Measurement of the ratio of the $B^0 \to D^{*-} τ^+ ν_τ$ and $B^0 \to D^{*-} μ^+ ν_μ$ branching fractions using three-prong $τ$-lepton decays

Abstract: The ratio of branching fractions ${\cal{R}}(D^{*-})\equiv {\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau})/{\cal{B}}(B^0 \to D^{*-} \mu^+\nu_{\mu})$ 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$^{-1}$. For the first time ${\cal{R}}(D^{*-})$ is determined using the $\tau$ lepton decays with three charged pions in the final state. The $B^0 \to D^{*-} \tau^+\nu_{\tau}$ yield is normalized to that of the $B^0\to D^{*-} \pi^+\pi^-\pi^+$ mode, providing a measurement of ${\cal{B}}(B^0\to D^{*-}\tau^+\nu_{\tau})/{\cal{B}}(B^0\to D^{*-}\pi^+\pi^-\pi^+) = 1.97 \pm 0.13 \pm 0.18$, where the first uncertainty is statistical and the second systematic. The value of ${\cal{B}}(B^0 \to D^{*-} \tau^+ \nu_{\tau}) = (1.42 \pm 0.094 \pm 0.129 \pm 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 $B^0 \to D^{*-} \mu^+\nu_{\mu}$ decay, a value of ${\cal{R}}(D^{*-}) = 0.291 \pm 0.019 \pm 0.026 \pm 0.013$ is established, where the third uncertainty is due to the limited knowledge of the branching fractions of the normalization and $B^0\to D^{*-}\mu^+\nu_{\mu}$ modes. This measurement is in agreement with the Standard Model prediction and with previous results.

• The paper presents the first measurement of the B0→D*-τ+ντ branching fraction using hadronic τ decays with three charged pions.
• It employs a normalization strategy based on B0→D*-π+π-π+ decays and rigorous multivariate techniques to suppress backgrounds.
• The results, consistent with the Standard Model, offer precise constraints on lepton universality and guide searches for new physics.

Measurement of the Ratio of Semileptonic Decay Branching Fractions at LHCb

This paper presents a detailed study performed by the LHCb collaboration on the ratio of the branching fractions of two semileptonic decay processes of the neutral B meson ($B^0$): the decay into $D^{*-} \tau^+ \nu_\tau$ and the decay into $D^{*-} \mu^+ \nu_\mu$. Such measurements are crucial for testing the lepton universality—a fundamental principle of the Standard Model (SM)—which asserts that the coupling strengths of the $W$ boson to different lepton families should be identical when accounting for differences in lepton masses.

Methodology

The analysis used data from proton-proton collisions at center-of-mass energies of 7 and 8 TeV collected by the LHCb detector, corresponding to an integrated luminosity of 3 fb$^{-1}$. This work is significant in that it marks the first measurement of $\mathcal{R}(D^{*-})$ using hadronic $\tau$ decays involving three charged pions ($\tau^+ \to \pi^+ \pi^- \pi^+ \nu_\tau$ and $\tau^+ \to \pi^+ \pi^- \pi^+ \pi^0 \nu_\tau$).

The analysis employed a normalization strategy based on the well-understood $B^0 \to D^{*-} \pi^+ \pi^- \pi^+$ decay to reduce systematic uncertainties. Various backgrounds were considered and suppressed using multivariate techniques and stringent topological cuts, such as requiring the distance between decay vertices to enhance signal purity.

Results and Uncertainties

The branching fraction ratio $\mathcal{R}(D^{*-})$ was determined to be $$0.291 \pm 0.019\, (\text{stat}) \pm 0.026\, (\text{syst}) \pm 0.013\, (\text{ext})$$, where the last uncertainty stems from external factors such as known branching fractions of decay modes used for normalization. This result is consistent with the Standard Model prediction and aligns with previous measurement results which have indicated a tendency towards higher values compared to SM expectations.

Systematic uncertainties were thoroughly evaluated, focusing on factors such as the modeling of signal and background decay dynamics, the limited size of simulated samples, and event reconstruction efficiencies. Despite these uncertainties, the level of precision achieved in this measurement reflects significant advancement in experimental techniques and statistical handling.

Implications and Future Outlook

The implications of this measurement extend to constraining new physics scenarios, including those that predict lepton universality violation such as models with leptoquarks or additional Higgs bosons. The results from LHCb contribute to a growing body of evidence suggesting possible deviations from the SM, though not yet at a level of statistical significance that would warrant definitive claims of new physics.

Future analyses will benefit from larger datasets expected from upcoming LHC runs, which will allow for more precise determinations of $\mathcal{R}(D^{*-})$ and other related ratios. These efforts might include further refinements in experimental techniques to reduce systematic contributions and exploiting updated theoretical calculations. The pursuit of such measurements remains a cornerstone in the search for physics beyond the Standard Model, bridging the gap between current experimental results and theoretical advancements.