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

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.

💡 Research Summary

The paper presents a holographic study of spin‑3/2 Δ baryon resonances using the soft‑wall AdS/QCD framework combined with a five‑dimensional Rarita‑Schwinger field. After setting up the bulk action, the authors introduce the usual AdS metric, a dilaton background that generates linear confinement, and a bulk scalar X(z) that encodes the quark mass and condensate. The Rarita‑Schwinger field Ψ_M is decomposed into left‑ and right‑handed components Ψ_1 and Ψ_2, each obeying a first‑order Dirac‑type equation with a bulk mass parameter m_− related to the scaling dimension Δ_{3/2}=9/2, giving |m_−|=5/2. Boundary conditions are imposed at the UV (z→0) and IR (z=z_m) cut‑offs, with an additional scaling factor ξ=1.5 to allow a different confinement scale for baryons. A Yukawa coupling g_{3/2}X^3Ψ_1Ψ_2 mixes the two chiral fields and implements chiral symmetry breaking. Solving the coupled equations yields normalizable wave‑functions expressed in terms of Bessel functions J_{m_−±1/2}(M_Δ z). The zeros of these Bessel functions determine the discrete mass spectrum. By fixing ξ and g_{3/2}=375, the model reproduces the experimental masses of the first three Δ resonances: Δ(1232), Δ(1600) and Δ(1920) with deviations of order 5–10 %. The authors then compute the bulk energy‑density τ_{00}(x_A) from the stress‑energy tensor of the Rarita‑Schwinger Lagrangian and perform a Fourier transform to momentum space τ_{00}(k_A). From the normalized modal fraction \tilde τ_{00}(k_A) they construct the differential configurational entropy (DCE) and the differential configurational complexity (DCC) as Shannon‑type integrals over the five‑dimensional momentum space. Both DCE and DCC increase monotonically with the radial excitation number n, and a linear Regge‑like relation is observed between DCE (or DCC) and n, as well as between DCE/DCC and the squared mass M_n^2. These “information trajectories” provide a novel way to encode the spectral information of the Δ family. Using the fitted linear relations, the authors extrapolate to higher n (n = 4, 5, 6…) and predict masses for yet‑unobserved Δ resonances. The predicted values are compared with PDG entries that are omitted from the summary table, showing reasonable agreement and suggesting that the information‑theoretic approach can serve as a complementary tool for hadron spectroscopy. The paper concludes that the holographic description of spin‑3/2 baryons, together with configurational information measures, captures essential aspects of non‑perturbative QCD dynamics, offers a quantitative link between bulk geometry and boundary spectroscopy, and opens the possibility of using DCE/DCC as phenomenological predictors for heavy resonances in strongly coupled gauge theories.