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We present a search for the B0s→π+π−μ+μ− and B0→π+π−μ+μ− decays using data collected by the LHCb detector in proton-proton collisions at centre-of-mass energies of 7 and 8TeV and corresponding to an integrated luminosity of 3 fb−1. We obtain the first observation of the B0s→π+π−μ+μ− decay with a statistical significance of 7.2σ and the first evidence of the B0→π+π−μ+μ− decay with a statistical significance of 4.8σ. The branching ratios of these decays are measured to beB(B0s→π+π−μ+μ−) = (8.6±1.5 (stat)±0.7 (syst)±0.7(norm))×10−8 and B(B0→π+π−μ+μ−) = (2.11±0.51 (stat)±0.15 (syst)±0.16(norm))×10−8, where the third uncertainty is due to the branching fraction of the decay B0→ J/ψ(→μ+μ−)K∗(892)0(→K+π−), used as a normalisation. We present also the first measurement of the production cross-section of J/ψ mesons in proton-proton collisions at centre-of-mass energy of 13TeV using the data collected by LHCb in 2015 and corresponding to an integrated luminosity of 3.02 ± 0.12 pb−1. The production cross-section is measured as a function of the transverse momentum pT and the rapidity y of the J/ψ meson in the region pT < 14GeV/c and 2.0 < y < 4.5, for both prompt J/ψ mesons and J/ψ mesons from b-hadron decays. The production cross-sections integrated over the kinematic coverage are found to be 15.30±0.03(stat)±0.86(syst)μb for prompt J/ψ and 2.34±0.01(stat)±0.13(syst)μb for J/ψ from b-hadron decays, assuming zero polarisation of the J/ψ meson. The ratios between these cross sections and the ones measured at the centre-of-mass-energy of 8TeV are also determined and compared with theoretical expectations. This measurement also validated a novel approach for online collection of ready-to-use data, which was implemented for the first time. The study of the performances of the Silicon Tracker of the LHCb experiment during the 2012 and 2015 years of operation is also reported, and my contribution to a novel monitoring system of this sub-detector is presented.

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