QCD at Large $\theta$ Angle and Axion Cosmology

Abstract

We use the chiral Lagrangian to investigate the global properties of the $N$-flavor QCD vacuum as a function of the $\theta$ parameter. In the case of exact quark degeneracy we find evidence for first order phase transitions at $\theta =\pi \cdot (\mathrm{odd}\mathrm{integer})$. The first order transitions are smoothed by quark mass splittings, although interesting effects remain at realistic quark masses. We emphasize the role of the ${\eta }^{\prime }$ condensate in our analysis. Finally, we discuss the implications of our results on the internal hadronic structure of axion domain walls and axion cosmology.

Comments: 12 pages, LaTeX, 5 epsf figures