Higgs Naturalness Research Articles

Dogmas of Effective Field Theory: Scheme Dependence, Fundamental Parameters, and the Many Faces of the Higgs Naturalness Principle

The earliest formulation of the Higgs naturalness argument has been criticized on the grounds that it relies on a particular cutoff-based regularization scheme. One response to this criticism has been to circumvent the worry by reformulating the naturalness argument in terms of a renormalized, regulator-independent parametrization. An alternative response is to deny that regulator dependence poses a problem for the naturalness argument, because nature itself furnishes a particular, physically correct regulator for any effective field theory (EFT) in the form of that EFT’s physical cutoff, together with an associated set of bare parameters that constitute the unique physically preferred “fundamental parameters” of the EFT. Here, I argue that both lines of defense against the initial worry about regulator dependence are flawed. I argue that reformulation of the naturalness argument in terms of renormalized parameters simply trades dependence on a particular regularization scheme for dependence on a particular renormalization scheme, and that one or another form of scheme dependence afflicts all formulations of the Higgs naturalness argument. Concerning the second response, I argue that the grounds for suspending the principle of regularization or renormalization scheme independence in favor of a physically preferred parametrization are thin; the assumption of a physically preferred parametrization, whether in the form of bare “fundamental parameters” or renormalized “physical parameters,” constitutes a theoretical idle wheel in generating the confirmed predictions of established EFTs, which are invariably scheme-independent. I highlight certain features of the alternative understanding of EFTs, and the EFT-based approach to understanding the foundations of QFT, that emerges when one abandons the assumption of a physically preferred parametrization. I explain how this understanding departs from several dogmas concerning the mathematical formulation and physical interpretation of EFTs in high-energy physics.

Crunching Dilaton, Hidden Naturalness.

We introduce a new approach to the Higgs naturalness problem. The Higgs mixes with the dilaton of a conformal field theory (CFT) sector whose true ground state has a large negative vacuum energy. If the Higgs vacuum expectation value is nonzero and below O(TeV), the CFT admits a second metastable vacuum, where the expansion history of the Universe is conventional. As a result, only Hubble patches with unnaturally small values of the Higgs mass do not immediately crunch. The main experimental prediction of this mechanism is a dilaton in the 0.1-10GeV range that mixes with the Higgs and can be detected at future colliders and experiments searching for weakly coupled particles.

Heavy dark matter, neutrino masses, and Higgs naturalness from a strongly interacting hidden sector

We consider the extension of the Standard Model (SM) with a strongly interacting QCD-like hidden sector, at least two generations of right-handed neutrinos and one scalar singlet. Once scalar singlet obtains a nonzero vacuum expectation value, active neutrino masses are generated through type-I seesaw mechanism. Simultaneously, the electroweak scale is generated through the radiative corrections involving these massive fermions. This is the essence of the scenario that is known as the "neutrino option" for which the successful masses of right-handed neutrinos are in the range $10^7-10^8$ GeV. The main goal of this work is to scrutinize the potential to accommodate dark matter in such a realization. The dark matter candidates are Nambu-Goldstone bosons which appear due to the dynamical breaking of the hidden chiral symmetry. The mass spectrum studied in this work is such that masses of Nambu-Goldstone bosons and singlet scalar exceed those of right-handed neutrinos. Having the masses of all relevant particles several orders of magnitude above $\mathcal{O}$(TeV), the freeze-out of dark matter is not achievable and hence we turn to alternative scenarios, namely freeze-in. The Nambu-Goldstone bosons can interact with particles that are not in SM but, however, have non-negligible abundance through their not-too-small couplings with SM. Utilizing this, we demonstrate that the dark matter in the model is successfully produced at temperature scale where the right-handed neutrinos are still stable. We note that the lepton number asymmetry sufficient for the generation of observable baryon asymmetry of the Universe can be produced in right-handed neutrino decays. Hence, we infer that the model has the potential to simultaneously address several of the most relevant puzzles in contemporary high-energy physics.

Neutrino mass models: new classification and model-independent upper limits on their scale

We propose a model-independent framework to classify and study neutrino mass models and their phenomenology. The idea is to introduce one particle beyond the Standard Model which couples to leptons and carries lepton number together with an operator which violates lepton number by two units and contains this particle. This allows to study processes which do not violate lepton number, while still working with an effective field theory. The contribution to neutrino masses translates to a robust upper bound on the mass of the new particle. We compare it to the stronger but less robust upper bound from Higgs naturalness and discuss several lower bounds. Our framework allows to classify neutrino mass models in just 20 categories, further reduced to 14 once nucleon decay limits are taken into account, and possibly to 9 if also Higgs naturalness considerations and direct searches are considered.

