The solution to the strong CP problem at the BCS level of chiral rotations

Abstract

We briefly review the cases of forced and spontaneous chiral symmetry breaking. In particular the chiral condensate of q anti-q pairs is parametrized with two angles, phi which measures the chiral condensation, and theta which measures the chiral rotation. The strong CP problem arises when it is assumed that the current quark masses of the Standard Model, have a theta phase that differs from the phase induced by the instanton term wich is originated in the QCD sector of the Standard Model. We show how chiral symmetry breaking may solve the strong CP problem at the BCS level. We show variationally that the physical vacuum is CP conserving and therefore the interplay of the instanton and the current mass terms cannot produce any strong CP violation. We also study the possible effect of theta in weak interactions, and conclude that it does not produce weak CP.