Measurement of the ratio of the Bc⁺ → J / ψ τ⁺ ν_τ and Bc⁺ → J / ψ μ⁺ ν_μ branching fractions using three-prong τ lepton decays

The ratio between the 𝐵⁺_𝑐→𝐽/𝜓⁢𝜏⁺⁢𝜈_𝜏 and 𝐵⁺_𝑐→𝐽/𝜓⁢𝜇⁺⁢𝜈_𝜇 branching fractions is measured using a data sample of proton-proton collisions collected by CMS at a center-of-mass energy of 13 TeV in the years 2016–2018 and corresponding to an integrated luminosity of 138 fb⁻¹. The 𝐽/𝜓 meson is identified through its 𝐽/𝜓 →𝜇⁺⁢𝜇^− decay and the tau lepton is reconstructed in the hadronic three-prong final state. The measured ratio of branching fractions in this tau decay mode, ℛʰᵃᵈ𝐽/𝜓 =1.0⁢4+0.50−0.44, is combined with the previous analysis based on the 𝜏⁺→𝜇⁺⁢𝜈_𝜇⁢𝜈̄_𝜏$ leptonic decay channel, leading to ℛ$𝐽/𝜓$ =0.49±0.26. As this result is consistent with the standard model prediction of 0.258 ±0.004, no evidence of lepton flavor universality violation is found.