Search for the lepton flavour violating decay $\tau^+\to\mu^+\mu^-\mu^+$ with the LHCb experiment

This thesis presents a search for the lepton flavour violating decay $\tau^+\to\mu^+\mu^-\mu^+$ using data collected by the LHCb experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 5.4~fb$^{-1}$. As of today, no lepton flavour violation has been observed in decays of charged leptons. When accounting for neutrino oscillations in the Standard Model, such processes are expected at undetectable decay rates, thus the observation of the $\tau^+\to\mu^+\mu^-\mu^+$ decay would be a clear sign of new physics. Even if the decay is not observed, improving the upper limit on the branching fraction of $\tau^+\to\mu^+\mu^-\mu^+$ would allow us to constrain theories of physics beyond the Standard Model that predict a decay rate within the sensitivity of the current experimental facilities. The main challenge of the analysis is the identification and rejection of the background sources, originating from accidental combinations of tracks wrongly associated with a $\tau$ decay and from the misidentification of hadrons ($\pi^{\pm}$, $K^{\pm}$) coming from $D^+$ or $D_s$ decays. The analysis is designed by removing the signal region in data in order to avoid biases in the optimisation of the signal selection. The background suppression is achieved by means of multivariate classification models trained to distinguish between signal and background events. The number of $\tau$ leptons produced in the LHCb acceptance is normalised to the yield observed in the $D_s^+\to\phi(\mu^+\mu^-)\pi^+$ channel. An expected upper limit of $$\mathcal{B}(\tau^+\to\mu^+\mu^-\mu^+)<1.8(2.1)\times 10^{-8}$$ is found at 90%(95%) confidence level using the $CL_s$ method.