The branching fraction $\mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })$ is measured relative to that of the normalization mode $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ using hadronic ${\tau }^{+}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}({\pi }^0){\overline{\nu }}_{\tau }$ 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 $2{\mathrm{fb}}^{-1}$. The measured ratio is $\mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })/\mathcal{B}(B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+})=1.70\pm 0.10_{-0.10}^{+0.11}$, where the first uncertainty is statistical and the second is related to systematic effects. Using established branching fractions for the $B^0\to D^{*-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ and $B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu }$ modes, the lepton universality test $\mathcal{R}(D^{*-})\equiv \mathcal{B}(B^0\to D^{*-}{\tau }^{+}{\nu }_{\tau })/\mathcal{B}(B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu })$ is calculated, $\mathcal{R}(D^{*-})=0.247\pm 0.015\pm 0.015\pm 0.012$, where the third uncertainty is due to the uncertainties on the external branching fractions. This result is consistent with the Standard Model prediction and with previous measurements.

• Received 3 May 2023
• Accepted 6 June 2023

DOI:https://doi.org/10.1103/PhysRevD.108.012018

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