu^-$ data via a global fit, one finds $4-5,sigma$ difference for NP compared to the SM and combining $Bto D^{*}tau u$ with $Bto Dtau u$ one obtains $3.9,sigma$. While $Bto D^{(*)}tau u$ and $htotaumu$ can be naturally explained by an extended Higgs sector, the $bto smu^+mu^-$ anomalies point at a $Z$ gauge boson. However, it is also possible to explain $Bto D^{(*)}tau u$ and $bto smu^+mu^-$ simultaneously with leptoquarks while their effect in $htotau^pmmu^mp$ is far too small to account for current data. Combining a 2HDM with a gauged $L_mu-L_tau$ symmetry allows for explaining the $bto smu^+mu^-$ anomalies in combination with $htotau^pmmu^mp$, predicting interesting correlations with $tauto3mu$. In the light of these deviations from the SM we also discuss the possibilities of observing lepton flavour violating $B$ decays (e.g. $Bto K^{(*)}tau^pmmu^mp$ and $B_stotau^pmmu^mp$).