Search for Charged Lepton Flavour Violation at LHCb experiment

The thesis describes searches for charged lepton flavour violation in the process $\tau^-\rightarrow\mu^-\mu^+\mu^-$. The study is performed at the LHCb experiment data sample corresponding to an integrated luminosity of 3 fb$^{-1}$ of proton-proton collisions at a centre-of-mass energy of 7 $TeV$ (8 $TeV$), collected in 2011 (2012), respectively. No significantly statistical signal of the decay in question has been found and as a result the upper limit was set: $B(\tau^-\rightarrow\mu^-\mu^+\mu^-)<4.6 \times 10^{-8}$ at $90\%$ confidence level. The limit was then interpreted in terms of an effective field theory approach including beyond the Standard Model operators with different lepton chirality structures. We found that the limits are within the range: $(4.1-6.8) \times 10^{-8}$ at $90\%$ confidence level. The thesis presents also the combination of upper limits for all lepton flavour violating $\tau$ lepton decays. For the decay in question, i.e. $\tau^-\rightarrow\mu^-\mu^+\mu^-$, the combination leads to the upper limit of $B(\tau^-\rightarrow\mu^-\mu^+\mu^-) <1.2 \times 10^{-8}$ at $90\%$ confidence level.