Test of lepton flavour universality using $B^0 \to D^{*-}τ^+ν_τ$ decays with hadronic $τ$ channels
The branching fraction $\mathcal{B}(B^0 \to D^{*-}τ^+ν_τ)$ is measured relative to that of the normalization mode $B^0 \to D^{*-}π^+π^-π^+$ using hadronic $τ^+ \to π^+π^-π^+(π^0)\overlineν_τ$ decays in proton-proton collision data at a center-of-mass energy of 13 TeV collected by the LHCb experiment, corresponding to an integrated luminosity of 2 fb$^{-1}$. The measured ratio is $\mathcal{B}(B^0 \to D^{*-}τ^+ν_τ)/\mathcal{B}(B^0 \to D^{*-}π^+π^-π^+) = 1.79 \pm 0.11 \pm 0.11$, where the first uncertainty is statistical and the second is related to systematic effects. Using established branching fractions for the $B^0 \to D^{*-}π^+π^-π^+$ and $B^0 \to D^{*-}μ^+ν_μ$ modes, the lepton universality test, $\mathcal{R}(D^{*-}) \equiv \mathcal{B}(B^0 \to D^{*-}τ^+ν_τ)/\mathcal{B}(B^0 \to D^{*-}μ^+ν_μ)$ is calculated, $$ \mathcal{R}(D^{*-}) = 0.260 \pm 0.015 \pm 0.016 \pm 0.012\, , $$ where the third uncertainty is due to the uncertainties on the external branching fractions. This result is consistent with the Standard Model prediction and with previous measurements.