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

TL;DR

This paper introduces a neural-network approach to holographically model heavy quarkonium spectra and decay constants, achieving high accuracy without relying on predefined analytic forms.

Contribution

It develops a neural-network-based method to reconstruct the dilaton profile in holographic QCD, improving the simultaneous fit of spectra and decay constants for heavy quarkonia.

Findings

Achieved RMS deviations of 1.26% for charmonium and 3.32% for bottomonium.

Resolved the challenge of fitting both spectra and decay constants.

Demonstrated neural networks as a flexible tool for holographic modeling.

Abstract

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 \(\Phi'(z)\) as a smooth function of the holographic coordinate, with \(\Phi(0)=0\) imposed to ensure ultraviolet consistency. The dilaton and its derivatives obtained by automatic differentiation generate the holographic potential \(U(z)\), and the associated Schr\"odinger-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.