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The branching fraction $\mathcal{B}(B^0 \to D^{*-}\tau^+\nu_{\tau})$ ismeasured relative to that of the normalisation mode $B^0 \toD^{*-}\pi^+\pi^-\pi^+$ using hadronic $\tau^+ \to\pi^+\pi^-\pi^+(\pi^0)\bar{\nu}_{\tau}$ decays in proton-proton collision dataat a centre-of-mass energy of 13 TeV collected by the LHCb experiment,corresponding to an integrated luminosity of 2 fb$^{-1}$. The measured ratio is$\mathcal{B}(B^0 \to D^{*-}\tau^+\nu_{\tau})/\mathcal{B}(B^0 \toD^{*-}\pi^+\pi^-\pi^+)= 1.70 \pm 0.10^{+0.11}_{-0.10}$, where the firstuncertainty is statistical and the second is related to systematic effects.Using established branching fractions for the $B^0 \to D^{*-}\pi^+\pi^-\pi^+$and $B^0 \to D^{*-} \mu^+\nu_\mu$ modes, the lepton universality test,$\mathcal{R}(D^{*-}) \equiv \mathcal{B}(B^0 \toD^{*-}\tau^+\nu_{\tau})/\mathcal{B}(B^0 \to D^{*-} \mu^+\nu_\mu)$ iscalculated, $$ \mathcal{R}(D^{*-}) = 0.247 \pm 0.015 \pm 0.015 \pm 0.012\, , $$where the third uncertainty is due to the uncertainties on the externalbranching fractions. This result is consistent with the Standard Modelprediction and with previous measurements.

Test of lepton flavour universality using $B^0 \to D^{*-}\tau^+\nu_{\tau}$ decays with hadronic $\tau$ channels