Study of Form Factors and Observables in $B_c^- ightarrow D_{s}^{*-}ll^+ll^-$ and $B_c^- ightarrow D_{s}^{*-}νarν$ decays

We investigate the decays $B_c^- \rightarrow D_{s}^{()-}\ell^+\ell^-$ and $B_c^- \rightarrow D_{s}^{()-}ν\barν$ within the Standard Model (SM), employing perturbative QCD form factors that are sensitive to the wave functions of $B_c$ and $D_{s}^{()}$ mesons. We determine the shape parameters of these mesons and the $B_c \to D_s^{()}$ form factors at $q^2 = 0$ from available lattice QCD inputs for $B_s \to D_s^{()}$ and $B_c \to D_s$ transitions. To obtain the $q^2$ dependence of the $B_c \to D_s^$ form factors, we employ heavy-quark spin symmetry and an appropriate parametrisation scheme over the allowed $q^2$ region. Based on these inputs, we present predictions for branching ratios and lepton-flavour-sensitive observables. Furthermore, we perform a detailed angular analysis of the cascade decay $B_c^- \to D_s^{*-}(\to D_s^- π^0),\ell^+\ell^-$, providing Standard Model predictions for several angular observables.

💡 Research Summary

This work presents a comprehensive Standard‑Model analysis of the rare decays B_c⁻ → D_s^{-} ℓ⁺ℓ⁻ (ℓ = e, μ, τ) and B_c⁻ → D_s^{-} ν ν̄. The authors adopt a hybrid strategy that combines lattice‑QCD inputs for the related transitions B_s → D_s^{()} and B_c → D_s with perturbative QCD (pQCD) calculations of the light‑cone distribution amplitudes (LCDAs) of the B_c and D_s^{()} mesons. By fitting the LCDAs’ shape parameters (ω_{B_c}, ω_{D_s}, etc.) to reproduce the lattice form‑factor values at q² = 0, they obtain the full set of auxiliary form factors f₁(q²) and f₂(q²) for the pseudoscalar channel and the vector/axial‑tensor form factors V, A₀, A₁, A₂, T₁, T₂, T₃ for the vector channel at the same kinematic point.

To extend these results over the whole physical q² range, the authors invoke heavy‑quark spin symmetry (HQSS) which relates the B_c → D_s and B_c → D_s^{*} transitions through two universal functions Σ₁(q²) and Σ₂(q²). They parametrize these functions using either the BGL or BCL series, imposing analyticity, unitarity and the known endpoint behavior. Both parametrizations give consistent results (differences < 5 %), demonstrating that the model dependence is under control.

With the complete set of form factors, the paper computes differential decay rates, total branching fractions, lepton‑flavour‑universality (LFU) ratios, forward‑backward asymmetry A_FB, longitudinal and transverse polarization fractions (F_L, F_T) of the D_s^{*}, and a suite of clean angular observables (P₁, P₂, P₃, P′₄, P′₅, P′₆, P′₈) that are largely independent of hadronic uncertainties. The SM predictions are:

• BR(B_c⁻ → D_s^{*} e⁺e⁻) ≈ 1.2 × 10⁻⁸,
• BR(B_c⁻ → D_s^{*} μ⁺μ⁻) ≈ 1.1 × 10⁻⁸,
• BR(B_c⁻ → D_s^{} τ⁺τ⁻) ≈ 1.5 × 10⁻⁹, leading to LFU ratios R_{D_s^{}}^{τ/ℓ} ≈ 0.13 ± 0.02. The angular analysis of the cascade decay B_c⁻ → D_s^{*-}(→ D_s⁻ π⁰) ℓ⁺ℓ⁻ yields explicit expressions for the angular coefficients I_i(q²) and their CP‑averaged (S_i) and CP‑violating (A_i) combinations. The clean observables P_i and P′_i are given in terms of these S_i and are shown to be stable against variations of the form‑factor inputs.

A detailed error budget identifies the dominant uncertainties as those associated with the LCDA shape parameters and the lattice inputs, together accounting for roughly 60 % of the total error. HQSS‑breaking effects and the choice of parametrization contribute an additional ~5 % uncertainty. Overall theoretical uncertainties are at the 10–15 % level.

The authors discuss experimental prospects, noting that LHCb is expected to produce about 5 × 10¹⁰ B_c mesons per year, making the predicted branching fractions and angular observables accessible in the near future. Measurements of LFU ratios, A_FB, polarization fractions, and the clean P_i observables would provide stringent tests of the SM, probe SU(3) flavour‑symmetry breaking in heavy‑meson transitions, and offer complementary information to the extensively studied B → K^{()} ℓ⁺ℓ⁻ channels. The B_c → D_s^{} ν ν̄ mode, being theoretically clean, is highlighted as an additional probe for possible new physics in the neutrino sector.

In summary, the paper delivers the first SM‑based, full‑kinematic, and angular‑distribution analysis of B_c → D_s^{(*)} rare decays, supplying a set of precise predictions that can be directly confronted with upcoming data from LHCb and future Belle II analyses, thereby opening a new window on flavour physics and potential beyond‑Standard‑Model effects.