Measurement of the Ratio of the B^0→D^*-τ^+ν_τ and B^0→D^*-μ^+ν_μ Branching Fractions Using Three-Prong τ-Lepton Decays

The ratio of branching fractions R(D^*-)≡B(B^0→D^*-τ^+ν_τ)/B(B^0→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. For the first time, R(D^*-) is determined using the τ-lepton decays with three charged pions in the final state. The B^0→D^*-τ^+ν_τ yield is normalized to that of the B^0→D^*-π^+π^-π^+ mode, providing a measurement of B(B^0→D^*-τ^+ν_τ)/B(B^0→D^*-π^+π^-π^+)=1.97±0.13±0.18, where the first uncertainty is statistical and the second systematic. The value of B(B^0→D^*-τ^+ν_τ)=(1.42±0.094±0.129±0.054)% is obtained, where the third uncertainty is due to the limited knowledge of the branching fraction of the normalization mode. Using the well-measured branching fraction of the B^0→D^*-μ^+ν_μ decay, a value of R(D^*-)=0.291±0.019±0.026±0.013 is established, where the third uncertainty is due to the limited knowledge of the branching fractions of the normalization and B^0→D^*-μ^+ν_μ modes. This measurement is in agreement with the standard model prediction and with previous results.