Renormalization group flow of the Higgs potential

Gies, Holger; Sondenheimer, René

doi:10.1098/rsta.2017.0120

Cited by 13 publications

(13 citation statements)

References 58 publications

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“…In particular, this work makes use of the formulation of the exact renormalisation group by Wetterich [2], which has been applied to a wide range of systems, e.g. scalar field theories [3][4][5][6][7][8][9][10][11][12], fermionic systems [13][14][15][16][17][18][19], critical phenomena [20][21][22][23][24][25][26], gauge theories [27][28][29][30][31][32][33][34] and quantum gravity [35][36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51]…”

Section: Introductionmentioning

confidence: 99%

Solving functional flow equations with pseudospectral methods

Borchardt

Knorr

2016

Phys. Rev. D

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We apply pseudo-spectral methods to integrate functional flow equations with high accuracy, extending earlier work on functional fixed point equations [1]. The advantages of our method are illustrated with the help of two classes of models: first, to make contact with literature, we investigate flows of the O(N )-model in 3 dimensions, for N = 1, 4 and in the large N limit. For the case of a fractal dimension, d = 2.4, and N = 1, we follow the flow along a separatrix from a multicritical fixed point to the Wilson-Fisher fixed point over almost 13 orders of magnitude. As a second example, we consider flows of bounded quantum-mechanical potentials, which can be considered as a toy model for Higgs inflation. Such flows pose substantial numerical difficulties, and represent a perfect test bed to exemplify the power of pseudo-spectral methods.

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Section: Introductionmentioning

confidence: 99%

Solving functional flow equations with pseudospectral methods

Borchardt

Knorr

2016

Phys. Rev. D

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“…This model strongly simplifies the electroweak sector. Nevertheless, it contains the main ingredients to discuss the generic properties of the lower Higgs-mass bound and the stability properties of the effective Higgs potential [51][52][53][54]. Note that the model under consideration is invariant under a discrete chiral symmetry φ → −φ, t → e i π 2 γ5 t,t →t e i π 2 γ5 as well as a continuous U(1) symmetry ψ → e iα ψ,ψ → e −iαψ .…”

Section: Rg Flow Of a Simple Higgs-yukawa Model With Fermionic Damentioning

confidence: 99%

Higgs stability-bound and fermionic dark matter

Held¹,

Sondenheimer

2019

J. High Energ. Phys.

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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][...

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“…Furthermore, it is not enough that the vacuum is stable today, but it must have also been sufficiently stable throughout its history to survive until today [1,2,4]. Therefore, vacuum instability has to be analysed in the context of cosmology, and it can potentially constrain cosmological models.…”

Section: Running Coupling and Vacuum Instabilitymentioning

confidence: 99%

“…For the central experimental values of the masses, the rate is, however, very slow and the predicted lifetime of our current vacuum state is many orders of magnitude longer than the age of the Universe. On the other hand, the rate would be changed by any modification of the standard model, and therefore vacuum stability provides a test that any such theory has to satisfy [1,2].…”

Section: Running Coupling and Vacuum Instabilitymentioning

confidence: 99%

Higgs cosmology

Rajantie¹

2018

Phil. Trans. R. Soc. A.

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The discovery of the Higgs boson in 2012 and other results from the Large Hadron Collider have confirmed the standard model of particle physics as the correct theory of elementary particles and their interactions up to energies of several TeV. Remarkably, the theory may even remain valid all the way to the Planck scale of quantum gravity, and therefore it provides a solid theoretical basis for describing the early Universe. Furthermore, the Higgs field itself has unique properties that may have allowed it to play a central role in the evolution of the Universe, from inflation to cosmological phase transitions and the origin of both baryonic and dark matter, and possibly to determine its ultimate fate through the electroweak vacuum instability. These connections between particle physics and cosmology have given rise to a new and growing field of Higgs cosmology, which promises to shed new light on some of the most puzzling questions about the Universe as new data from particle physics experiments and cosmological observations become available. This article is part of the Theo Murphy meeting issue ‘Higgs cosmology’.

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Renormalization group flow of the Higgs potential

Cited by 13 publications

References 58 publications

Solving functional flow equations with pseudospectral methods

Solving functional flow equations with pseudospectral methods

Higgs stability-bound and fermionic dark matter

Higgs cosmology

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