Holographic information measures for spin-$3/2$ $Δ$ baryons in AdS/QCD

TL;DR

This work investigates spin-$3/2$ Δ baryons in a hard-wall AdS/QCD setup using Rarita–Schwinger fields, and analyzes their information content with differential configurational entropy (DCE) and differential configurational complexity (DCC). By deriving the bulk energy density and its momentum-space spectra, the authors extract Regge-like relations linking DCE and DCC to the radial excitation number and to the observed mass spectrum, enabling extrapolation to heavier Δ resonances. The study provides two independent extrapolation pathways—DCE-based and DCC-based—yielding consistent predictions for higher states such as $ ext{Δ}_4^ullet$, $ ext{Δ}_5^ullet$, and $ ext{Δ}_6^ullet$, with masses in the 2–3 GeV region and compatibility with PDG hints around 3000 MeV. The results highlight a meaningful connection between holographic QCD dynamics, configurational information theory, and baryon spectroscopy, offering a predictive framework for higher-spin baryons in strongly coupled QCD.

Abstract

Spin-$3/2$ $Δ$ baryon resonances are investigated within AdS/QCD, using Rarita-Schwinger fields. The differential configurational entropy (DCE) and differential configurational complexity (DCC) associated with their bulk energy densities are computed. It yields Regge-like trajectories relating configurational information measures to the radial excitation number and the experimental mass spectrum of the $Δ$ baryons. We then extrapolate the spectrum of heavier $Δ$ baryon resonances beyond currently established states in the PDG, also comparing them with states in PDG omitted from the summary table. Our results support a relevant interplay among holographic QCD dynamics, configurational information entropy, and baryon spectroscopy in strongly coupled QCD.

Figures (5)

• Figure 1: Mass spectra for the $\Delta$ baryon resonances obtained from the experimental values in PDG PDG2024 and the AdS/QCD model, for the resonances $\Delta(1232)$, $\Delta(1600)$, and $\Delta(1920)$.
• Figure 2: DCE of the $\Delta$ baryon resonances as a function of the radial quantum number.
• Figure 3: DCE of the $\Delta$ baryon resonances as a function of their squared mass, for $n=1,2,3$.
• Figure 4: DCC of the $\Delta$ baryon resonances as a function of the radial quantum number.
• Figure 5: DCC of the $\Delta$ baryon resonances as a function of their squared mass, for $n=1,2,3$.