Geometrization of vacuum condensate effects in quarkonium potential model

TL;DR

This paper introduces a geometric potential model for quarkonium that incorporates vacuum condensate effects through the metric of an effective space, leading to analytical solutions and accurate spectral predictions for charmonium and bottomonium.

Contribution

It proposes a novel geometric approach to modeling vacuum condensate effects in quarkonium, providing analytical solutions and improved spectral fits.

Findings

Accurate fit to charmonium and bottomonium spectra

Analytical solutions for nonrelativistic energy levels

Insights into vacuum condensate role in hadron structure

Abstract

It is suggested the modification of traditional potential model, in which nontrivial structure of inside-hadron vacuum condensate is simulated by geometric properties of inside-hadron space. Confinement of quarks is ensured by closed effective (Riemannian) space. Interquark potential represents itself Coulomb's low in the effective space (Poisson equation). In the framework of such approach the quarks dynamics completely is defined only by metric of the effective space, which in turn in conformally-Euclidean case (we consider) is defined by sole phenomenological function. Also it is supposed, that inside-hadron vacuum is essential nonperturbative one both on large and on small distances and this is taken into account by special parameter in the metric of effective space. For final Schr\"odinger equation the exact analytical solutions for nonrelativistic energy spectrum and wave functions of quarkonium are obtained. From the basic principles of geometrized potential model and under the perturbation theory the spin-dependent relativistic corrections are calculated. Charmonium and bottomonium spectra are simulated. Suggested model gives a very good fit to experimental data: accuracy of spectra fitting makes $4.06\cdot 10^{-2}$ for charmonium and $3.28\cdot 10^{-2}$ for bottomonium and many predictions are made. On the basis of charmonium and bottomonium analysis conclusions about role of vacuum condensate in hadron structure are done.