Diquark Condensate in QCD with Two Colors at Next-to-Leading Order

TL;DR

This paper investigates the phase transition in two-color QCD at finite baryon density using next-to-leading order chiral perturbation theory, confirming the second-order nature and critical chemical potential with refined calculations.

Contribution

It extends previous mean field analysis by calculating the free energy at next-to-leading order, demonstrating the renormalizability and stability of the phase transition characteristics.

Findings

The phase transition remains second order at NLO.

The critical chemical potential is half the NLO pion mass.

The theory is renormalizable at next-to-leading order.

Abstract

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau-Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is second order.