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

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 $D\to a_0(1450)\ell {\nu }_{\ell }$ with $\ell =(e,\mu )$ 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 $⟨{\xi }^n⟩{|}_{\mu }$ and Gegenbauer moments $a_n(\mu )$ at ${\mu }_0=1\mathrm{GeV}$ and ${\mu }_k=1.4\mathrm{GeV}$ for $n=(1,3,5)$. In the large recoil region, we obtain the transition form factors (TFFs): $f_{+}^{(S1)}(0)=0.836_{-0.116}^{+0.119}$, $f_{+}^{(S2)}(0)=0.767_{-0.105}^{+0.106}$ 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 $q^2=10^{-5}{\mathrm{GeV}}^2$, we compute angular distribution of the differential decay width $d\Gamma /d\cos {\theta }_{\ell }$ over the range $\cos {\theta }_{\ell }\in [-1,1]$. Subsequently, we obtain differential decay widths and branching fractions for $D^0\to a_0(1450{)}^{-}{\ell }^{+}{\nu }_{\ell }$ and $D^{-}\to a_0(1450{)}^0{\ell }^{-}{\bar{\nu }}_{\ell }$, where the branching fractions being of order $10^{-6}$. Finally, we analyze three angular observables for the semileptonic decay process $D^{-}\to a_0(1450{)}^0{\ell }^{-}{\bar{\nu }}_{\ell }$, the forward-backward asymmetry ${\mathcal{A}}_{\mathrm{FB}}$, lepton polarization asymmetry ${\mathcal{A}}_{{\lambda }_{\ell }}$ and $q^2$-differential flat term~${\mathcal{F}}_{\mathrm{H}}$.

Comments: 24 pages, 5 figures