The Selfish Higgs

We propose a mechanism to solve the Higgs naturalness problem through a cosmological selection process. The discharging of excited field configurations through membrane nucleation leads to discrete jumps of the cosmological constant and the Higgs mass, which vary in a correlated way. The resulting multitude of universes are all empty, except for those in which the cosmological constant and the Higgs mass are both nearly vanishing. Only under these critical conditions can inflation be activated and create a non-empty universe.

EFTs meet Higgs nonlinearity, compositeness and (neutral) naturalness

Composite Higgs and neutral-naturalness models are popular scenarios in which the Higgs boson is a pseudo Nambu-Goldstone boson (PNGB), and naturalness problem is addressed by composite top partners. Since the standard model effective field theory (SMEFT) with dimension-six operators cannot fully retain the information of Higgs nonlinearity due to its PNGB nature, we systematically construct low energy Lagrangian in which the information of compositeness and Higgs nonlinearity are encoded in the form factors, the two-point functions in the top sector. We classify naturalness conditions in various scenarios, and first present these form factors in composite neutral naturalness models. After extracting out Higgs effective couplings from these form factors and performing the global fit, we find the value of Higgs top coupling could still be larger than the standard model one if the top quark is embedded in the higher dimensional representations. Also we find the impact of Higgs nonlinearity is enhanced by the large mass splitting between composite states. In this case, pattern of the correlation between the t overline{t} h and t overline{t} hh couplings is quite different for the linear and nonlinear Higgs descriptions.

Higgs Naturalness and Renormalized Parameters

A recently popular formulation of the Higgs naturalness principle prohibits delicate cancellations between running renormalized Higgs mass parameters and EFT matching corrections, by contrast with the principle’s original formulation, which prohibits delicate cancellations between the bare Higgs mass parameter and its quantum corrections. While the need for this latter cancellation is sometimes viewed as unproblematic since bare parameters are thought by some to be divergent and unphysical, renormalized parameters are finite and measurable, and the need for delicate cancellations between the renormalized Higgs mass parameter and EFT matching corrections is therefore considered by some to constitute a more salient formulation of the Higgs naturalness problem. Here, we argue that to the contrary, the need for fine tuning of the renormalized Higgs mass parameter is an eliminable, unphysical artifact of renormalization scheme, and that this severely weakens the grounds for regarding it as a problematic instance of fine tuning. In doing so, we highlight what we take to be a number of important conceptual lessons about the physical interpretation of model parameters in QFT.

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

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.

The origin of particle masses and the naturalness problem

Electroweak symmetry breaking is the key ingredient of the standard model responsible for the generation of all elementary particle masses. The discovery of the Higgs boson is a major milestone towards understanding the mechanism of electroweak symmetry breaking but several important issues remain unexplained. Among them the key mystery is how to stabilize the electroweak symmetry scale, called the naturalness problem. To solve this problem, some new physics should be introduced to screen quantum corrections from higher energy scale. There are two classes of new physics theories: one is super symmetry model in which Higgs quadratic divergence is cancelled through the extended space-time symmetry between scalars and fermions. The other one is composite Higgs model in which the sensitivity to higher energy scale is reduced by the composite nature of Higgs. In super symmetry model, every field in standard model should have a super symmetric partner, which makes this theory very complicated. However, the composite Higgs models can address the naturalness problem in a very simple way. In this article we first review the Higgs mechanism in standard model and explain Higgs naturalness problem. Then we generally review the super symmetry model and its phenomenology. It is found that the tuning of this kind of model is worse than 1% when confronts experimental measurements. In the remaining parts we focus on discussing the composite Higgs model. We first review the structure of composite Higgs models and then discuss how to reduce Higgs mass through some symmetry collectively breaking or extra dimension mechanism. It is found that, in this kind of models, to produce a light Higgs the composite quarks canceling Higgs quadratic divergences should be relatively light, around 1 TeV. But the constraints from Large Hadron Collider (LHC) indicate that these fermions should be much heavier than 1 TeV, which results the difficulty in achieving a light Higgs. Moreover, to evade precise electroweak tests, the electroweak scale should be separated with Higgs confinement scale, called the Little Hierarchy, requiring more tuning in this model. In order to produce light Higgs while keeping composite quarks heavy, we plan to find a general principle to realize neutral naturalness mechanism in which Higgs quadratic divergences are cancelled by hidden sector. And then find the UV completion for this mechanism and fully study its phenomenology. In order to naturally solve Little Hierarchy, we plan to construct a mechanism to produce Higgs tree level or loop level self-quartic coupling, so that the big separation between electroweak and confinement scale can be achieved by adjusting properly this coupling without introducing any tuning. After solving above two problems, we combine these two mechanisms to construct the super-natural composite Higgs model which can successfully achieve electroweak symmetry breaking without any tuning.

