New Physics in Flavour Observables

LHCb found hints for physics beyond the Standard Model (SM) in $B\to K^\mu^+\mu^-$,$R(K)$and$B_s\to\phi\mu^+\mu^-$. These intriguing hints for NP have recently been confirmed by the LHCb measurement of $R(K^{\ast })$ giving a combined significance for NP above the $5\sigma$ level. In addition, the BABAR, BELLE and LHCb results for $B\to D^{(\ast )}\tau \nu$ also point towards lepton flavour universality (LFU) violating new physics (NP). Furthermore, there is the long-standing discrepancy between the measurement and the theory prediction of the anomalous magnetic moment of the muon ($a_{\mu }$) at the $3\sigma$ level. Concerning NP effects, $b\to s{\mu }^{+}{\mu }^{-}$ data can be naturally explained with a new neutral gauge bosons, i.e. a $Z^{\mathrm{\prime }}$ but also with heavy new scalars and fermions contributing via box diagrams. Another promising solution to $b\to s{\mu }^{+}{\mu }^{-}$, which can also explain $B\to D^{()}\tau\nu$, are leptoquarks. Interestingly, leptoquarks provide also a viable explanation of $a_{\mu }$ which can be tested via correlated effects in $Z\to {\mu }^{+}{\mu }^{-}$ at future colliders. Considering leptoquark models, we show that an explanation of $B\to D^{(\ast )}\tau \nu$ predicts an enhancement of $b\to s\tau^+\tau^-$ processes by around three orders of magnitude compared to the SM. In case of a simultaneous explanation of $B\to D^{(\ast )}\tau \nu$ and $b\to s\mu^+\mu^-$data,sizableeffectsin$b\to s\tau\mu$ processes are predicted.