High Level Trigger software performance profiling and $\chi_{b}$ production study at the LHCb experiment

Trigger is a crucial item in experiments at hadron colliders. In this thesis, a software profiling tool has been developed, which helps to analyze and improve the performance of the High Level Trigger software of the LHCb experiment. This tool is able to identify spots where the execution time of the trigger application is slow, thereby allowing the optimization of the trigger decision speed and minimizing dead times during data taking. The highly efficient LHCb trigger allows precision studies of decays of heavy flavoured particles in final states with muons. In this thesis, a study of $\chi_b$ production at LHCb is performed on a proton-proton collisions data set, corresponding to 3 fb$^{-1}$ integrated luminosity, collected at center-of-mass energies of $\sqrt{s}$=7 and 8 TeV. Radiative $\chi_b$ transitions to $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ are reconstructed, where the $\Upsilon(nS)$, indicated generally as $\Upsilon$ in the following, decays in two muon. The fraction of $\Upsilon$ originating from $\chi_b$ decays are measured as a function of $\Upsilon$ transverse momentum in the LHCb rapidity range $2.0 < y^{\Upsilon}<4.5$. The analyzed transverse momentum ranges for decays to $\Upsilon(1S)$, $\Upsilon(2S)$ and $\Upsilon(3S)$ are $6 < p_T^{\Upsilon(1S)}<40$~GeV/c, $18 < p_T^{\Upsilon(2S)}<40$~GeV/c and $27 < p_T^{\Upsilon(3S)}<40$ GeV/c, respectively. The measurement of $\Upsilon(3S)$ fractions in radiative $\chi_b(3P)$ decay is performed for the first time. The obtained $\Upsilon(3S)$ fractions are $42 \pm 12(stat){}^{+8.9}_{-11.6}(syst)^{+2.7}_{-3.1}(syst.pol) \%$ and $41 \pm 8(stat){}^{+1.3}_{-8.6}(syst)^{+2.6}_{-3.1}(syst.pol) \% $ for $\sqrt{s}$=7 and 8 TeV, respectively. The measured $\chi_{b1}(3P)$ mass is $10{,}508 \pm 2(stat) \pm 8(syst)$ MeV/c$^2$.