The $B^0_s \to \mu^+ \mu^−$ decay, lepton flavour violation and lepton flavour universality at the LHCb experiment

Rare decays of $b$ hadrons are sensitive indirect probes of effects beyond the Standard Model. These are processes that are suppressed because they are forbidden at tree level but they can proceed via loops, where new particles can contribute in principle at the same level as the Standard Model. In particular, $b \to s \ell \ell$ processes give access to many observables where effects of new physics can be observed. Recent results on these searches will be presented, including the new measurement of the $B^0_s \to \mu^{+} \mu^-$ branching fraction, lepton flavour violation and lepton flavour universality measurements performed at the LHCb experiment