Study of $B_c^{+}$ meson decays to charmonia plus multihadron final states

Four decay modes of the $B_c^{+}$ meson into a $J\mathrm{/}\psi$ meson and multiple charged kaons or pions are studied using proton-proton collision data, collected with the~LHCb detector at centre-of-mass energies of 7, 8, and 13~TeV and corresponding to an integrated luminosity of $9$~fb${}^{-1}$. The decay $B_c^{+}\to J\mathrm{/}\psi K^{+}{K}^{-}{\pi }^{+}{\pi }^{+}{\pi }^{-}$ is observed for the first time, and evidence for the $B_c^{+}\to J\mathrm{/}\psi 4{\pi }^{+}3{\pi }^{-}$ decay is found. The decay $B_c^{+}\to J\mathrm{/}\psi 3{\pi }^{+}2{\pi }^{-}$ is observedand and the previous observation of the $B_c^{+}\to \psi (2S){\pi }^{+}{\pi }^{+}{\pi }^{-}$ decay is confirmed using the $\psi (2S)\to J\mathrm{/}\psi {\pi }^{+}{\pi }^{-}$ decay mode. Ratios of the branching fractions of these four $B_c^{+}$ decay channels are measured.