Amplitude analysis of $\Lambda_b^0 \rightarrow \Lambda_c^+ \bar{D}^0 K^-$ decays and pentaquark searches in the $\Lambda_c^+ \bar{D}^0$ system at the LHCb experiment

This thesis reports the amplitude analysis of $\Lambda_b^0 \rightarrow \Lambda_c^+ \bar{D}^0 K^-$ decays using data collected by the LHCb experiment from proton-proton collisions, corresponding to an integrated luminosity of 9.1 $\text{fb}^{-1}$. A new amplitude fitter has been developed in the context of this analysis, which exploits novel computing concepts and software frameworks. \noindent Numerous models predict large couplings of the pentaquark candidates observed by LHCb to the $\Lambda_c^+ \bar{D}^0 K^-$ system. This makes the $\Lambda_b^0 \rightarrow \Lambda_c^+ \bar{D}^0 K^-$ channel meaningful to discriminate between models which attempt to describe the internal structure of the pentaquark states. \noindent Amplitude fits are performed to measure the contributions of intermediate resonances to $\Lambda_b^0 \rightarrow \Lambda_c^+ \bar{D}^0 K^-$ decays and upper limits are set for the observation of pentaquark states in this channel. The results obtained are in contrast with the expectations from the most popular theory models which describe the pentaquark states as $\Sigma \overline{\text{D}}^*$-$\Sigma^* \overline{\text{D}}$ molecules.