Flavour-tagging and particle-identification calibration in key measurements with electrons at LHCb

The $\textit{CP}$-violation observables $C$ and $S$ are measured in the study of decay-time-dependent $\textit{CP}$ violation in the $B^0 \rightarrow J\mskip -3mu/\mskip -2mu \psi \mskip 2mu K_\text{S}^{0}$ and $B^0 \rightarrow \psi(2S) K_\text{S}^{0}$ decays, where the $J\mskip -3mu/\mskip -2mu \psi \mskip 2mu$ candidate is reconstructed from two electrons and the $\psi(2S)$ candidate from two muons. The analysis uses data recorded by the LHCb experiment at centre-of-mass energies of $7$ and $8$ TeV corresponding to an integrated luminosity of $3 \, \text{fb}^{-1}$ and was recently brought to publication [arXiv: 1709.03944]. This thesis provides the underlying flavour-tagging calibration for the$B^0 \rightarrow J\mskip -3mu/\mskip -2mu \psi \mskip 2mu K_\text{S}^{0}$ decay, which uses $B^{+} \rightarrow J\mskip -3mu/\mskip -2mu \psi \mskip 2mu K^{+}$ and $B^0 \rightarrow J\mskip -3mu/\mskip -2mu \psi \mskip 2mu K^{*}$ decays, where the $J\mskip -3mu/\mskip -2mu \psi \mskip 2mu$ candidates are reconstructed from two electrons. It is the first systematic flavour-tagging study with electron modes included at LHCb. Additionally, first studies with particle-identification (PID) samples with electrons of the years 2015 and 2016 are performed. An algorithm, which was used for the PID calibration in the recently published LHCb measurement [JHEP 08 (2017) 055} of the lepton flavour universality ratio $R_{K^{*}}$ is implemented and validated. The algorithm determines regions of constant efficiency in the PID-calibration samples under the requirement of minimal systematic uncertainties.