Explaining the LHC flavour anomalies

The LHC observed deviations from the Standard Model (SM) in the flavour sector: LHCb found a $4.3\,\sigma$ discrepancy compared to the SM in $b\to s\mu\mu$ transitions and CMS reported a non-zero measurement of $h\to\mu\tau$ with a significance of $2.4\,\sigma$. Here we discuss how these deviations from the SM can be explained, focusing on two models with gauged $L_\mu-L_\tau$ symmetry. The first model contains two scalar doublets and vector-like quarks while the second one employs three scalar doublets but does not require vector-like fermions. In both models, interesting correlations between $b\to s\mu\mu$ transitions, $h\to\mu\tau$, and $\tau\to3\mu$ arise.