Rare hadronic decays of charged B mesons at LHCb

This thesis documents two searches for rare hadronic decays of $B^+$ mesons with the LHCb experiment at the Large Hadron Collider. Both are performed using proton-proton collision data corresponding to an integrated luminosity of 4.8 fb$^{-1}$, collected at centre-of-mass energies of 7, 8 and 13 TeV during 2011-2016. The first is a search for $B^{+} \to D_s^{+}K^{+}K^{-}$ decays. A significant signal is observed for the first time and the branching fraction is determined to be \begin{equation*} \mathcal{B}(B^{+} \to D_s^{+}K^{+}K^{-} ) = (7.1 \pm 0.5 \pm 0.6 \pm 0.7) \times 10^{-6}, \end{equation*} \noindent where the first uncertainty is statistical, the second systematic and the third due to the uncertainty on the branching fraction of the normalisation mode $B^{+} \to D_s^{+}\overline{D}^{0}$. The second search is performed for the rare pure annihilation decay $B^{+} \to D_s^{+}\phi$. No significant signal is observed and a limit of \begin{equation*} \mathcal{B}(B^{+} \to D_s^{+}\phi) < 4.9 \times 10^{-7} \end{equation*} is set on the branching fraction at 95 % confidence level.