A study of $B_{(s)}^{0}\rightarrow J/\psi \eta^{(')}$ decays with the LHCb experiment

The main objective of this thesis is the study of the decays of $B_{(s)}^{0}\rightarrow J/\psi \eta^{(')}$ with the LHCb experiment at CERN's Large Hadron Collider. At the quark level, these decays proceed by colour-suppressed $b \rightarrow c \overline{c} s$ transitions for the $B_{s}$ decays or Cabibbo-suppressed $b \rightarrow c \overline{c} d$ transitions for the $B^{0}$ decays. These neutral $B$ mesons can oscillate between the states of particle $B$ and antiparticle $\overline{B}$. As the final state $J/\psi \eta^{(')}$ is accessible to both $B$ mesons and $\overline{B}$ anti-mesons, it is possible to observe a violation of charge-parity symmetries ($CP$). This violation arises from the interference in the decays with and without $B_{s}-\overline{B}_{s}$ oscillations. This can be measured from the decaytime asymmetry between $B_{(s)}^{0}\rightarrow J/\psi \eta^{(')}$ and $\overline{B}_{(s)}^{0}\rightarrow J/\psi \eta^{(')}$ decays which is related to the difference in decay width $\Delta\Gamma_{s}$ and the phase $\phi_{s}$. A future measurement of $\phi_{s}$ in these channels can then be used to test the Standard Model. However, there is a contribution to this measurement that comes from loop decays called penguin diagrams. It is therefore necessary to constrain the parameters of the penguin diagrams. This is partly what is studied in this thesis through the following measurements of the branching ratios of the decays $B_{(s)}^{0}\rightarrow J/\psi \eta^{(')}$ and of the mixing between the mesons $\eta$ and $\eta^{'}$. In the measurement of this mixing, there could also enter a small contribution of a hypothetical meson formed by valence gluons, called gluonium or glueballs. This leads to the measurement of two mixing angles from the different branching ratio fractions. One of the angles is associated with the mixing between the quark states of the mesons $\eta$ and $\eta^{'}$ and the other for their mixing with the gluonium state. The objective of this thesis is to measure these branching ratios and mixing angles using the final states $J/\psi \rightarrow \mu^{+}\mu^{-}$ and the decays of mesons $\eta$ and $\eta^{'}$ in the final states: $\eta\rightarrow\pi^{+}\pi^{-}\gamma$, $\eta\rightarrow\pi^{+}\pi^{-}(\pi^{0}\rightarrow\gamma\gamma)$, $\eta^{'}\rightarrow(\rho^{0}\rightarrow\pi^{+}\pi^{-})\gamma$ and $\eta^{'}\rightarrow\pi^{+}\pi^{-}(\eta\rightarrow\gamma\gamma)$. These measurements were performed using a sample of data recorded in proton-proton collisions at $\sqrt{s}$ = 7, 8 and 13\,TeV which corresponds to an integrated luminosity of about 9\,fb$^{-1}$ that were collected during LHC operation periods I and II. The measurements of the final states $\eta$ and $\eta^{'}$ are complicated by the presence of photons and the hadronic environment. It was therefore necessary to also perform a simulation performance analysis to calibrate the efficiency of the photon and $\pi^{0}$ reconstruction.