$D^*_{(s)} o P$ form factors and their applications to semi-leptonic and non-leptonic weak decays

Similar to other heavy flavor mesons, the weak decays of $D^_{(s)}$ mesons can provide a platform to verify the standard model, explore new physics, and understand the mechanisms of weak interactions. At present, the theoretical and experimental studies on $D^{(s)}$ mesons are relatively limited. In addition to the dominant electromagnetic decays, the $D^*{(s)}$ weak decays should be feasible to explore the $D^_{(s)}$ mesons. In this study, we used the covariant light-front quark model to study the form factors of the transitions $D^{(s)}\to π, K, η{q,s}$, then calculated the branching ratios of the semi-leptonic decays $D^{(s)}\to P\ell^{+}ν{\ell}$ and the non-leptonic decays $D^{(s)}\to PP, PV$ with $P=π, K, η^{(\prime)}, V=ρ, K^*, ϕ$ and $\ell=e, μ$. The channels $D{s}^{+}\toη\ell^{+}ν_{\ell}$ and $D^{+}{s}\to ηρ^{+}$ possess the largest branching ratios, which can reach an order of $10^{-6}$ among these decays, and are most likely to be accessible in experiments at future high-luminosity colliders. Furthermore, we predict and discuss the longitudinal polarization fraction $f{L}$ and the forward-backward asymmetry $A_{FB}$ for the considered semi-leptonic $D^*_{(s)}$ decays.

💡 Research Summary

This paper presents a comprehensive theoretical study of the weak decays of the vector charm mesons D* and its strange partner D_s*. Using the covariant light‑front quark model (CLFQM), the authors first calculate the transition form factors for D*(s) → P where P = π, K, η_q, η_s. The CLFQM incorporates light‑front wave functions with a Gaussian ansatz and includes zero‑mode contributions, ensuring Lorentz‑covariant results. The vector and axial‑vector form factors V(q²), A₀(q²), A₁(q²), and A₂(q²) are obtained by performing four‑dimensional integrals over the internal momentum fractions (x) and transverse momenta (p⊥). These form factors are then parametrized over the full kinematic range (0 ≤ q² ≤ (m_{D*}−m_P)²).

With the form factors in hand, the authors compute the differential and total decay widths for the semileptonic processes D*_(s) → P ℓ⁺ ν_ℓ (ℓ = e, μ). The helicity amplitudes H_V,±,0 and the scalar amplitude H_V,t are constructed from the form factors, and the lepton‑mass effects are retained throughout. From the integrated widths they obtain branching ratios, the longitudinal polarization fraction f_L = Γ_L/(Γ_L+Γ_T), and the forward‑backward asymmetry A_FB as functions of q². The results show f_L values typically between 0.6 and 0.8, while A_FB exhibits a sign change across the q² spectrum, reflecting the interplay of vector and axial contributions. The η–η′ mixing angle θ = 39.3° ± 1.0° is incorporated, affecting both f_L and A_FB for channels involving η or η′.

For non‑leptonic two‑body decays D*(s) → PP and D*(s) → PV (with V = ρ, K*, φ), the authors adopt the factorization approach. The effective weak Hamiltonian includes the tree‑level operators with Wilson coefficients C₁ and C₂, and the relevant CKM matrix elements. Decay amplitudes are expressed as products of decay constants (f_P, f_V) and the previously computed transition form factors. Specific amplitudes for modes such as D_s*⁺ → η K⁺, D_s*⁺ → η π⁺, D⁺* → η K⁺, etc., are listed, and the η–η′ mixing is treated by replacing sin θ ↔ cos θ where appropriate. The predicted branching fractions are generally in the 10⁻⁷–10⁻⁶ range; the most promising channels are D_s*⁺ → η ℓ⁺ ν_ℓ and D_s*⁺ → η ρ⁺, both reaching O(10⁻⁶).

The paper also provides a realistic assessment of experimental prospects. Using existing measurements of e⁺e⁻ → D^{()} \bar D^{()} cross sections and fragmentation fractions, the authors estimate the numbers of D* and D_s* mesons that will be collected at current and future facilities: BESIII (~5×10⁷ D*±), the upcoming Super Tau‑Charm Facility (STCF) (~8×10¹⁰ D*), SuperKEKB (~2×10¹⁰ D_s*), CEPC and FCC‑ee (10¹¹–10¹² D_s*), and the High‑Luminosity LHC (≈2×10¹⁴ D*). Given these yields, branching ratios of order 10⁻⁶ should be within reach of upcoming high‑luminosity experiments.

Finally, the authors compare their CLFQM results with other non‑perturbative approaches, including lattice QCD, QCD sum rules, the Bauer‑Stech‑Wirbel (BSW) model, Bethe‑Salpeter calculations, and light‑cone sum rules. The CLFQM predictions are largely consistent, while the covariant treatment of zero‑mode contributions reduces theoretical uncertainties. The paper concludes that the presented form‑factor calculations and decay‑rate predictions constitute the first systematic phenomenological analysis of D*_(s) weak decays, offering valuable benchmarks for future experimental tests of the Standard Model and searches for new physics.