Study of <i>B_c</i><SUP>+</SUP> meson decays to charmonia plus multihadron final states

Four decay modes of the B _c ⁺ meson into a J/ψ 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 ⁺→ J/ψK ⁺K ⁻π ⁺π ⁺π ⁻ is observed for the first time, and evidence for the B _c ⁺→ J/ψ4π ⁺3π ⁻ decay is found. The decay B _c ⁺→ J/ψ3π ⁺2π ⁻ is observed and the previous observation of the B _c ⁺→ ψ(2S)π ⁺π ⁺π ⁻ decay is confirmed using the ψ(2S) → J/ψπ ⁺π ⁻ decay mode. Ratios of the branching fractions of these four B _c ⁺ decay channels are measured.