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Chiral symmetry breaking with no bilinear condensate revisited

While chiral symmetry breaking in the QCD vacuum is attributed to nonzero chiral condensate, an alternative symmetry breaking pattern with no chiral condensate is also possible, as pointed out by Stern. This hypothetical phase was excluded in QCD at zero density long time ago, but nothing forbids it at finite baryon density. In this work, we study the $θ$ dependence of this unorthodox phase on the basis of chiral perturbation theory. Physical observables such as energy density, topological susceptibility, non-local chiral order parameter and meson masses are computed analytically in the epsilon-regime. At nonzero $θ$ we find an exotic phase that breaks vectorial flavor symmetries in a way analogous to the Aoki phase in lattice QCD.