Search for lepton-flavour violating decays of the Higgs boson at the LHC

In this thesis, a search for lepton-flavour violating (LFV) decays of the Higgs boson to an electron and a tau lepton is presented. LFV decays of the Higgs boson are forbidden in the Standard Model of particle physics (SM). However, extensions of the SM, such as multi-Higgs doublet models,can introduce LFV Yukawa couplings.The search is performed for tau decays to a muon and corresponding neutrinos. Proton-proton collision data were collected with the CMS detector in 2012 and 2015, while the LHC was operating at a centre-of-mass energy of $\sqrt{s}=8~\text{TeV}$ and $\sqrt{s}=13~\text{TeV}$, respectively, accounting for integratedluminosities of $19.7~\text{fb}^{-1}$ and $2.3~\text{fb}^{-1}$. The dominant SM background contributions for this search are coming from the Drell-Yan process,misidentified leptons, and the top-quark pair-production process. Top-quarkspredominantly decay into a b quark and a W boson. Jets originating from b quarks can be identified, with processes including c-quark jets being the mainbackground. The impact of heavy flavour modelling on the misidentification of c-quark jets as b-quark jets is studied. Differencesin the charmed-hadron modelling regarding the production fraction, decay, and momentum fractions affect the discrimination. Furthermore, themisidentification probability is found to depend on the type of the charmed-hadron. In the LFV search, a new algorithm is developed to improve the optimisation of the event selection, which determines iteratively the best set of requirementson the discriminating variables. The search is done in three exclusive jet categories.Improvements on the modelling on the misidentified lepton background are studied.No excess of events is observed in the reconstructed mass distribution of the Higgs boson. An observed (expected) 95% CL upper limit on the branching fraction$B(H\rightarrow\text{e}\tau)<0.74\%$ ($<0.85^{+0.37}_{-0.25}\%$) can be set using the collision data at $\sqrt{s}=8~\text{TeV}$. Results were combined with the channel for hadronic taudecays and an observed (expected) 95% CL upper limit on the branching fraction $B(H\rightarrow\text{e}\tau)<0.69\%$ ($<0.75\%$) was obtained, with the leptonic channel being themost sensitive one. This model independent limit improves upon indirect limits from low energy measurements. An observed (expected) 95% CL upper limit onthe branching fraction $B(H\rightarrow\text{e}\tau)<2.01\%$ ($<1.32^{+0.59}_{-0.39}\%$) can be set using the collision data at $\sqrt{s}=13~\text{TeV}$. This limit is weaker due to smallerluminosity. However, the sensitivity was improved with respect to the $8~\text{TeV}$ analysis, which will be important for the analysis of the2016 collision data with higher integrated luminosity.