Study of $\mathrm{B}_{c}^{+}$ decays to charmonia and three light hadrons
Using proton-proton collision data, corresponding to an integrated luminosity of 9 fb -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 $B^+_c$ → $(ψ(2S)$ →J/$ψπ^+π^-$)$π^+$, $B^+_c$→$ψ(2S)π^+π^-π^+, B^+_c$→ J/$ψK^+π^-π^+$ and $B^+_c$ → J/$ψK^+K^-K^+$ are observed for the first time, and evidence for the $B^+_c$ →$ψ(2S)K^+K^-π^+$, 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.