Study of B+c decays to charmonia and three light hadrons

Using proton-proton collision data, corresponding to an integrated luminos-
ity 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/ψ π+π−)π+, B+c → ψ(2S)π+π−π+, B+
c → J/ψ K+π−π+and B+c → J/ψ K+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.