Symmetries and mass degeneracies in the scalar sector

Abstract

We explore some aspects of models with two and three SU(2) scalar doublets that lead to mass degeneracies among some of the physical scalars. In Higgs sectors with two scalar doublets, the exact degeneracy of scalar masses, without an artificial fine-tuning of the scalar potential parameters, is possible only in the case of the inert doublet model (IDM), where the scalar potential respects a global U(1) symmetry that is not broken by the vacuum. In the case of three doublets, we introduce and analyze the replicated inert doublet model, which possesses two inert doublets of scalars. We then generalize this model to obtain a scalar potential, first proposed by Ivanov and Silva, with a CP4 symmetry that guarantees the existence of pairwise degenerate scalar states among two pairs of neutral scalars and two pairs of charged scalars. Here, CP4 is a generalized CP symmetry with the property that (CP4) n is the identity operator only for integer n values that are multiples of 4. The form of the CP4-symmetric scalar potential is simplest when expressed in the Higgs basis, where the neutral scalar field vacuum expectation value resides entirely in one of the scalar doublet fields. The symmetries of the model permit a term in the scalar potential with a complex coefficient that cannot be removed by any redefinition of the scalar fields within the class of Higgs bases (in which case, we say that no real Higgs basis exists). A striking feature of the CP4-symmetric model is that it preserves CP even in the absence of a real Higgs basis, as illustrated by the cancellation of the contributions to the CP violating form factors of the effective ZZZ and ZW W vertices. *

Dark matter from CP symmetry of order 4: evolution in the asymmetric regime

“…Thus, CP4 is a genuinely novel form of CP symmetry, physically distinct from the "standard" CP . This distinction was also established at the level of observables [27].…”

“…Due to this degeneracy, the spectrum of the model resembles a typical 2HDM spectrum: three values of neutral Higgs masses and one value of charged Higgs mass. However, the counting of additional scalars is different from 2HDM, which can be detected in principle by different production and decay rates, see more discussion in [27]. The two neutral fields h and a are the DM candidates protected by CP4 symmetry.…”

“…A first discussion of the qualitative features of the DM sector in CP4 3HDM was given in [26,27]. A more detailed quantitative insight into the DM evolution was given in [31].…”

“…The position of the minimum x * can be read off Eq. (27). Neglecting the slowly varying ln(x/x 0 ) term, one obtains a transcendental equation for x * :…”

S3 -inspired three-Higgs-doublet models: A class with a complex vacuum

“…Examples of the connection between symmetries and mass degeneracies in two-and three-Higgs-doublet models with vanishing vevs can be found in Ref. [22].…”