Test of lepton flavor universality by the measurement of the B⁰ →d^∗-τ⁺ν_τ branching fraction using three-prong τ decays

The ratio of branching fractions R(D^∗-)≡B(B⁰→D^∗-τ⁺ν_τ)/B(B⁰→D^∗-μ⁺ν_μ) is measured using a data sample of proton-proton collisions collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3 fb^-1. The τ lepton is reconstructed with three charged pions in the final state. A novel method is used that exploits the different vertex topologies of signal and backgrounds to isolate samples of semitauonic decays of b hadrons with high purity. Using the B⁰→D^∗-π⁺π^-π⁺ decay as the normalization channel, the ratio B(B⁰→D^∗-τ⁺ν_τ)/B(B⁰→D^∗-π⁺π^-π⁺) is measured to be 1.97±0.13±0.18, where the first uncertainty is statistical and the second systematic. An average of branching fraction measurements for the normalization channel is used to derive B(B⁰→D^∗-τ⁺ν_τ)=(1.42±0.094±0.129±0.054)%, where the third uncertainty is due to the limited knowledge of B(B⁰→D^∗-π⁺π^-π⁺). A test of lepton flavor universality is performed using the well-measured branching fraction B(B⁰→D^∗-μ⁺ν_μ) to compute R(D^∗-)=0.291±0.019±0.026±0.013, where the third uncertainty originates from the uncertainties on B(B⁰→D^∗-π⁺π^-π⁺) and B(B⁰→D^∗-μ⁺ν_μ). This measurement is in agreement with the Standard Model prediction and with previous measurements.