A quadratic potential in a light cone QCD inspired model

TL;DR

This paper develops a light cone QCD inspired model with a quadratic potential to analyze meson spectra, achieving better agreement with experimental data than previous models by incorporating a position-dependent mass and fine/hyperfine interactions.

Contribution

It introduces a quadratic potential in a light cone QCD inspired model and demonstrates improved spectral predictions for mesons compared to prior approaches.

Findings

Results agree with experimental data within errors.

The model outperforms previous calculations by Godfrey and Isgur, and Baldicchi and Prosperi.

The approach can be refined further to address current limitations.

Abstract

The general equation from previous work is specialized to a quadratic potential $V(r)=-a+\frac12 f r^2$ acting in the space of spherically symmetric S wave functions. The fine and hyperfine interaction creates then a position dependent mass $\widetilde m(r)$ in the effective kinetic energy of the associated Schr\"odinger equation. The results are compared with the available experimental and theoretical spectral data on the $\pi$ and $\rho$. Solving the eigenvalue problem within the usual oscillator approach induces a certain amount of arbitrariness. Despite of this, the agreement with experimental data is within the experimental error and better than other calculations, including Godfrey and Isgur \cite{GodIsg85} and Baldicchi and Prosperi \cite{BalPro02}. The short coming can be removed easily in more elaborate work.