Abstract
We investigate the effects of a ℤ2 symmetry in the mathcal{C}mathcal{P} -conserving Two-Higgs-Doublet-Model (2HDM); which is often imposed to prevent Flavor-Changing-Neutral-Currents (FCNCs) at tree-level. Specifically, we analyze how a breaking of the ℤ2 symmetry spreads during renormalization group evolution; employing general 2-loop renormalization group equations that we have derived. Evolving the model from the electroweak to the Planck scale, we find that while the case of an exact ℤ2 symmetric 2HDM is very constrained, a soft breaking of the ℤ2 symmetry extends the valid parameter space regions. The effects of a hard ℤ2 breaking in the scalar sector as well as the stability of the flavor alignment ansatz are also investigated. We find that while a hard breaking of the ℤ2 symmetry in the potential is problematic, since it speeds up the growth of quartic couplings, the generated FCNCs are heavily suppressed. Conversely, we also find that hard ℤ2 breaking in the Yukawa sector at most gives moderate ℤ2 breaking in the potential; whereas the FCNCs can become quite sizable far away from the ℤ2 symmetric regions.
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