On the Symmetry Constraints of CP Violations in QCD

Three symmetry constraints on the CP violations in QCD are discussed in this paper. In order to generate CP violating observables from QCD, these constraints require: (1) spontaneous chiral symmetry breaking, (2) explicit chiral symmetry breaking, e.g., finite quark masses, (3) $U_A(1)$ anomaly, in addition to a nonzero $\thetabar$ parameter. A pictorial illustration is used to unify and elucidate these constraints and indicate a dual relation between quark mass and the quark condensate. Based on the symmetry constraints, a dynamical suppression scenario to solve the strong CP problem within QCD is examined. We conclude that a solution of the strong CP problem has to involve physics beyond the standard model.