Color symmetrical superconductivity in a schematic nuclear quark model

TL;DR

This paper introduces a new BCS-type formalism for color symmetrical superconductivity in a schematic quark model, ensuring invariance under color rotations and symmetric pairing across all three quark colors.

Contribution

It proposes a novel color symmetrical superconducting state formalism that maintains color invariance and affects all quark colors equally, unlike previous models.

Findings

Ground state energy closely matches the average energy of the proposed superconducting state.

Color symmetry is preserved in the superconducting state.

The formalism automatically ensures zero net color charge.

Abstract

In this note, a novel BCS-type formalism is constructed in the framework of a schematic QCD inspired quark model, having in mind the description of color symmetrical superconducting states. The physical properties of the BCS vacuum (average numbers of quarks of different colors) remain unchanged under an arbitrary color rotation. In the usual approach to color superconductivity, the pairing correlations affect only the quasi-particle states of two colors, the single particle states of the third color remaining unaffected by the pairing correlations. In the theory of color symmetrical superconductivity here proposed, the pairing correlations affect symmetrically the quasi-particle states of the three colors and vanishing net color-charge is automatically insured. It is found that the groundstate energy of the color symmetrical sector of the Bonn model is well approximated by the average energy of the color symmetrical superconducting state proposed here.