$\theta -$ 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 $\theta$ parameter, chemical potentials for baryon number, ${\mu }_B$ and for isospin charge, ${\mu }_I$. We pay special attention to $\theta$, ${\mu }_B$, ${\mu }_I$ dependence of different vacuum condensates, including chiral and diquark condensates, as well as the gluon condensate, $<G^2>$, and the topological susceptibility. We find that two phase transitions of the second order will occur when $\theta$ relaxes from $\theta =2\pi$ to $\theta =0$, if $\mu$ is of order of the pion mass. We demonstrate that the transition to the superfluid phase at $\theta =\pi$ occurs at a much lower chemical potential than at $\theta =0$. We also show that the strong $\theta$ dependence present near $\theta =\pi$ 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.

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• Cold Dark Matter as Compact Composite Objects
• Axion field and the quark nugget's formation at the QCD phase transition
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• A Novel Mechanism for Type-I Superconductivity in Neutron Stars
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