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

TL;DR

This work examines whether the scalar meson $a_0(1450)$ can be described as a diquark-state component by studying the semileptonic decay $D\to a_0(1450)\ell\nu_\ell$ using QCD light-cone sum rules. Two twist-2 light-cone distribution amplitude schemes derived from a light-cone harmonic oscillator model are constructed, and their moments $\langle\xi^n\rangle$ and Gegenbauer moments $a_n$ are evolved from $\mu_0=1\ \mathrm{GeV}$ to $\mu_k=1.4\ \mathrm{GeV}$. The resulting transition form factors $f_+(q^2)$ and $f_-(q^2)$ are extrapolated over the full $q^2$ range with a $z$-expansion; differential widths, branching fractions on the order of $10^{-6}$, and angular observables ${\cal A}_{\rm FB}$, ${\cal A}_{\lambda_\ell}$, and ${\cal F}_{\rm H}$ are predicted. The predictions are broadly consistent with other theoretical approaches such as QCDSR, CLFQM, and RQM, supporting the plausibility of treating $a_0(1450)$ as a conventional $q\bar{q}$ state within the studied framework and providing guidance for future experimental tests.

Abstract

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~${\cal F}_{\rm H}$.

Figures (5)

• Figure 1: Feynman diagram representing the tree-level charged current process $D^- \to a_0(1450)^0 \ell^- \bar{\nu}_\ell$.
• Figure 2: Behavior of twist-2 LCDAs for $a_0(1450)$ at the $\mu_0 = 1~\rm{GeV}$. As a comparison, the QCDSR-I and QCDSR-II (I and II in QCDSR Cheng:2005nb correspond to the orders of Gegenbauer moments $\mathcal{N}=1$ and $\mathcal{N}=3$, respectively) are also presented.
• Figure 3: Behaviors of $D \to a_0(1450)$ TFFs $f_{\pm} (q^2)$ in the entire $q^2$-region, where solid lines represent the central values and shaded regions represent the uncertainty ranges. For comparison, predictions from RQM Galkin:2025emi and QCDSR-II Cheng:2005nb are also provided.
• Figure 4: Angular distribution of ${d\Gamma}/{d\cos\theta}$ with respect to $\cos\theta$ for the decay channels $D^0 \to a_0(1450)^- \ell^+ \nu_\ell$ and $D^- \to a_0(1450)^0 \ell^- \bar{\nu}_\ell$ with $\ell=(e,\mu$), where $q^2=10^{-5}~{\rm GeV}^2$. As make a comparison, the prediction results of QCDSR-II Cheng:2005nb is also given.
• Figure 5: Decay widths for the semileptonic decay channels $D^0 \to a_0(1450)^- \ell^+ \nu_\ell$ and $D^- \to a_0(1450)^0 \ell^- \bar{\nu}_\ell$ with $\ell=(e ,\mu)$. QCDSR-II Cheng:2005nb predictions are present for comparison. Shaded bands indicate uncertainties.