$Z_2$ breaking effects in 2-loop RG evolution of 2HDM

TL;DR

This paper studies how breaking a $Z_2$ symmetry in the Two-Higgs-Doublet-Model affects its behavior during renormalization group evolution, revealing that soft breaking extends parameter space while hard breaking introduces challenges.

Contribution

It derives general 2-loop RG equations for the 2HDM and analyzes the impact of $Z_2$ symmetry breaking on model stability and flavor-changing neutral currents.

Findings

Soft $Z_2$ breaking extends parameter space.

Hard $Z_2$ breaking accelerates quartic coupling growth.

FCNCs are suppressed with hard $Z_2$ breaking in the potential.

Abstract

We investigate the effects of a $Z_2$ symmetry in the CP-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 $Z_2$ 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 $Z_2$ symmetric 2HDM is very constrained, a soft breaking of the $Z_2$ symmetry extends the valid parameter space regions. The effects of a hard $Z_2$ 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 $Z_2$ 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 $Z_2$ breaking in the Yukawa sector at most gives moderate $Z_2$ breaking in the potential; whereas the FCNCs can become quite sizable far away from the $Z_2$ symmetric regions.