First principle quadratic and linear mass operators, quarkonium spectrum and Regge trajectories

TL;DR

This paper develops first principle quadratic and linear mass operators for quarkonium, successfully reproducing meson spectra and Regge trajectories, with initial insights into spin-dependent effects.

Contribution

It introduces a novel approach based on the Wilson loop correlator to derive mass operators and applies it to quarkonium, achieving accurate spectral and trajectory predictions.

Findings

Successfully reproduces meson spectrum

Finds straight Regge trajectories with correct slope and intercepts

Provides initial analysis of spin-dependent contributions

Abstract

In previous works, a squared mass operator M^2 and a more common centre of frame Hamiltonian H_CM for the quark-antiquark system were obtained by using the only assumption that ln W (W being the Wilson loop correlator) can be written in QCD as the sum of its perturbative expression and an area term. We evaluated the spectrum of these operators by neglecting all the spin-dependent terms but for a spin-spin term. We succeeded in reproducing rather well the entire meson spectrum and for the light-light systems we found straight Regge trajectories with the right slope and intercepts. A first attempt to study the contribution of the spin dependent terms has been made.