Measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$ with a semileptonic tagging method

Abstract: The experimental results on the ratios of branching fractions $\mathcal{R}(D) = {\cal B}(\bar{B} \to D \tau^- \bar{\nu}{\tau})/{\cal B}(\bar{B} \to D \ell^- \bar{\nu}{\ell})$ and $\mathcal{R}(D^*) = {\cal B}(\bar{B} \to D^* \tau^- \bar{\nu}{\tau})/{\cal B}(\bar{B} \to D^* \ell^- \bar{\nu}{\ell})$, where $\ell$ denotes an electron or a muon, show a long-standing discrepancy with the Standard Model predictions, and might hint to a violation of lepton flavor universality. We report a new simultaneous measurement of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$, based on a data sample containing $772 \times 10^6$ $B\bar{B}$ events recorded at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB $e^+ e^-$ collider. In this analysis the tag-side $B$ meson is reconstructed in a semileptonic decay mode and the signal-side $\tau$ is reconstructed in a purely leptonic decay. The measured values are $\mathcal{R}(D)= 0.307 \pm 0.037 \pm 0.016$ and $\mathcal{R}(D^*) = 0.283 \pm 0.018 \pm 0.014$, where the first uncertainties are statistical and the second are systematic. These results are in agreement with the Standard Model predictions within $0.2$, $1.1$ and $0.8$ standard deviations for $\mathcal{R}(D)$, $\mathcal{R}(D^*)$ and their combination, respectively. This work constitutes the most precise measurements of $\mathcal{R}(D)$ and $\mathcal{R}(D^*)$ performed to date as well as the first result for $\mathcal{R}(D)$ based on a semileptonic tagging method.

• The paper presents precise measurements of R(D) = 0.307 ± 0.037 ± 0.016 and R(D*) = 0.283 ± 0.018 ± 0.014 that closely align with Standard Model predictions.
• It introduces a novel semileptonic tagging method to reconstruct B meson decays, offering improved extraction over traditional hadronic tagging techniques.
• The analysis employs a two-dimensional extended maximum-likelihood fit with XGBoost to effectively mitigate systematic uncertainties in the decay reconstruction process.

Measurement of B Meson Decays: \RD and \RDSt with Semileptonic Tagging

This paper presents the measurement of the ratios of branching fractions $\RD$ and $\RDSt$ in the context of semitauonic $B$ meson decays, specifically $\bar{B} \to D^{(*)} \tau^- \bar{\nu}_{\tau}$ versus $\bar{B} \to D^{(*)} \ell^- \bar{\nu}_{\ell}$ where $\ell$ denotes an electron or muon. The study aims to investigate possible deviations from the Standard Model (SM) predictions, which suggest lepton flavor universality between different lepton generations. In this analysis, the Belle detector data, which comprises 772 million $B\bar{B}$ pairs collected at the \YFS\ resonance with the KEKB accelerator complex, is utilized. The experiment applies a novel semileptonic tagging method to reconstruct the $B$ mesons in semileptonic decays.

Key Results and Methodology

• Findings: The study reports $\RD = 0.307 \pm 0.037 \pm 0.016$ and $\RDSt = 0.283 \pm 0.018 \pm 0.014$, with respective statistical and systematic uncertainties. These are consistent with SM expectations by 0.2, 1.1, and 0.8 standard deviations.
• Experimental Technique: A semileptonic decay tag for one $B$ meson, alongside the purely leptonic decay reconstruction of the $\tau$ lepton, was employed in opposition to conventional hadronic tagging, which usually involves fully reconstructing one $B$ meson.
• Statistical Analysis: A two-dimensional extended maximum-likelihood fit to \eecl and classifier outputs obtained using \verb|XGBoost| was employed to distinguish the signal and normalization channels. This analysis mitigates systematic uncertainties, especially those shared by the detection efficiency and the quark-mixing matrix element $|V_{cb}|$.

Systematic Uncertainties

Several systematic uncertainties affect the precise measurement of $\RDall$. These uncertainties include:

• Composition of $D^{**}$ Decays: The uncertainty in branching fractions of $B \to D^{**} \ell \nu$ transitions contributes significantly due to limited knowledge of these states.
• Monte Carlo Simulation Size: Variations in outcomes based on limited particle decay simulations reflect a substantial source of systematic error, influencing PDF shapes and feed-down effects.
• Lepton Identification and Efficiency: Any discrepancy in lepton identification between simulation and reality further propagates uncertainties across different momentum spectra and decay form factors.

Implications and Future Research

The results make significant progress towards reconciling experimental outcomes with SM predictions, suggesting only marginal deviations. These findings do not conclusively indicate new physics interactions, such as those involving charged Higgs bosons or leptoquarks, hypothesized to affect semitauonic $B$ decay rates. However, the enhanced precision obtained via semileptonic tagging provides a robust foundation for future analyses. The further refinement of experimental techniques and statistical models is expected to tighten constraints on possible new physics, urging additional experimentation and theoretical rigor.

Moreover, these measurements support ongoing investigations into lepton flavor universality, a core tenet of the Standard Model, by delineating potential bounds for new particle interactions within high-energy physics frameworks. The pursuit of complementary collider experiments and comparative global data analysis remains crucial in determining whether intrafamily lepton distinctions may unravel previously undisclosed phenomena within quantum field theory.