Vacuum stability and radiative electroweak symmetry breaking in an SO(10) dark matter model

Abstract

Vacuum stability in the Standard Model is problematic as the Higgs quartic self-coupling runs negative at a renormalization scale of about 10 10 GeV. We consider a non-supersymmetric SO(10) grand unification model for which gauge coupling unification is made possible through an intermediate scale gauge group, Gint = SU(3)C ⊗ SU(2)L ⊗ SU(2)R ⊗ U(1)B−L. Gint is broken by the vacuum expectation value of a 126 of SO(10) which not only provides for neutrino masses through the seesaw mechanism, but also preserves a discrete Z2 that can account for the stability of a dark matter candidate, here taken to be the Standard Model singlet component of a bosonic 16. We show that in addition to these features, the model insures the positivity of the Higgs quartic coupling through its interactions to the dark matter multiplet and 126. We also show that the Higgs mass-squared runs negative triggering electroweak symmetry breaking. Thus the vacuum stability is achieved along with radiative electroweak symmetry breaking and captures two more important elements of supersymmetric models without low energy supersymmetry. The conditions for perturbativity of quartic couplings and for radiative electroweak symmetry breaking lead to tight upper and lower limits on the dark matter mass, respectively, and this dark matter mass region (1.35-2 TeV) can be probed in future direct detection experiments.Introduction.-With the discovery of the Higgs boson at both the ATLAS [1] and CMS [2] detectors, the Standard Model (SM) of particle physics appears to be very well established. However, as yet, there is no verified explanation for neutrino masses, and the nature of dark matter (DM) remains elusive. Both signal the need for beyond the SM physics. The experimental value of the Higgs mass, m h = 125.09 ± 0.24 GeV [3], also points to new physics at some higher energy scale. The Higgs quartic self-coupling, λ, runs toward negative values at high energy. The lower limit on m h to ensure the posititivity of λ out to the Planck scale is 129.4 ± 1.8 GeV [4] which appears to be violated. DM is often introduced in supersymmetric extensions of the SM with R-parity [5]. In supersymmetric models, the problem of vacuum stability associated with the Higgs quartic coupling is avoided as the tree level coupling is determined by a combination of the gauge couplings and is positive definite. In addition, supersymmetric models offer a mechanism for triggering electroweak symmetry breaking via radiative effects [6].

Dark matter seeping through dynamic gauge kinetic mixing

“…One such option is a masssuppressed coupling, such as Planck scale suppressed couplings in supergravity as shown in [29][30][31][32], where the gravitino production is just sufficient to respect cosmological constraints in high-scale supersymmetric scenarios. In SO(10) unified theories, massive gauge bosons can play the role of heavy mediators yielding also small couplings [33][34][35]. Similar suppressions also arise in massive spin-2 theories [36,37], string theory inspired moduli portal scenarios [38] and in scenarios containing Chern-Simons type couplings [39].…”

Dark Matter after LHC Run I: Clues to Unification

“…If the intermediate scale is broken by a Higgs in a 126 representation, a residual Z 2 discrete symmetry survives enabling the possibility of a stable dark matter candidate [5,[31][32][33]. Furthermore, in models with gauge coupling unification and a stable dark matter candidate, it is also possible to stabilize the electroweak vacuum while at the same time radiatively break the electroweak symmetry [34]. The coupling of the 126 to SM matter fields embedded in a 16 representation of SO (10) naturally gives rise to a majorana mass mass to the ν R component of the 16 of order 126 ∼ M int which when combined with the Dirac mass arising from the vev of the SM Higgs (now residing in a 10-plet of SO (10)) gives rise to the seesaw mechanism for light neutrino masses [35].…”

Inflation and leptogenesis in high-scale supersymmetry

“…For example, gauge coupling unification in high-scale supersymmetry has been shown to be effective in SO (10) models of grand unification [31]. To be more precise, it is known that gauge coupling unification also occurs in non-supersymmetric models SO(10) models when the unified gauge symmetry is broken down to the Standard Model (SM) gauge group through an intermediate scale gauge group [32][33][34][35][36]. Similarly, the stability of the Higgs vac-uum can be maintained in both high-scale supersymmetry [31] and non-supersymmetric models [36], when an additional scalar field below 10 10 GeV is present (which can also drive radiative electroweak symmetry breaking).…”