The CP-Conserving Direction

Abstract

A symmetry transformation is well defined in the case of an invariant theory, being the corresponding operator undetermined otherwise. However, we show that, even with CP violation, it is possible to determine the CP transformation by separating the Lagrangian of the Standard Model in a CP-conserving and a CP-violating part, in a unique way, making use of the empirically known quark mixing hierarchy. To order \lambda^3 for the Bd-system, the CP-conserving direction matches one of the sides of the (bd) unitarity triangle. We use this determination to calculate the rephasing invariant parameter \epsilon, which measures CP-mixing in the B0-B0bar system.