A symmetry for ${\epsilon }_K$

Abstract

We show a symmetry that, in the context of a composite Higgs with anarchic flavor, can suppress the dominant CP violating contributions to $K-\bar{K}$ mixing. Based on previous extensions of SU(3)${}_c$, we consider the case in which the composite sector has a global SU(6) symmetry, spontaneously broken to a subgroup containing SU(3)$\times$SU(3). We show that the interactions with the Standard Model can spontaneously break the remaining symmetry to the diagonal subgroup, identified with the group of color interactions, and naturally suppress ${\epsilon }_K$. We consider this scenario in the context of the Minimal Composite Higgs Model based on SO(5)/SO(4) for the electroweak sector. By working in the framework of 2-site models, we compute the scalar potential, determine the conditions for a successful breaking of the symmetries and calculate the spectrum of lightest states. We find that ${\epsilon }_K$ can be suppressed and the top mass reproduced for a large region of the parameter space where the symmetries are dynamically broken. Besides other new resonances, the model predicts the presence of a new singlet scalar state, generally lighter than the Higgs, that could have evaded detection at colliders.

arXiv comment33 pages, 4 figures, v2: discussion on bounds from dipole moments added, references added

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