$b \to c$ semileptonic sum rule: Extension to angular observables

TL;DR

The work addresses lepton flavor universality tests in $b\to c l\overline{\nu}$ decays by deriving a new sum rule for double-differential rates that remains exact in the heavy-quark limit and extends the existing single-differential framework. It introduces two angular sum rules involving the tau polarization $P_{\tau}$ and the forward-backward asymmetry $A_{\rm FB}^{\tau}$, which are connected to the standard ratios $R_{H_c}$ via multiplicative factors, and shows how integrating over the kinematic variable $w$ recovers the known $R_{H_c}$-based relation while preserving NP independence in the heavy-quark limit. Corrections from heavy-quark symmetry breaking are quantified within HQET, with $\alpha_{P_\tau} \approx -0.258$ and $\alpha_{A_{\rm FB}^\tau} \approx 2.53$, and they are found to be small for the $P_\tau$ sum rule but potentially large for the $A_{\rm FB}^\tau$ sum rule depending on the NP scenario. These angular sum rules offer a complementary, NP-sensitive cross-check for current and future measurements (e.g., Belle II, LHCb) and can help discriminate among explanations of the $R_{D^{(*)}}$ anomalies.

Abstract

Lepton flavor universality is a key prediction of the Standard Model of particle physics and any violation of it immediately indicates the existence of new physics. Given the recent more than $4σ$ discrepancy in charged current semileptonic B meson decays and the absence of evident signals at the large hadron collider, independent cross-checks become invaluable. In this context, $b \to c$ semileptonic sum rules based on heavy quark symmetry are interesting since they allow us to check the consistency of experimental results. In this paper, we report newly found sum rules among angular observables of mesonic and baryonic $b\to c l \overlineν$ decays holding exactly in the large mass limit of heavy quarks. Moreover, we investigate corrections to the sum rule in realistic situations and discuss phenomenological implications.

Figures (4)

• Figure 1: Probability distribution of $\alpha_{P_\tau}$ and the corrections $\delta_{P_\tau}^{ij}$.
• Figure 2: Probability distribution of $\alpha_{A_{{\rm FB}}^\tau}$ and the corrections $\delta_{A_{{\rm FB}}^\tau}^{ij}$.
• Figure 3: Probability distribution of the correction $\delta_{P_\tau}$ based on the benchmark NP scenarios shown in Table \ref{['Tab:result']}.
• Figure 4: Probability distribution of the correction $\delta_{A_{{\rm FB}}^\tau}$ based on the benchmark NP scenarios shown in Table \ref{['Tab:result']}.