Naturalness in testable type II seesaw scenarios

New physics coupling to the Higgs sector of the Standard Model can lead to dangerously large corrections to the Higgs mass. We investigate this problem in the type II seesaw model for neutrino mass, where a weak scalar triplet is introduced. The interplay of direct and indirect constraints on the type II seesaw model with its contribution to the Higgs mass is analyzed. The focus lies on testable triplet masses and (sub) eV-scale triplet vacuum expectation values. We identify scenarios that are testable in collider and/or lepton flavor violation experiments, while satisfying the Higgs naturalness criterion.

A clockwork theory

The clockwork is a mechanism for generating light particles with exponentially suppressed interactions in theories which contain no small parameters at the fundamental level. We develop a general description of the clockwork mechanism valid for scalars, fermions, gauge bosons, and gravitons. This mechanism can be implemented with a discrete set of new fields or, in its continuum version, through an extra spatial dimension. In both cases the clockwork emerges as a useful tool for model-building applications. Notably, the continuum clockwork offers a solution to the Higgs naturalness problem, which turns out to be the same as in linear dilaton duals of Little String Theory. We also elucidate the similarities and differences of the continuum clockwork with large extra dimensions and warped spaces. All clockwork models, in the discrete and continuum, exhibit novel phenomenology with a distinctive spectrum of closely spaced resonances.

Solving the standard model problems in softened gravity

The Higgs naturalness problem is solved if the growth of Einstein's gravitational interaction is softened at an energy $ \lesssim 10^{11}\,$GeV (softened gravity). We work here within an explicit realization where the Einstein-Hilbert Lagrangian is extended to include terms quadratic in the curvature and a non-minimal coupling with the Higgs. We show that this solution is preserved by adding three right-handed neutrinos with masses below the electroweak scale, accounting for neutrino oscillations, dark matter and the baryon asymmetry. The smallness of the right-handed neutrino masses (compared to the Planck scale) and the QCD $\theta$-term are also shown to be natural. We prove that a possible gravitational source of CP violation cannot spoil the model, thanks to the presence of right-handed neutrinos. Inflation is approximately described by the Starobinsky model in this context, and can occur even if we live in a metastable vacuum.

Softening Higgs Naturalness – an EFT Analysis

We investigate naturalness in the Standard Model (SM) Higgs sector using effective field theory (EFT) techniques and find the requirements on the new heavy physics that can potentially cure the little hierarchy problem below a scale Λ≫O(1 TeV), assuming the new heavy particles have a mass larger than Λ. In particular, we determine the conditions under which the 1-loop corrections to mh from the heavy new physics can balance those created by SM loop effects up to the naturalness scale Λ, a condition we denote by “EFT Naturalness”. We obtain the higher dimensional (n≥5) operators in the effective Lagrangian that can lead to EFT Naturalness, and classify the underlying heavy theories that can generate such operators at tree-level. We also address the experimental constraints on our EFT Naturalness setup and discuss the expected experimental signals of the new heavy physics associated with EFT Naturalness.

Higgs naturalness and dark matter stability by scale invariance

Extending the spacetime symmetries of standard model (SM) by scale invariance (SI) may address the Higgs naturalness problem. In this article we attempt to embed accidental dark matter (DM) into SISM, requiring that the symmetry protecting DM stability is accidental due to the model structure rather than imposed by hand. In this framework, if the light SM-like Higgs boson is the pseudo Goldstone boson of SI spontaneously breaking, we can even pine down the model, two-Higgs-doublets plus a real singlet: The singlet is the DM candidate and the extra Higgs doublet triggers electroweak symmetry breaking via the Coleman–Weinberg mechanism; Moreover, it dominates DM dynamics. We study spontaneously breaking of SI using the Gillard–Weinberg approach and find that the second doublet should acquire vacuum expectation value near the weak scale. Moreover, its components should acquire masses around 380 GeV except for a light CP-odd Higgs boson. Based on these features, we explore viable ways to achieve the correct relic density of DM, facing stringent constraints from direct detections of DM. For instance, DM annihilates into bb¯ near the SM-like Higgs boson pole, or into a pair of CP-odd Higgs boson with mass above that pole.

Effective field theory analysis of Higgs naturalness

Assuming the presence of physics beyond the Standard Model (SM) with a characteristic scale $M\ensuremath{\sim}\mathcal{O}(10)\text{ }\text{ }\mathrm{TeV}$, we investigate the naturalness of the Higgs sector at scales below $M$ using an effective field theory (EFT) approach. We obtain the complete set of higher-dimensional effective operators (at any dimension $n\ensuremath{\ge}5$) that give the leading one-loop EFT contributions to the Higgs mass with a Wilsonian-like hard cutoff and discuss the (fine-) tuning between these terms and the SM one-loop contribution, which is required in order to alleviate the little hierarchy problem. We then show that this tuning can be translated into a condition for naturalness in the underlying new physics, a condition we denote by ``EFT naturalness'' and which we express as constraints on the corresponding higher-dimensional operator coefficients up to the scale of the effective action $\mathrm{\ensuremath{\Lambda}}lM$. We also determine the types of physics that can lead to EFT naturalness and discuss the current experimental constraints on the relevant operator coefficients. We show that these types of new physics are best probed in vector-boson and multiple-Higgs production.

