Spectroscopy of charmonium-like mesons, heavy-light mesons with charm, AdS/QCD, and configurational entropy

TL;DR

The work addresses the nonperturbative charmonium-like and heavy-light charmed meson spectra by combining a bottom-up 4-flavor AdS/QCD model with the differential configurational entropy ($DCE$). It computes $DCE$ for the $D^0$, $D^*$, $ta_c$, and $hi_{c1}$ families, constructing $DCE$-Regge trajectories of the first kind (vs principal quantum number $n$) and the second kind (vs $m^2$) to interpolate experimental data and predict higher resonances. The study provides concrete mass forecasts, e.g., $m_{(D^0)_4}=3689.27$ MeV and $m_{(D^0)_5}=4126.97$ MeV, $m_{(D^*)_4}=3180.62$ MeV, $m_{ta_c(3S)}=4190.57$ MeV, and $m_{(hi_{c1})_6}=4981.27$ MeV, among others, with several suggested matches to PDG candidates like $X(4160)$, $X(3250)$, and $X(4630)$. This dual approach—mass spectra from Schrödinger-like AdS/QCD and $DCE$-driven extrapolations—offers a data-informed, phenomenological route to anticipate heavier resonances and guides experimental searches in high-energy colliders. The results demonstrate the utility of $DCE$ as a bridge between holographic models and experimental hadron spectroscopy. The methodology provides a reproducible framework to extend the spectra for future discoveries in the charmed sector.

Abstract

Heavy-light-flavor meson resonances with charm, in the $D^0$ and $D^*$ families, and charmonium-like states, in the $η_c$ and $χ_{c1}$ families, are explored and discussed in the AdS/QCD model with four quark flavors. The differential configurational entropy is computed and analyzed for these four charmed meson families, also combining 4-flavor AdS/QCD to experimental data for the $D^0$, $D^*$, $η_c$, and $χ_{c1}$ meson families. It makes it possible to predict the mass spectrum of unexplored heavier charmed meson resonances and to identify further charmed meson states reported in PDG.

Figures (8)

• Figure 1: DCE of $D^0$ meson resonances as a function of the principal quantum number $n$, for $n=1,2, 3$ (respectively corresponding to the states $D^0$, $D^0(2550)^0$, and $D^0(3000)^0$pdg). The DCE-Regge trajectory of the first kind, Eq. (\ref{['itp1']}), is plotted by a dashed line.
• Figure 2: DCE of the $D^0$ meson family displayed as a function of their respective squared mass, for $n=1,2,3$ (corresponding, respectively, to the $D^0$, $D^0(2550)^0$, and $D^0(3000)^0$ heavy-light-flavor meson states pdg). The DCE-Regge trajectory of the second kind in Eq. (\ref{['itq11']}) corresponds to the interpolating dot-dashed line.
• Figure 3: DCE of $D^*$ meson resonances as a function of the principal quantum number $n$, for $n=1,2,3$ (respectively corresponding to the states $D^*(2007)^0$, $D^*_1(2600)^0$, $D^*_1(2760)^0$pdg). The DCE-Regge trajectory of the first kind, Eq. (\ref{['itp1']}), is plotted by a dot-dashed line.
• Figure 4: DCE of the $D^*$ meson family displayed as a function of their respective squared mass, for $n=1,2,3$ (corresponding, respectively, to the $D^*(2007)^0$, $D^*_1(2600)^0$, $D^*_1(2760)^0$ heavy-light-flavor meson states pdg). The DCE-Regge trajectory of the second kind in Eq. (\ref{['itq11']}) corresponds to the interpolating dot-dashed line.
• Figure 5: DCE of the $\eta_c$ charmonium-like meson family, for $n=1,2$ (respectively corresponding to the $\eta_c(1S)$ and $\eta_c(2S)$ meson states in PDG pdg). The DCE-Regge trajectory of the first kind (\ref{['itp11etac']}) is displayed as the interpolating dot-dashed line.