Non linear Regge trajectories of quarkonia from holography

TL;DR

The paper tackles nonlinear Regge trajectories of heavy quarkonia by developing a holographic AdS/QCD model that combines a mass-shift mechanism for heavy quarks with a WKB quantization incorporating the Langer correction. It derives a trajectory form $m_n^2 = β(n+c_0)^{2/3} + c_1$ by solving a Schrödinger-like problem with a tailored potential, and maps holographic parameters to the QSSE/Cornell potential framework, identifying $β$, $c_0$, and $c_1$ in terms of $κ$, $M_q$, and the quark masses. The authors introduce a 1/√z term in the potential to tune the intercept $c_0$, obtaining $c_0=3/4$ in a preferred two-parameter setup, and demonstrate excellent mass fits for charmonium and bottomonium, with reasonable decay constants, in addition to a physically meaningful interpretation of $M_q$ as the sum of constituent-quark masses and $κ$ related to the string tension. The work provides a robust bottom-up AdS/QCD framework linking QSSE-inspired spectra to gauge/gravity duality and suggests future extensions to finite temperature, density, magnetic fields, or angular momentum for studying quarkonium dissociation. Overall, it advances the description of heavy quarkonia by integrating nonlinear Regge behavior into holographic models with controlled mass shifts and WKB-based spectral analysis.

Abstract

We propose a holographic model for quarkonia using the WKB approximation with the Langer correction to properly reproduce nonlinear Regge trajectories of the form $m_n^2 = β(n + c_0)^{2/3} + c_1$. This form is expected from previous studies involving the solution of Cornell Potential for heavy quark anti-quark interactions using a model based on the quadratic form of the spinless Salpeter-type equation (QSSE). The model fits experimental masses with very good accuracy. As a by product, the corresponding decay constants also show a reasonable agreement with the results obtained from experimental data.

Figures (3)

• Figure 1: Charmonium and bottomonium masses. Experimental data and results from the model with 3 parameters, that are very close to the case with two parameters.
• Figure 2: Comparison of charmonium experimental decay constants to the decay constants predicted by the model with 2 parameters, and the ones given by the best fit of the model with 3 parameters.
• Figure 3: Dilatons for the model with 2 and 3 parameters with the parameter values presented in Table \ref{['tab: best fits']}.