Study of the $B_c^+$ decays into charmonia and three light hadrons
Using proton-proton collision data, corresponding to an integrated luminosity of $9fb^{-1}$ collected with the LHCb detector, seven decay modes of the $B_c^+$ meson into a $J/ψ$ or $ψ(2S)$ meson and three charged hadrons, kaons or pions, are studied. The decays $B_c^+\rightarrow ( ψ(2S) \rightarrow J/ψπ^+ π^-)π^+ $, $B_c^+\rightarrow ψ(2S)π^+π^+π^-$, $B_c^+\rightarrow J/ψK^+π^+π^-$ and $B_c^+\rightarrow K^+K^+K^-$ are observed for the first time, and evidence for the $B_c^+\rightarrow ψ(2S)K^+K^-π^+$ decay is found, where $J/ψ$ and $ψ(2S)$ mesons are reconstructed in their dimuon decay modes. The ratios of branching fractions between the different $B_c^+$ decays are reported as well as the fractions of the decays proceeding via intermediate resonances. The results largely support the factorisation approach used for a theoretical description of the studied decays.