Vacuum stability in the Standard Model is problematic as the Higgs quartic self-coupling runs negative at a renormalization scale of about 1010 GeV. We consider a nonsupersymmetric 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.
Bibliographical noteFunding Information:
This work was supported by the Spanish MICINN's Consolider-Ingenio 2010 Programme under Grant No.Multi-Dark CSD2009-00064 and the LIA-TCAP of CNRS and the France-US PICS Grant No.06482. Y. M. acknowledges partial support from the European Union FP7 ITN INVISIBLES (Marie Curie Actions, Grant No.PITN- GA-2011- 289442) and the ERC advanced grants Higgs@LHC. The work of N. N. and K. A. O. was supported in part by DOE Grant No.DE-SC0011842 at the University of Minnesota.
© 2016 American Physical Society.