θ-parameter in 2 color QCD at finite baryon and isospin density

Abstract

We use 2-color QCD as a model to study the effects of simultaneous presence of the so-called θ parameter, chemical potentials for baryon number, µ B and for isospin charge, µ I . We pay special attention to θ, µ B , µ I dependence of different vacuum condensates, including chiral and diquark condensates, as well as the gluon condensate, bg 2 32π 2 G a µν G µνa , and the topological susceptibility. We find that two phase transitions of the second order will occur when θ relaxes from θ = 2π to θ = 0, if µ is of order of the pion mass, m π . We demonstrate that the transition to the superfluid phase at θ = π occurs at a much lower chemical potential than at θ = 0. We also show that the strong θ dependence present near θ = π in vacuum (Dashen's phenomenon), becomes smoothed out in the superfluid phase. Finally, we comment on the relevance of this study for the real world with N c = 3.PACS numbers: I. MOTIVATIONIn this paper we investigate the behavior of 2-color QCD under the influence of three parameters: θ, µ B and µ I . The main motivation for such a study is, of course, the attempt to understand the cosmological phase transition when θ, being non-zero and large at the very beginning of the phase transition, slowly relaxes to zero, as the axion resolution of the strong CP problem suggests. Therefore, the universe may undergo many QCD phase transitions when θ relaxes to zero. Another motivation is the attempt to understand the complicated phase diagram of QCD as a function of external parameters θ, µ B and µ I . Finally, our study may be of interests for the lattice community -the determinant of the Dirac operator for N c = 2 is real when θ = π in the presence of nonzero µ. As we show, in this case the superfluid phase is realized at a much lower chemical potential than at θ = 0. This gives a unique chance to study the superfluid phase on the lattice at a much smaller µ than would normally be required.To study all these problems in real 3 color QCD at finite µ B is, of course, a very difficult task. To get some insight into what might happen we shall use a controlled analytical method to study these questions in the non-physical (but nevertheless, very suggestive) N c = 2 theory. We use the chiral effective Lagrangian approach to attack the problem. We shall determine the phase diagram in the µ B , µ I , θ planes, various condensates and lowest lying excitations. We expect that our approach is valid as long as all external parameters * Electronic address: mmetlits@phas.ubc.ca † Electronic address: arz@phas.ubc.ca

Axion field and the quark nugget’s formation at the QCD phase transition

“…The fundamental consequence of this framework, Ω dark ≈ Ω visible , which is given by (1) is universal, and not sensitive to any parameters as both components are proportional to Λ QCD . The observed ratio (2), (66) corresponds to a specific value of c(T form ) −1.5 as discussed in section VII B.…”

“…In other words, we need to understand the structure of possible phases along the third dimension parametrized by θ on Fig 1. Presently, very few results are available regarding the phase structure at θ = 0. First of all, the phase structure is understood in simplified version of QCD with two colours, N c = 2 at T = 0, µ = 0, see [66]. In fact, the studies [66] were mostly motivated by the subject of the present work and related to the problem of formation of the quark nuggets during the QCD phase transition in early Universe with non vanishing θ.…”

“…First of all, the phase structure is understood in simplified version of QCD with two colours, N c = 2 at T = 0, µ = 0, see [66]. In fact, the studies [66] were mostly motivated by the subject of the present work and related to the problem of formation of the quark nuggets during the QCD phase transition in early Universe with non vanishing θ. With few additional assumptions the phase diagram can be also conjectured for the system with large number of colours N c = ∞, at non vanishing T, µ, θ, see [67,68].…”

SpontaneousCPviolation in the strong interaction atθ=π

“…Even in lattice QCD, studies are limited to small θ, because of the problem of how to deal with complex phases. Therefore, the θ-dependence of the strong interaction and Dashen's phenomenon have been studied extensively using low energy effective theories, such as chiral perturbation theory [6,7,8,9,10,11,12,13], or by using specific models, such as the NJL model [14]. In a quark model, like the NJL model, the effects of instantons and the θ-term are incorporated via an effective interaction, the 't Hooft determinant interaction [15,16].…”

Neutron Star masses from the Field Correlator Method Equation of State

“…as computed in [21] (dashed green) and in [24] (dot-dashed blue) with G 2 (μ B = 0) = 0.012 GeV 4 . The solid red line is the effective approximation used in our analysis [5].…”