$\mathcal{C}\mathcal{P}$ violation with an unbroken $\mathcal{C}\mathcal{P}$ transformation

Abstract

A $\mathcal{C}\mathcal{P}$ conserving $\mathrm{SU}(3)$ gauge theory is spontaneously broken to ${\mathrm{T}}_7$ by the vacuum expectation value (VEV) of a $15$-plet. Even though the $\mathrm{SU}(3)$-$\mathcal{C}\mathcal{P}$ transformation is not broken by the VEV, the theory exhibits physical $\mathcal{C}\mathcal{P}$ violation in the broken phase. This is because the $\mathrm{SU}(3)$-$\mathcal{C}\mathcal{P}$ transformation corresponds to the unique order-two outer automorphism of ${\mathrm{T}}_7$, which is not a physical $\mathcal{C}\mathcal{P}$ transformation for the ${\mathrm{T}}_7$ 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.

19 pages, 2 figures, 2 tables; v2: considering a different contribution to the decay asymmetry, conclusion unchanged

References in corpus (7)

• Updated fit to three neutrino mixing: exploring the accelerator-reactor complementarity
• Tri-Bimaximal Neutrino Mixing and the Family Symmetry Z_7 x Z_3
• Observation of Time Reversal Violation in the B0 Meson System
• Simple Finite Non-Abelian Flavor Groups
• Observable T_7 Lepton Flavor Symmetry at the Large Hadron Collider
• Symmetries of symmetries and geometrical CP violation
• Breaking classical Lie groups to finite subgroups - an automated approach

Cited by in corpus (3)

• Spontaneous CP violation in multi-Higgs potentials with triplets of $\Delta (3n^2)$ and $\Delta (6n^2)$
• Vacuum Stability and Perturbativity of SU(3) Scalars
• Simultaneous Block Diagonalization of Matrices of Finite Order