Measurement of the Ratio of Branching Fractions B(B_c^+→J/ψτ^+ν_τ)/B(B_c^+→J/ψμ^+ν_μ)

A measurement is reported of the ratio of branching fractions R(J/ψ)=B(B_c^+→J/ψτ^+ν_τ)/B(B_c^+→J/ψμ^+ν_μ), where the τ^+ lepton is identified in the decay mode τ^+→μ^+ν_μν[over ¯]_τ. This analysis uses a sample of proton-proton collision data corresponding to 3.0  fb^-1 of integrated luminosity recorded with the LHCb experiment at center-of-mass energies of 7 and 8 TeV. A signal is found for the decay B_c^+→J/ψτ^+ν_τ at a significance of 3 standard deviations corrected for systematic uncertainty, and the ratio of the branching fractions is measured to be R(J/ψ)=0.71±0.17(stat)±0.18(syst). This result lies within 2 standard deviations above the range of central values currently predicted by the standard model.