Searching the possibility of $a_0(1450)$ scalar state being a diquark structure via charmed meson semileptonic decays

The internal structure of light scalar state $a_0(1450)$ has not been definitively determined, it may consist of multiple possible states. Among them, it has the possibility of being regarded as a diquark state. Based on this possibility, we use QCD light-cone sum rules to study the semileptonic decay process $D \to a_0(1450)\ell ν_\ell $ with $\ell=(e, μ)$ to verify its rationality. Firstly, we construct two types of twist-2 light-cone distribution amplitude schemes based on the light-cone harmonic oscillator model, and present their moments $\langleξ^{n}\rangle |μ$ and Gegenbauer moments $a{n}(μ)$ at $μ_0=1~{\rm GeV}$ and $μ_k= 1.4~{\rm GeV}$ for $n=(1,3,5)$. In the large recoil region, we obtain the transition form factors (TFFs): $f_+^{\rm (S1)}(0) = 0.836_{-0.116}^{+0.119}$, $f_+^{\rm (S2)}(0)=0.767_{-0.105}^{+0.106}$ and $f_-(0)=0.630_{-0.077}^{+0.078}$. A simplified series expansion $z(q^2, t)$ is used to extrapolate TFFs to the entire physical $q^2$-region. For $q^2=10^{-5} {\rm GeV}^2$, we compute angular distribution of the differential decay width ${dΓ}/{d\cosθ_\ell }$ over the range $\cosθ_\ell \in [-1,1]$. Subsequently, we obtain differential decay widths and branching fractions for $D^0 \to a_0(1450)^- \ell^+ ν_\ell $ and $D^- \to a_0(1450)^0 \ell^- \barν_\ell $, where the branching fractions being of order $10^{-6}$. Finally, we analyze three angular observables for the semileptonic decay process $D^- \to a_0(1450)^0 \ell^- \barν_\ell $, the forward-backward asymmetry ${\cal A}{\rm FB}$, lepton polarization asymmetry ${\cal A}{λ_\ell}$ and $q^2$-differential flat term${\cal F}_{\rm H}$.

💡 Research Summary

The paper investigates whether the light scalar meson a₀(1450) can be interpreted as a diquark (qq̄) state by studying the semileptonic decays D → a₀(1450) ℓ νₗ (ℓ = e, μ). Using QCD light‑cone sum rules (LCSR), the authors calculate the hadronic transition matrix element ⟨a₀| \bar c γ^μγ⁵ d |D⟩, which is parameterized by two form factors f₊(q²) and f₋(q²). A crucial non‑perturbative input is the twist‑2 light‑cone distribution amplitude (LCDA) of a₀(1450). Two distinct LCDA models (named Scheme S1 and Scheme S2) are constructed within the light‑cone harmonic‑oscillator (LCHO) framework. The LCHO model connects equal‑time wave functions to light‑cone wave functions via the Brodsky‑Huang‑Lepage prescription, allowing a realistic description of the momentum distribution.

For each scheme the authors compute the moments ⟨ξⁿ⟩_μ (n = 1, 3, 5) and the corresponding Gegenbauer coefficients aₙ(μ) at the renormalization scales μ₀ = 1 GeV and μ_k = 1.4 GeV. The resulting coefficients differ by roughly 10–15 % between the two schemes, reflecting different longitudinal corrections in the LCDA.

Applying LCSR in the large‑recoil region (q² ≈ 0) yields the form‑factor values
f₊^{(S1)}(0) = 0.836^{+0.119}{‑0.116},
f₊^{(S2)}(0) = 0.767^{+0.106}{‑0.105}, and
f₋(0) = 0.630^{+0.078}_{‑0.077}.
To cover the full physical q² range, the authors employ a simplified z‑expansion, z(q²,t) = (√{t₊ − q²} − √{t₊ − t₀})/(√{t₊ − q²} + √{t₊ − t₀}), and fit the LCSR results to obtain smooth q²‑dependence for both f₊ and f₋.

Using these form factors, the double differential decay width d²Γ/(dq² dcosθ_ℓ) is derived, where θ_ℓ is the angle between the charged lepton and the a₀(1450) in the lepton‑pair rest frame. At a near‑zero momentum transfer (q² = 10⁻⁵ GeV²) the angular distribution dΓ/dcosθ_ℓ is computed across the full cosθ_ℓ ∈