Measurement of the $τ$ lepton polarization and $R(D^*)$ in the decay $\bar{B} \rightarrow D^* τ^- \barν_τ$ with one-prong hadronic $τ$ decays at Belle (1709.00129v2)

Abstract: With the full data sample of $772 \times 10^6$ $B{\bar B}$ pairs recorded by the Belle detector at the KEKB electron-positron collider, the decay $\bar{B} \rightarrow D^* \tau^- \bar{\nu}\tau$ is studied with the hadronic $\tau$ decays $\tau^- \rightarrow \pi^- \nu\tau$ and $\tau^- \rightarrow \rho^- \nu_\tau$. The $\tau$ polarization $P_\tau(D^*)$ in two-body hadronic $\tau$ decays is measured, as well as the ratio of the branching fractions $R(D^{*}) = \mathcal{B}(\bar {B} \rightarrow D^* \tau^- \bar{\nu}\tau) / \mathcal{B}(\bar{B} \rightarrow D^* \ell^- \bar{\nu}\ell)$, where $\ell^-$ denotes an electron or a muon. Our results, $P_\tau(D^*) = -0.38 \pm 0.51 {\rm (stat)} ^{+0.21}_{-0.16} {\rm (syst)}$ and $R(D^*) = 0.270 \pm 0.035{\rm (stat)} ^{+0.028}_{-0.025}{\rm (syst)}$, are consistent with the theoretical predictions of the Standard Model. The polarization values of $P_\tau(D^*) > +0.5$ are excluded at the 90\% confidence level.

• The paper precisely measures τ lepton polarization and R(D*) in B → D* τ ν decays, providing key tests of the Standard Model.
• It employs one-prong hadronic τ decays (π and ρ modes) from the Belle detector to achieve robust experimental sensitivity.
• The results, including R(D*) = 0.270 ± 0.035(stat) and constraints on τ polarization, limit New Physics scenarios and guide future Belle II studies.

Overview of the Measurement of $\tau$ Lepton Polarization and $R(D^*)$ in $B$ Meson Decays

The presented paper describes the analysis of the decay $\bar{B} \rightarrow D^* \tau^- \bar{\nu}_\tau$ using data from the Belle detector. This analysis provides measurements of the $\tau$ lepton polarization $P_\tau(D^*)$ and the ratio of branching fractions $R(D^*)$, which is defined as $$\mathcal{B}(\bar{B} \to D^* \tau^- \bar{\nu}_\tau) / \mathcal{B}(\bar{B} \to D^* \ell^- \bar{\nu}_\ell)$$, where $\ell^-$ includes both electron and muon. The paper utilizes hadronic $\tau$ decays characterized by one-prong, specifically $\tau^- \rightarrow \pi^- \nu_\tau$ and $\tau^- \rightarrow \rho^- \nu_\tau$.

Key Numerical Results and Comparison with Standard Model

Numerically, the paper reports:

• $$R(D^*) = 0.270 \pm 0.035{\rm (stat)} ^{+0.028}_{-0.025}{\rm (syst)}$$.
• $$P_\tau(D^*) = -0.38 \pm 0.51 {\rm (stat)} ^{+0.21} _{-0.16} {\rm (syst)}$$.

Both measurements align with the expectations from the Standard Model (SM), where $R(D^*)$ has been a critical area of interest due to its sensitivity to potential New Physics (NP) beyond the SM. The paper's results limit $P_\tau(D^*) > +0.5$ at the 90% confidence level, providing new constraints on NP models, such as those including charged Higgs bosons within the two-Higgs-doublet models (2HDM).

Implications and Future Developments

The implications of these measurements are significant as they not only validate the SM predictions for these decay processes but also set constraints on hypothetical NP. The ratio $R(D^*)$ was previously observed to deviate from SM predictions, suggesting potential signs of NP, such as leptoquarks or additional Higgs bosons that can preferentially couple to massive particles.

Pertaining to theoretical implications, accurate measurements of $P_\tau(D^*)$ are crucial as different NP models predict substantial deviations in polarization from the SM values. The measured polarization, aligning closely with the SM hypothesis, presents challenges to many NP scenarios unless they predict effects smaller than the current experimental sensitivity.

On a practical level, the methodology used in this analysis demonstrates the viability of the Belle detector for sensitive measurements of complex final-state particles such as the $\tau$ lepton in hadronic decay modes, laying groundwork for further analyses with upcoming data sets from Belle II.

Conclusion

The analysis presents a critical contribution to the understanding of $B$ meson semileptonic decays involving $\tau$ leptons. The precision achieved in the measurement of $R(D^*)$ and $P_\tau(D^*)$ provides key tests of the SM and potential deviations thereof, marking a milestone in the ongoing endeavor to probe for new physics via flavor processes. Future research, especially with enhanced luminosity and upgraded detector capabilities in Belle II, is anticipated to sharpen these measurements further, possibly uncovering discrepancies that could signal new fundamental physics.