Where to look for solving the gauge hierarchy problem?

Wetterich, C.

doi:10.1016/j.physletb.2012.11.020

Cited by 38 publications

(43 citation statements)

References 29 publications

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“…In terms of the RG, the quadratic divergence indicates the position of the phase boundary in the space of bare couplings. This boundary or "critical surface" separates the symmetric and broken phases and corresponds to the massless (critical) situation [73,[79][80][81][82][83][84]. The position of the phase boundary depends on the precise definition and choice of the bare couplings and on the precise regularization.…”

Section: Scalar Mass Flow and Gauge Hierarchy Problemmentioning

confidence: 99%

Higgs scalar potential in asymptotically safe quantum gravity

et al. 2019

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The effect of gravitational fluctuations on the quantum effective potential for scalar fields is a key ingredient for predictions of the mass of the Higgs boson, understanding the gauge hierarchy problem and a possible explanation of an-asymptotically-vanishing cosmological constant. We find that the quartic self-interaction of the Higgs scalar field is an irrelevant coupling at the asymptotically safe ultraviolet fixed point of quantum gravity. This renders the ratio between the masses of the Higgs boson and top quark predictable. If the flow of couplings below the Planck scale is approximated by the Standard Model, this prediction is consistent with the observed value. The quadratic term in the Higgs potential is irrelevant if the strength of gravity at short distances exceeds a bound that is determined here as a function of the particle content. In this event, a tiny value of the ratio between the Fermi scale and the Planck scale is predicted.

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Section: Scalar Mass Flow and Gauge Hierarchy Problemmentioning

confidence: 99%

Higgs scalar potential in asymptotically safe quantum gravity

et al. 2019

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“…The second view has had substantially fewer proponents in the literature on naturalness, but has been advanced in the work of Wetterich and Bianchi/Rovelli (Bianchi and Rovelli, 2010), (Wetterich, 1984), (Wetterich, 2012). Within the philosophical literature, Williams has more recently adopted this deflationary view of fine tuning formulations of the Higgs naturalness as grounds for characterizing naturalness in terms of inter-scale autonomy rather than fine tuning (Williams, 2015).…”

Section: The Higgs Fine Tuning Naturalness Problemmentioning

confidence: 99%

Naturalness, Wilsonian renormalization, and “fundamental parameters” in quantum field theory

Rosaler

Harlander

2019

Studies in History and Philosophy of Science Part B: Studies in

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The Higgs naturalness principle served as the basis for the so far failed prediction that signatures of physics beyond the Standard Model (SM) would be discovered at the LHC. One influential formulation of the principle, which prohibits fine tuning of bare Standard Model (SM) parameters, rests on the assumption that a particular set of values for these parameters constitute the "fundamental parameters" of the theory, and serve to mathematically define the theory. On the other hand, an old argument by Wetterich suggests that fine tuning of bare parameters merely reflects an arbitrary, inconvenient choice of expansion parameters and that the choice of parameters in an EFT is therefore arbitrary. We argue that these two interpretations of Higgs fine tuning reflect distinct ways of formulating and interpreting effective field theories (EFTs) within the Wilsonian framework: the first takes an EFT to be defined by a single set of physical, fundamental bare parameters, while the second takes a Wilsonian EFT to be defined instead by a whole Wilsonian renormalization group (RG) trajectory, associated with a one-parameter class of physically equivalent parametrizations. From this latter perspective, no single parametrization constitutes the physically correct, fundamental parametrization of the theory, and the delicate cancellation between bare Higgs mass and quantum corrections appears as an eliminable artifact of the arbitrary, unphysical reference scale with respect to which the physical amplitudes of the theory are parametrized. While the notion of fundamental parameters is well motivated in the context of condensed matter field theory, we explain why it may be superfluous in the context of high energy physics.

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“…To apply the results of the non-perturbative analysis to the actual hierarchy problem (1.1), it is necessary to have a theory which is compatible with the models on which the mechanism is tested and is consistent with observations and experiment. A good candidate for such theory is the Higgs-Dilaton model [32,33,37,42,43]. We will show how eq.…”

Section: Introductionmentioning

confidence: 99%

Gravity, scale invariance and the hierarchy problem

Shaposhnikov

Shkerin

2018

J. High Energ. Phys.

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Combining the quantum scale invariance with the absence of new degrees of freedom above the electroweak scale leads to stability of the latter against perturbative quantum corrections. Nevertheless, the hierarchy between the weak and the Planck scales remains unexplained. We argue that this hierarchy can be generated by a non-perturbative effect relating the low energy and the Planck-scale physics. The effect is manifested in the existence of an instanton configuration contributing to the vacuum expectation value of the Higgs field. We analyze such configurations in several toy models and in a phenomenologically viable theory encompassing the Standard Model and General Relativity in a scale-invariant way. Dynamical gravity and a non-minimal coupling of it to the Higgs field play a crucial role in the mechanism. arXiv:1804.06376v2 [hep-th] 5 Oct 2018 ContentsRegardless the particular content of a model extending the SM at high energies, a common approach to the hierarchy problem lies within the effective field theory framework. The latter implies that the low energy description of Nature, provided by the SM, can be affected by an unknown UV physics only through a finite set of parameters. Two of them -the mass of the Higgs boson and the cosmological constant -are most sensitive to the scale and to the dynamics of physics beyond the SM, being quadratically and quartically divergent. In "natural" theories the quadratically divergent UV contributions to the Higgs mass are eliminated by introducing new physics right above the Fermi scale. It is this naturalness principle that is seriously questioned now in light of the absence of signatures of new physics at the TeV scale [10]. While some parameter regions of the theories with M X ∼ 1 TeV still survive at the price of a moderate fine-tuning, a relatively radical step would be to suggest that the UV physics can affect the low energy behavior in a way that is not captured by the perturbation theory. Going back to the ratio (1.1), this would imply the existence of a non-perturbative effect linking the scales separated by 17 orders of magnitude.The idea of some principle that can shape the behavior of a theory at very different energy scales is not novel to particle physics. For example, it is tempting to use such kind of reasoning when investigating a probable (near-)degeneracy of the minima of the Renormalization Group (RG) improved SM Higgs potential, which is supported by the recent measurements of the Higgs and top quark masses [22,23]. A possible mechanism that makes the form of the potential special and, hence, predicts the values of the low energy parameters, can manifest itself in a number of ways. For example, in [24] bounds on the Higgs and top quark masses were put based on the principle of multiple point criticality [25], while in [26] the prediction of m H was made, guiding by an asymptotic safety of gravity [27]. Inspired by these ideas, in this paper we make an attempt to resolve the problem (1.1) by looking for an inherently non-perturbative effect relati...

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Where to look for solving the gauge hierarchy problem?

Cited by 38 publications

References 29 publications

Higgs scalar potential in asymptotically safe quantum gravity

Higgs scalar potential in asymptotically safe quantum gravity

Naturalness, Wilsonian renormalization, and “fundamental parameters” in quantum field theory

Gravity, scale invariance and the hierarchy problem

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