High-scale validity of a model with three Higgs doublets

Abstract

We consider a three-Higgs doublet scenario in this paper, invariant under the discrete group S3, and probe its high-scale validity by allowing the model parameters to evolve under renormalisation group.We choose two particular alignments of vacuum expectation values (vev) for our study, out of a set of several such possible ones. All three doublets receive non-zero vacuum expectation values in the first case, and in the second case, two of the doublets remain without vev. The constraints on the parameter space at low energy, including the measured value of the Higgs mass and the signal strengths, oblique corrections and also measurements of relic density and direct detection rates are juxtaposed with the conditions of vacuum stability, perturbativity and unitarity at various scales. We find that the scenario with three non-zero vevs is not valid beyond 10 7 GeV, assuming no additional physics participates at the intermediate scales. On the contrary, the scenario with only one non-zero vev turns out to be a successful model for cold dark matter phenomenology, which also turns out to be valid up to the Planck scale at the same time. Stringent restrictions are obtained on the model parameter space in each case. Thus, the S3 symmetric scalar sector emerges as an ultraviolet (UV) complete theory. 1 nabarunc@hri.res.in 1 arXiv:1511.08137v2 [hep-ph] 22 Apr 2016 , m A1 , m A2 , m H1 , m H2 , c β−α } basis in scenario A and, {λ 1 , λ 2 , λ 3 , m H1 , m A1 , m H + 1 , λ L } in scenario B. We discuss below the various theoretical and experimental constraints imposed to shape the results. 6

Spontaneous symmetry breaking in the S 3-symmetric scalar sector

“…The high-scale validity of models based on two of these vacua, namely R-I-1 and R-II-1c, has recently been studied in Ref. [27].…”

Three-Higgs-doublet model under A4 symmetry implies alignment

“…The scalar spectrum of such models with possible discrete and continuous symmetries have been investigated in [12] while the potential minima and CP-violation options have been examined in [13,14]. For a three-Higgs-doublet model with S3 symmetry novel scalar decays [15], the spectrum of the scalar sector and its consequences [16], and the high energy behaviour of the potential [17] have been explored. A4 as a flavour symmetry for lepton and quark masses was first considered in [18] who introduced three scalar doublets transforming as a triplet of the A4 group and wrote down the most general potential consistent with the symmetry.…”

On the Higgs mass fine-tuning problem with multi-Higgs doublet models

“…Besides we have also considered S 3 -symmetric 2HDM [19] and inert doublet models [12] for the sake of completeness of discussion. Likewise A 4 -symmetric [14,15,18], S 4 -symmetric [14,18] and S 3 -symmetric 3HDMs [20,21] have been considered as variants of 3HDMs. In a nutshell our objectives are the following :…”

“…+ λ 2 + 4λ 3 − 14λ 5 − 7λ 6 − 24(λ 8 − 2y 2 + 3λ 2 + 2λ 4 sin 2β + λ 5 + λ 6 ) − λ 2 + λ 5 + λ 6 ) + 3 cos 4β(−λ 1 + λ 2 + 2(λ 5 + λ 6 )) + 31λ 1 -symmetry is imposed that demands Φ 1,2 to carry negative Z 2 charges and all other fields to carry positive charges[20]. In this case therefore, fermions are forbidden to couple to Φ 1,2 .…”