Full kinematic reconstruction of charged B mesons with the upgraded Inner Tracking System of the ALICE Experiment

In this thesis, the performance of the full kinematic reconstruction of $\mathrm{{B}}^{+}$ mesons in the decay channel $\mathrm{{B}}^{+}\rightarrow\mathrm{\overline{D}^{0}}\pi^{+}$ ($\mbox{$\mathrm{\overline{D}^{0}}\rightarrow \mathrm{K}^{+}\pi^{-}$}$) and charge conjugates for the 0-10 % most central Pb-Pb collisions at $\sqrt{s_{_{\mathrm{NN}}}}$ = 5.5 TeV is demonstrated for the upgraded ALICE Experiment, which is planned before Run 3 of the Large Hadron Collider (LHC), beginning in 2020. Within the scope of the foreseen detector and readout upgrades to inspect all Pb-Pb collisions at their interaction rate of 50 kHz, in particular through the installation of a new high-granularity pixel inner tracker, for the first time these rare signals will become accessible using full kinematic reconstruction in central Pb-Pb collisions in ALICE at mid-rapidity at the LHC. Topological and kinematic criteria are used to select the beauty signal against the large combinatorial and correlated background. In addition to available full Monte Carlo (MC) simulations, a fast MC simulation, which includes parameterizations of all relevant detector effects, was developed and is now generally available for all rare probe studies with the upgraded ALICE detector. The fast simulation was used to improve the estimate on the residual combinatorial background in order to maximize the expected signal-to-background ratio and statistical significance. Within the uncertainties of the expected signal yield, a significant measurement ($\geq\,5$) will be possible down to $p_{\rm T}$ $\geq\,$2.0 GeV/$c$, corresponding to about 88 % of the yield. The signal-to-background ratio lies between 0.01 and 4.0, increasing with $p_{\rm T}$. The required reference statistics in p+p collisions at $\sqrt{s}\,=\,5.5\,$TeV was estimated to be about 100 pb$^{-1}$. Considering the calculated expected statistics, the precision of the measurements of the nuclear modification factor $R_{\mathrm{AA}}$ and the elliptic flow $v_{2}$ were estimated. A measurement of the theoretically predicted $R_{\mathrm{AA}}$ of 0.2-0.5 above $p_{\rm T}\,\geq\,5.0\,\mathrm{GeV/}c$ will be possible, while the sensitivity for lower momenta on the enhancement above $R_{\mathrm{AA}}$ = 1.0 is strongly model dependent. The separation power between the theoretically predicted $v_{2}$ and a non-flow scenario is within 1.6-5.3 $\sigma$ for central and more peripheral collisions, depending on the actual magnitude and the available statistical precision.