Combined analysis of semileptonic $B$ decays to $D$ and $D^*$: $R(D^{(*)})$, $|V_{cb}|$, and new physics (1703.05330v4)

Abstract: The measured $\bar{B}\to D^{(*)} l \bar\nu$ decay rates for light leptons ($l=e,\mu$) constrain all $\bar{B}\to D^{(*)}$ semileptonic form factors, by including both the leading and ${\cal O}(\Lambda_{\text{QCD}}/m_{c,b})$ subleading Isgur-Wise functions in the heavy quark effective theory. We perform a novel combined fit to the $\bar{B}\to D^{(*)} l \bar\nu$ decay distributions to predict the $\bar{B} \to D^{(*)} \tau\bar\nu$ rates and determine the CKM matrix element $|V_{cb}|$. Most theoretical and experimental papers have neglected uncertainties in the predictions for form factor ratios at order $\Lambda_{\text{QCD}}/m_{c,b}$, which we include. We also calculate ${\cal O}(\Lambda_{\text{QCD}}/m_{c,b})$ and ${\cal O}(\alpha_s)$ contributions to semileptonic $\bar{B}\to D^{(*)} \ell \bar\nu$ decays for all possible $b \to c$ currents. This result has not been available for the tensor current form factors, and for two of those, which are ${\cal O}(\Lambda_{\text{QCD}}/m_{c,b})$, the corrections are of the same order as approximations used in the literature. These results allow us to determine with improved precision how new physics may affect the $\bar{B}\to D^{(*)} \tau\bar\nu$ rates. Our predictions can be systematically improved with more data; they need not rely on lattice QCD results, although these can be incorporated.

• The paper presents a combined HQET analysis that incorporates leading and subleading corrections to improve predictions of semileptonic B decay observables.
• Using a novel fitting approach, the study determines |Vcb| = (39.3 ± 1.0) × 10⁻³ and finds SM predictions of R(D) = 0.299 ± 0.003 and R(D*) = 0.257 ± 0.003.
• The refined methodology highlights potential new physics signals and provides a foundation for further investigations with Belle II and LHCb data.

Insights into Semileptonic $B$ Decays: A Combined Analysis

The paper "Combined analysis of semileptonic $B$ decays to $D$ and $D^*$: $R(D^{(*)})$, $|V_{cb}|$, and new physics" by Bernlochner et al. presents a comprehensive examination of semileptonic decays of $B$ mesons into $D$ and $D^*$ states. The paper leverages the constraints provided by measurements of $\bar{B} \to D^{(*)} \ell \bar{\nu}$ decay rates to explore form factors within the framework of Heavy Quark Effective Theory (HQET). Notably, the authors include both leading and subleading Isgur-Wise functions in their analysis, which adds significant precision to their predictions and accommodates previously neglected uncertainties in form factor ratios.

The researchers utilize a novel fitting approach to analyze the decay distributions, aiming to provide accurate predictions of $\bar{B} \to D^{(*)} \tau \bar{\nu}$ decay rates and the Cabibbo-Kobayashi-Maskawa (CKM) matrix element $|V_{cb}|$. Their methodology integrates $\mathcal{O}(\Lambda_{\text{QCD}}/m_{c,b})$ and $\mathcal{O}(\alpha_s)$ corrections, which are critical for all potential $b \to c$ currents. The inclusion of these corrections, particularly for tensor current form factors, represents new contributions to the literature.

Key Numerical Results and Implications

The combined fit results in a determination of $|V_{cb}| = (39.3 \pm 1.0) \times 10^{-3}$, aligning well with existing exclusive decay measurements. Furthermore, the standard model (SM) predictions for $R(D)$ and $R(D^*)$ are determined to be $0.299 \pm 0.003$ and $0.257 \pm 0.003$, respectively. Despite reducing uncertainties, these values remain in tension with experimental averages, indicating potential avenues for new physics exploration.

The paper's findings underpin the significance of HQET in providing a robust framework for understanding heavy meson decays, enhancing the ability to investigate both SM processes and potential new physics scenarios. The precision achieved in the form factor predictions, buoyed by comprehensive theoretical calculations and fit strategies, establishes a benchmark for future experimental and theoretical work.

Theoretical Contributions and Future Prospects

The treatment of semileptonic decays in this paper highlights the importance of accurately accounting for subleading contributions in theoretical models. The authors underscore the possibility of systematic improvements in their predictions as more data becomes available, notably from Belle II and LHCb experiments. This methodology does not solely depend on lattice QCD data, allowing it to incorporate theoretical advancements dynamically.

The availability of these refined predictions provides a better understanding of how potential new physics might manifest in these decay channels. Specifically, the framework allows for systematic analyses of how new operators beyond the SM might impact decay rates and other observables.

In conclusion, Bernlochner et al.'s work on semileptonic $B$ decays represents a significant step forward in the precise characterization of these processes. By incorporating detailed theoretical insights and addressing previously unaccounted uncertainties, the paper sets a precedent for both current investigations and future innovations in the search for new physics and the refinement of our understanding of CKM matrix elements.