Search for the lepton-flavour violating decay $\tau^- \to \phi \mu^-$ at LHCb

Lepton flavour conservation is an approximate symmetry at the perturbative level in the Standard Model of Particle Physics, and neutrino oscillations represent the first and, so far, the only observed violation of this symmetry. Neutrino mixing implies that lepton flavour violation also occurs in charged decays, albeit with extremely low branching fractions of order O(10−50). The direct observation of charged lepton-flavour violating processes would be an indisputable sign of new physics beyond the Standard Model. The search for the tau- -> Phi mu- decay allows to test several new physics scenarios, such as vector leptoquark models which predict values for the branching ratio up to 10-8, close to current experimental limits. This contribution describes the search for the tau- -> phi mu- decay at the LHCb experiment at CERN, conducted for the first time in hadronic collisions. An expected upper limit of BR(tau- -> phi mu-) < 1.1 x 10-6 at 90% of confidence level was achieved by performing a blind analysis using the full Run 2 data sample. A new analysis is ongoing with the goal of improving this limit, looking also at the Run 3 data being collected by the brand-new LHCb-Upgrade I detector.