Abstract
We confront the perturbativity problem in the real scalar quintuplet minimal dark matter model. In the original model, the quintuplet quartic self-coupling inevitably hits a Landau pole at a scale ~1014 GeV, far below the Planck scale. In order to push up this Landau pole scale, we extend the model with a fermionic quintuplet and three fermionic singlets which couple to the scalar quintuplet via Yukawa interactions. Involving such Yukawa interactions at a scale ~1010 GeV can not only keep all couplings perturbative up to the Planck scale, but can also explain the smallness of neutrino masses via the type-I seesaw mechanism. Furthermore, we identify the parameter regions favored by the condition that perturbativity and vacuum stability are both maintained up to the Planck scale.
Highlights
One of the biggest mysteries of Nature, dark matter (DM) has drawn much attention from astrophysicists, cosmologists, and particle physicists
Introducing one nontrivial SU(2)L multiplet leads to the so-called minimal dark matter (MDM) models [5,6,7,8,9,10,11,12,13,14,15,16,17,18], which only involve the minimal content of new fields
Setting f2(0) = −69/52, which corresponds to λ2 = 0 at μ = Λs, we find that the maximal Landau pole (LP) scale for λ2 is Λ(LλP2) = 5.6×1014 GeV, which is far below the Planck scale
Summary
One of the biggest mysteries of Nature, dark matter (DM) has drawn much attention from astrophysicists, cosmologists, and particle physicists. The philosophy of the MDM models is to extend the standard model (SM) in a minimal way to involve dark matter [5] For this purpose, a fermionic or scalar SU(2)L × U(1)Y multiplet in a representation (n, Y ) is introduced. One can always introduce an artificial Z2 symmetry to make the model work again, but considering n = 7 would not be special any more In this case, discussing a triplet (n = 3) or quintuplet (n = 5) real scalar multiplet with Y = 0 would be more economic. With two independent septuplet self-interaction terms, the real scalar septuplet model hits a Landau pole at a scale around 108 GeV if the DM particle mass is fixed to satisfy the observed relic abundance. Appendix A gives the β functions and initial values of SM couplings, while Appendix B gives the detailed calculation of the Sommerfeld enhancement effect
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