Heavy Quarkonium Spectrum and Decay Constants from a Neural-Network-Based Holographic Model

We present a data-driven inverse construction of the dilaton field in a bottom-up AdS/QCD description of heavy vector quarkonia. Instead of adopting an \emph{ad hoc} analytic ansatz, we use a multilayer perceptron to learn (Φ’(z)) as a smooth function of the holographic coordinate, with (Φ(0)=0) imposed to ensure ultraviolet consistency. The dilaton and its derivatives obtained by automatic differentiation generate the holographic potential (U(z)), and the associated Schrödinger-like equation is discretized and diagonalized to extract the low-lying eigenmodes. Masses and decay constants are then evaluated from the eigenvalues and the near-boundary behavior of the bulk-to-boundary modes. Training on PDG data for charmonium and bottomonium yields a non-quadratic dilaton profile that resolves the longstanding difficulty of simultaneously reproducing both the heavy-quarkonium spectrum and the monotonic suppression of leptonic decay constants with radial excitation. The combined fit achieves RMS deviations of (1.26%) (charmonium) and (3.32%) (bottomonium). This work establishes neural-network reconstruction as a flexible tool for holographic modeling and provides a basis for future extensions incorporating additional channels, lattice constraints, or finite-temperature backgrounds.

💡 Research Summary

The paper introduces a novel data‑driven inverse method for constructing the dilaton profile Φ(z) in a bottom‑up AdS/QCD description of heavy vector quarkonia (charmonium and bottomonium). Rather than imposing an ad‑hoc analytic ansatz (e.g., the quadratic soft‑wall Φ(z)=κ²z²), the authors train a multilayer perceptron (MLP) to learn the derivative Φ′(z) as a smooth function of the holographic coordinate z, with the ultraviolet (UV) boundary condition Φ(0)=0 enforced explicitly. Automatic differentiation supplies Φ′′(z), which together with Φ′(z) defines the holographic potential

U(z)=¾ z⁻² +