CPviolation as a quantum effect

Abstract

For gauge theories with perturbative spontaneous symmetry breakdown it may happen that the question of $\mathrm{CP}$ invariance is solely settled by the structure of the quantum corrections to the classical scalar potential. It is shown that this can occur if and only if there exist spinless bosons which are massless in the tree aproximation and which are non-Goldstone modes. This can be achieved in a natural way (in the technical sense) if an accidental symmetry is present. The general theorem is illustrated with a few formal examples, some of which yield $\mathrm{CP}$ invariance and some $\mathrm{CP}$ violation. Our theorem also implies that if the leading radiative corrections opt for $\mathrm{CP}$ invariance, then the theory is $\mathrm{CP}$-invariant to all orders. Our examples further reveal the possibility that some gross features of the particle spectrum may also be solely determined by quantum effects.