Higgs stability-bound and fermionic dark matter

Abstract

Higgs-portal interactions of fermionic dark matter -in contrast to fermions coupled via Yukawa interactions -can have a stabilizing effect on the standard-model Higgs potential. A non-perturbative renormalization-group analysis reveals that, similar to higher-order operators in the Higgs potential itself, the fermionic portal coupling can increase the metastability scale by only about one order of magnitude. Furthermore, this regime of very weakly coupled dark matter is in conflict with relic-density constraints. Conversely, fermionic dark matter with the right relic abundance requires either a low cutoff scale of the effective field theory or a strongly interacting scalar sector. This results in a triviality problem in the scalar sector which persists at the non-perturbative level. The corresponding breakdown of the effective field theory suggests a larger dark sector to be present not too far above the dark-fermion mass-scale. I. THE HIGGS POTENTIAL AND NEW PHYSICSThe most surprising result obtained at the Large Hadron Collider might be, that the masses and couplings conspire to render the standard model consistent up to very high energy scales, possibly even all the way up to the Planck scale [1][2][3][4][5]. It is a delicate balance between the running of gauge couplings, Yukawa couplings and the Higgs potential that results in this unexpected experimental result. Although this so-called "desert" disfavors new degrees of freedom to be discovered any time soon, it should maybe not be taken as discouragement. Experimental evidence suggests that our knowledge of the Universe is more complete than we might have hoped for. The vast other parts of parameter space, in which the standard model as an effective field theory (EFT) could in principle be realized, results either in an instability of the scalar potential or in a sub-Planckian triviality problem. Both of these could be interpreted as a clear sign for a breakdown of the standard model and an associated new physics scale.Focusing on the central measurement values [6], the standard model as an EFT is potentially valid up to Λ (SM) EFT ≈ 10 41 GeV. At this scale, the theory reaches a U (1) Landau-pole in perturbation theory [7], reflected in a triviality problem at the non-perturbative level [8][9][10]. This would suggest that the next energy scale that theorists should be concerned about is the Planck scale, at which a joint theory of gravity and matter becomes necessary, see e.g., [11][12][13][14][15][16][17]. On the other hand, the standard model Higgs-potential, assuming that the current central values of measured mass and coupling parameters were exact, develops a metastability. The energy scale associated with this metastability is Λ (SM) meta ≈ 10 10 − 10 11 GeV [1-5, 18]. Much interesting physics can be associated with this metastability [19][20][21][22][23], and the metastable * a.held@thphys.uni-heidelberg.de † rene.sondenheimer@uni-jena.de electroweak vacuum could be long-lived enough to allow for the current age of the universe [24][25][26][27][28][...

The nonperturbative functional renormalization group and its applications

“…In [1018] the vacuum stability was studied with spectral methods, that allow to explore the global form of the potential. Studies of vacuum stability with new degrees of freedom, specifically scalar and fermionic dark matter, coupled through a Higgs portal, can be found in [1019,1020]. For a summary and references on this question with other techniques, see [1021].…”

Towards a Higgs mass determination in asymptotically safe gravity with a dark portal

“…These values were obtained with a top mass Mt = 172.8GeV[23] 2. If a different UV completion is valid above the scale Λ M Pl , but below Λ effective metric degrees of freedom govern the RG flow, then effective asymptotic safety could play a role and enhance predictivity, see e.g.,[137][138][139][140][141].3 For an FRG study of vacuum stability in the Higgs portal to fermionic dark matter, see[168].…”

Universal gravitational-wave signatures from heavy new physics in the electroweak sector

“…We use the functional renormalization group (FRG) [73] as a non-perturbative tool, for reviews of the FRG, see, e.g., [74][75][76][77][78][79]. In the context of Higgs physics, this method is particularly well suited to explore various questions related to the Higgs potential, such as its (non-perturbative) stability [80][81][82][83][84][85], as well as the impact of a portal to dark matter [86,87]. The method is well-suited to be used in the context of an effective theory with a finite new-physics scale, where it can in particular be used to go beyond perturbation theory and analyze generic new-physics contributions not restricted by perturbativity.…”