Higgs naturalness and the scalar boson proliferation instability problem

Sensitivity to the square of the cutoff scale of quantum corrections of the Higgs boson mass self-energy has led many authors to conclude that the Higgs theory suffers from a naturalness or fine-tuning problem. However, speculative new physics ideas to solve this problem have not manifested themselves yet at high-energy colliders, such as the Large Hadron Collider at CERN. For this reason, the role of naturalness as a guide to theory model-building is being severely questioned. Most attacks suggest that one should not resort to arguments involving gravity, which is a much less understood quantum field theory. Another line of attack is against the assumption that there exists a multitude of additional heavy states specifically charged under the Standard Model gauge symmetries. Nevertheless, if we give ground on both of these assaults on naturalness, what remains is a naturalness concern over the prospect of numerous additional spin-zero scalar states in nature. The proliferation of heavy scalars generically destabilizes the Higgs boson mass, raising it to the highest and most remote scalar mass values in nature, thus straining the legitimacy of the Standard Model. The copious use of extra scalars in theory model building, from explaining flavor physics to providing an inflationary potential and more, and the generic expectation of extra scalar bosons in nature argues for the proliferation instability problem being the central concern for naturalness of the Standard Model. Some approaches to solving this problem are presented.

Stop on top: SUSY parameter regions and fine-tuning constraints

We analyze minimal supersymmetric models in order to determine in what parameter regions with what amount of fine-tuning they are capable of accomodating the LHC-allowed top-stop degeneracy window. The stops must be light enough to enable Higgs naturalness yet heavy enough to induce a 125 GeV Higgs boson mass. These two constraints imply a large mass splitting. By an elaborate scan of the parameter space, we show that stop-on-top scenario requires at least Delta_CMSSM ~ O(10^4) fine-tuning in the CMSSM. By relaxing the CMSSM parameter space with nonuniversal Higgs masses, we find that Delta_NUHM1 ~ O(10^4). The CMSSM with gravitino LSP works slightly better than the NUHM1 model. Compared to all these, the CMSSM with mu<0 and nonuniversal gauginos yield a much smaller fine-tuning Delta_{mu,g} ~ O(100). Our results show that gaugino sector can pave the road towards a more natural stop-on-top scenario.

Guises and disguises of quadratic divergences

In this contribution, we present a new perspective on the control of quadratic divergences in quantum field theory, in general, and in the Higgs naturalness problem, in particular. Our discussion is essentially based on an approach where UV divergences are parameterized, after being reduced to basic divergent integrals (BDI) in one internal momentum, as functions of a cutoff and a renormalization group scale λ. We illustrate our proposal with well-known examples, such as the gluon vacuum self energy of QCD and the Higgs decay in two photons within this approach. We also discuss frameworks in effective low-energy QCD models, where quadratic divergences are indeed fundamental.

Gauge-Higgs unification in spontaneously created fuzzy extra dimensions

We propose gauge-Higgs unification in fuzzy extra dimensions as a possible solution to the Higgs naturalness problem. In our approach, the fuzzy extra dimensions are created spontaneously as a vacuum solution of certain four-dimensional gauge theory. As an example, we construct a model which has a fuzzy torus as its vacuum. The Higgs field in our model is associated with the Wilson loop wrapped on the fuzzy torus. We show that the quadratic divergence in the mass of the Higgs field in the one-loop effective potential is absent. We then argue based on symmetries that the quantum corrections to the Higgs mass is suppressed including all loop contributions. We also consider a realization on the worldvolume theory of D3-branes probing $C^3/(Z_N \times Z_N)$ orbifold with discrete torsion.

SUSY splits, but then returns

We study the phenomenon of accidental or “emergent” supersymmetry within gauge theory and connect it to the scenarios of Split Supersymmetry and Higgs compositeness. Combining these elements leads to a significant refinement and extension of the proposal of Partial Supersymmetry, in which supersymmetry is broken at very high energies but with a remnant surviving to the weak scale. The Hierarchy Problem is then solved by a non-trivial partnership between supersymmetry and compositeness, giving a promising approach for reconciling Higgs naturalness with the wealth of precision experimental data. We discuss aspects of this scenario from the AdS/CFT dual viewpoint of higher-dimensional warped compactification. It is argued that string theory constructions with high scale supersymmetry breaking which realize warped/composite solutions to the Hierarchy Problem may well be accompanied by some or all of the features described. The central phenomenological considerations and expectations are discussed, with more detailed modelling within warped effective field theory reserved for future work.