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Abstract
For large isospin asymmetries, perturbation theory predicts the quantum chromodynamic (QCD) ground state to be a superfluid phase of u and d ¯ Cooper pairs. This phase, which is denoted as the Bardeen-Cooper-Schrieffer (BCS) phase, is expected to be smoothly connected to the standard phase with Bose-Einstein condensation (BEC) of charged pions at μ I ≥ m π / 2 by an analytic crossover. A first hint for the existence of the BCS phase, which is likely characterised by the presence of both deconfinement and charged pion condensation, comes from the lattice observation that the deconfinement crossover smoothly penetrates into the BEC phase. To further scrutinize the existence of the BCS phase, in this article we investigate the complex spectrum of the massive Dirac operator in 2+1-flavor QCD at nonzero temperature and isospin chemical potential. The spectral density near the origin is related to the BCS gap via a generalization of the Banks-Casher relation to the case of complex Dirac eigenvalues (derived for the zero-temperature, high-density limits of QCD at nonzero isospin chemical potential).
Highlights
Quantum chromodynamics (QCD) is established as the fundamental theory governing nuclear matter and hadrons
We must map the phase diagram of QCD as a function of both temperature and “doping”, which we can express in terms of isospin density n I = nu − nd or, equivalently, in the grand canonical approach to QCD, in terms of isospin chemical potential μ I =/2
The main questions we address revolve around the existence of the BCS phase and the location of its boundaries
Summary
Quantum chromodynamics (QCD) is established as the fundamental theory governing nuclear matter and hadrons. In the physical systems mentioned above, this translates into an excess of neutrons over protons or positively charged pions over negatively charged pions To understand these systems, we must map the phase diagram of QCD as a function of both temperature and “doping”, which we can express in terms of (negative) isospin density n I = nu − nd or, equivalently, in the grand canonical approach to QCD, in terms of isospin chemical potential μ I = (μu − μd )/2. Lattice simulations show large values for the Polyakov loop within the BEC phase [3] Those can be considered to be a hint for a superconducting ground state with deconfined quarks, that is for the BCS phase. Banks-Casher type relation [5] (cf. Equation (6))
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