Abstract
A \( \mathcal{C}\mathcal{P} \) conserving SU(3) gauge theory is spontaneously broken to T7 by the vacuum expectation value (VEV) of a 15-plet. Even though the SU(3)-\( \mathcal{C}\mathcal{P} \) transformation is not broken by the VEV, the theory exhibits physical \( \mathcal{C}\mathcal{P} \) violation in the broken phase. This is because the SU(3)-\( \mathcal{C}\mathcal{P} \) transformation corresponds to the unique order-two outer automorphism of T7, which is not a physical \( \mathcal{C}\mathcal{P} \) transformation for the T7 states, and there is no other possible \( \mathcal{C}\mathcal{P} \) transformation. We explicitly demonstrate that \( \mathcal{C}\mathcal{P} \) is violated by calculating a \( \mathcal{C}\mathcal{P} \) odd decay asymmetry in the broken phase. This scenario provides us with a natural protection for topological vacuum terms, ensuring that \( \theta {G}_{\mu \nu }{\tilde{G}}^{\mu \nu } \) is absent even though \( \mathcal{C}\mathcal{P} \) is violated for the physical states of the model.
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ArXiv ePrint: 1612.08984
On leave of absence from Physik Department T30, Technische Universität München, James-Franck-Straße 1, 85748 Garching, Germany. (Michael Ratz)
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Ratz, M., Trautner, A. \( \mathcal{C}\mathcal{P} \) violation with an unbroken \( \mathcal{C}\mathcal{P} \) transformation. J. High Energ. Phys. 2017, 103 (2017). https://doi.org/10.1007/JHEP02(2017)103
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DOI: https://doi.org/10.1007/JHEP02(2017)103