BCS solutions and effective quarks energies of the QCD Hamiltonian in the Coulomb gauge

TL;DR

This paper applies the BCS method to study quark pair correlations and effective quark energies within the QCD Hamiltonian in Coulomb gauge, aiming to understand low-energy hadron spectra.

Contribution

It introduces a BCS-based approach to analyze quark correlations in the non-perturbative regime of QCD using an effective Coulomb plus linear potential.

Findings

Quark pair correlations influence low-energy meson spectra.

Parameter dependence of quasiparticle energies is analyzed.

BCS provides a simplified framework for non-perturbative QCD studies.

Abstract

The exploration of the non-perturbative regime of QCD, that is the low-energy portion of the hadron spectrum, requires the adoption of theoretical methods more frequently applied to other, more conventional, quantum many body systems, like the atomic nucleus, solid state systems, etc. In this work we have adopted, as a first step, the well-known BCS method to describe correlations between pairs of quarks and the associated ground state. Going beyond the BCS method would imply the inclusion of correlations by means of the TDA or RPA approximations. Since, we are interested in analyzing the role of constituent quark-pair correlations in the structure of hadrons we are restricted to the use of BCS as said before. The starting Hamiltonian is the effective Coulomb plus linear potential which we have used in previous calculations and performed a two-step approach, firstly by pre-diagonalizing it to built a single particle spectrum, and then, secondly, by applying the BCS transformations to it. Then, we have explored the resulting structure of the low energy meson spectra in terms of quasiparticle degrees of freedom. The dependence of the results upon the parameters which enter in the calculations is explored in detail, at the level of the quasiparticle mean-field approximation.