Test of Lepton Flavor Universality by the measurement of the $B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau }$ branching fraction using three-prong $\tau$ decays

Abstract

The ratio of branching fractions $\mathcal{R}(D^{\ast -})\equiv \mathcal{B}(B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau })/\mathcal{B}(B^0\to D^{\ast -}{\mu }^{+}{\nu }_{\mu })$ 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 $\tau$ 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 $B^0\to D^{\ast -}{\pi }^{+}{\pi }^{-}{\pi }^{+}$ decay as the normalization channel, the ratio $\mathcal{B}(B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau })/\mathcal{B}(B^0\to D^{\ast -}{\pi }^{+}{\pi }^{-}{\pi }^{+})$ is measured to be $1.97\pm 0.13\pm 0.18$, where the first uncertainty is statistical and the second systematic. An average of branching fraction measurements for the normalization channel is used to derive $\mathcal{B}(B^0\to D^{\ast -}{\tau }^{+}{\nu }_{\tau })=(1.42\pm 0.094\pm 0.129\pm 0.054)\%$, where the third uncertainty is due to the limited knowledge of $\mathcal{B}(B^0\to D^{\ast -}{\pi }^{+}{\pi }^{-}{\pi }^{+})$. A test of lepton flavor universality is performed using the well-measured branching fraction $\mathcal{B}(B^0\to D^{\ast -}{\mu }^{+}{\nu }_{\mu })$ to compute $\mathcal{R}(D^{\ast -})=0.291\pm 0.019\pm 0.026\pm 0.013$, where the third uncertainty originates from the uncertainties on $\mathcal{B}(B^0\to D^{\ast -}{\pi }^{+}{\pi }^{-}{\pi }^{+})$ and $\mathcal{B}(B^0\to D^{\ast -}{\mu }^{+}{\nu }_{\mu })$. This measurement is in agreement with the Standard Model prediction and with previous measurements.

All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2017-027.html

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