[Paper Review] Lepton Flavor Universality tests through angular observables of $\overline{B} o D^{(\ast)}\ell\overlineν$ decay modes

Damir Bečirević, Marco Fedele+2 more|arXiv (Cornell University)|Jul 4, 2019

Particle physics theoretical and experimental studiesPhysics and Astronomy77 references19 citations

TL;DR

This paper proposes using angular observables in $ar{B} \to D^{(*)}\ell\bar{\nu}$ decays to test lepton flavor universality violation (LFUV) beyond the $R(D^{(*)})$ ratios. By constructing a general low-energy effective theory with all allowed Lorentz structures, it shows that measuring angular distributions can distinguish the Lorentz structure of New Physics (NP) contributions, even if $R(D^{(*)})$ becomes SM-compliant. The key result is that angular observables can probe NP effects not detectable through $R(D^{(*)})$ alone.

ABSTRACT

We discuss the possibility of using the observables deduced from the angular distribution of the $B o D^{(\ast)} \ell\barν$ decays to test the effects of lepton flavor universality violation (LFUV). We show that the measurement of even a subset of these observables could be very helpful in distinguishing the Lorentz structure of the New Physics contributions to these decays. To do so we use the low energy effective theory in which besides the Standard Model contribution we add all possible Lorentz structures with the couplings (Wilson coefficients) that are determined by matching theory with the measured ratios $R{(D^{(\ast)})}^\mathrm{exp}$. We argue that even in the situation in which the measured $R{(D^{(\ast)})}^\mathrm{exp}$ becomes fully compatible with the Standard Model, one can still have significant New Physics contributions the size of which could be probed by measuring the observables discussed in this paper and comparing them with their Standard Model predictions.

Motivation & Objective

• To investigate whether angular observables in $\bar{B} \to D^{(*)}\ell\bar{\nu}$ decays can provide additional sensitivity to lepton flavor universality violation (LFUV) beyond the $R(D^{(*)})$ ratios.
• To determine whether the Lorentz structure of New Physics (NP) contributions can be uniquely identified using angular distributions, even when $R(D^{(*)})$ measurements are consistent with the Standard Model.
• To construct a general low-energy effective theory including all possible Lorentz-invariant NP operators (vector, axial-vector, scalar, pseudoscalar, tensor) to systematically explore NP effects.
• To assess the sensitivity of angular observables to NP couplings involving third-generation leptons, assuming negligible couplings to electrons and muons.
• To provide a framework for distinguishing between different NP models based on angular distributions, independent of $|V_{cb}|$ uncertainties or form factor assumptions.

Proposed method

• Formulate a general low-energy effective field theory for $b \to c\ell\bar{\nu}$ decays, including all Lorentz-invariant operators (vector, axial-vector, scalar, pseudoscalar, tensor) with Wilson coefficients as free parameters.
• Match the effective theory to experimental $R(D^{(*)})$ measurements to constrain NP Wilson coefficients, assuming deviations arise only from couplings to $\tau$ leptons.
• Derive the full angular distribution of $\bar{B} \to D^{(*)}\ell\bar{\nu}$ decays in terms of 9 independent angular observables, including forward-backward asymmetries, $\lambda_\ell$-asymmetries, and $R_{L,T}$, $R_{A,B}$ ratios.
• Compute the SM predictions and NP contributions to each angular observable using the constrained Wilson coefficients, with uncertainties propagated via Monte Carlo sampling.
• Perform a fit to experimental $R(D)$ and $R(D^*)$ values to determine best-fit NP couplings, then compute the corresponding predictions for all angular observables.
• Compare the resulting NP predictions with SM values to identify observable deviations, even in scenarios where $R(D^{(*)})$ is SM-compliant.

Experimental results

Research questions

• RQ1 Can angular observables in $\bar{B} \to D^{(*)}\ell\bar{\nu}$ decays distinguish the Lorentz structure of New Physics contributions to lepton flavor universality violation?
• RQ2 If $R(D^{(*)})$ becomes fully compatible with the Standard Model, can angular observables still detect New Physics effects?
• RQ3 Which angular observables are most sensitive to specific NP operators (e.g., vector, scalar, tensor) in the effective field theory framework?
• RQ4 How do the predictions for angular observables differ between various NP scenarios (e.g., $g_V$, $g_A$, $g_S$, $g_T$) when constrained by $R(D^{(*)})$ data?
• RQ5 Can the angular distribution analysis resolve ambiguities in NP models that are indistinguishable via $R(D^{(*)})$ alone?

Key findings

• Even if $R(D^{(*)})$ becomes fully compatible with the Standard Model, angular observables such as $A_{FB}^{D^*}$, $A_{\lambda_\ell}^{D^*}$, and $A_5$ can still reveal significant New Physics effects.
• The $A_{\lambda_\ell}^{D^*}$ asymmetry is particularly sensitive to NP contributions: it predicts $-0.25 \pm 0.05$ for $g_S$ and $0.22 \pm 0.02$ for $g_T$, deviating significantly from the SM value of $0.47 \pm 0.02$.
• The $R(R_{L,T})$ observable is highly sensitive to scalar and tensor NP: it predicts $0.99 \pm 0.04$ for $g_S$ and $0.46 \pm 0.02$ for $g_T$, far from the SM value of $0.79 \pm 0.02$.
• The $A_5$ asymmetry shows strong sensitivity to NP: it predicts $1.24 \pm 0.02$ for $g_V$, $0.71 \pm 0.03$ for $g_A$, and $0.55 \pm 0.05$ for $g_T$, deviating from the SM $1.15 \pm 0.02$.
• The $A_7$ and $A_8$ observables are sensitive to scalar and tensor NP: $D(A_7)$ predicts $-5.6 \pm 0.2 \times 10^{-3}$ for $g_P$ and $-2.2 \pm 0.1 \times 10^{-3}$ for $g_{S_R}$, while $A_9$ predicts $-0.047 \pm 0.001$ for $g_{S_R}$.
• The $A_{FB}^{D^*}$ forward-backward asymmetry shows strong NP sensitivity: it predicts $-0.37 \pm 0.04$ for $g_A$ and $0.37 \pm 0.03$ for $g_V$, deviating from the SM $0.23 \pm 0.04$.