CP violation with an unbroken CP transformation

A bstract A C P conserving SU(3) gauge theory is spontaneously broken to T 7 by the vacuum expectation value (VEV) of a 15 -plet. Even though the SU(3)- C P transformation is not broken by the VEV, the theory exhibits physical C P violation in the broken phase. This is because the SU(3)- C P transformation corresponds to the unique order-two outer automorphism of T 7 , which is not a physical C P transformation for the T 7 states, and there is no other possible C P transformation. We explicitly demonstrate that C P is violated by calculating a C P odd decay asymmetry in the broken phase. This scenario provides us with a natural protection for topological vacuum terms, ensuring that θ G μ ν G ˜ μ ν is absent even though C P is violated for the physical states of the model.