Abstract
In Two Higgs Doublet Models (2HDMs) shaped by some unbroken symmetry, imposing perturbativity requirements on the quartic couplings can imply that the allowed masses of all the fundamental scalars are bounded from above. This important property is analysed in detail for the only two realistic 2HDMs with an exact symmetry, the case with $\mathbb{Z}_2$ symmetry and the case with CP symmetry. It is also noticeable that one exception arises in each case: when the vacuum is assumed to respect the imposed symmetry, a decoupling regime can nevertheless appear without violating perturbativity requirements. In both models with an exact symmetry and no decoupling regime, soft symmetry breaking terms can however lead to a decoupling regime: the possibility that this regime might be unnatural, since it requires some fine tuning, is also analysed.
Highlights
Two Higgs doublets models (2HDMs) were introduced by Lee in [1,2]
For 2HDMs shaped by an exact Z2 symmetry [6,7,8,9,10,11,12], this precludes a spontaneous origin of CP violation: having natural flavor conservation (NFC) and spontaneous CP violation (SCPV) requires more than two doublets [13,14]. 2HDMs with spontaneous CP violation have been widely studied in the literature [15,16,17,18,19,20,21,22,23,24,25,26,27]
The possibility that perturbativity requirements on the quartic couplings of a 2HDM could imply that all the new scalars cannot have large masses is analyzed
Summary
Two Higgs doublets models (2HDMs) were introduced by Lee in [1,2]. One central and appealing motivation was the possibility that the origin of CP violation is exclusively spontaneous: with CP invariance at the Lagrangian level, CP violation can arise from the vacuum configuration. One important aspect of that model is the fact that the new scalars are necessarily light: their masses are all below 950 GeV. This kind of property, that the new scalars may not have arbitrarily large masses, has been noticed and explored by different authors in the context of some 2HDMs [29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. The Appendixes provide further details on different aspects of the previous sections
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