Study of 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 Bc+ meson into a J/ψ or ψ(2S) meson and three charged hadrons, kaons or pions, are studied. The decays Bc+ → (ψ(2S) → J/ψπ⁺π⁻)π⁺, Bc+ → ψ(2S)π⁺π⁻π⁺, Bc+ → J/ψK⁺π⁻π⁺ and Bc+ → J/ψK⁺K⁻K⁺ are observed for the first time, and evidence for the Bc+ → 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 Bc+ 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. [Figure not available: see fulltext.]