Diquarks in the nilpotency expansion of QCD and their role at finite chemical potential

TL;DR

This paper develops a lattice QCD framework incorporating diquark correlations via Bogoliubov transformations, enabling the study of multiquark states and free energy at finite chemical potential.

Contribution

It introduces a gauge-invariant formalism with correlated quark pairs for analyzing multiquark states in lattice QCD at finite density.

Findings

Derived a gauge-invariant quark contribution to free energy at finite chemical potential.

Established a formalism suitable for multiquark mesons and baryons as quark-diquark states.

Identified a definite sign in the approximate expression for the free energy contribution.

Abstract

We assume that the most important quark correlations are pairwise at all baryon densities. We introduce correlated pairs by means of Bogoliubov transformations which are functions of time and spatial gauge fields, in the formalism of the transfer matrix with lattice regularization. The dependence on time and gauge fields allows us to enforce gauge invariance and other symmetries term by term in the transformed quantities. The resulting action should be suitable for the description of multiquark mesons and baryons as states of a quark and a diquark. We derive the quark contribution to the free energy at finite chemical potential in a certain approximation. Its expression cannot be evaluated analytically, but it has a definite sign.