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

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.

Lattice QCD$_2$ effective action with Bogoliubov transformations

“…In the future, we aim to study models at finite temperature and chemical potential, to verify, for example, how diquarks states can be realized using the approach in [17].…”

Transfer matrix for Kogut-Susskind fermions in the spin basis

“…We became interested in a formulation of the transfer matrix in the spin basis in the framework of relativistic field theories of fermions whose partition function is dominated by bosonic composites [22]. This subject became for us more relevant in the development of an approach to QCD hadronization (meant as the replacement of the QCD degrees of freedom by hadronic ones) that makes use of the operator form of the transfer matrix [23][24][25][26]. Using Kogut-Susskind fermions, because of the lack of a convenient formulation of the transfer matrix, we were able to express our results only in the flavour basis.…”