hierarchy problem (physics)
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| hierarchy problem (physics) | |
|---|---|
| Name | Hierarchy problem (physics) |
| Field | Particle physics, Quantum field theory, Cosmology |
| Discovered | 1970s |
| Discoverer | Gerard 't Hooft, K. Symanzik |
hierarchy problem (physics)
The hierarchy problem (physics) is the tension between the observed low mass of the Higgs boson and the large energy scales associated with gravity and proposed high-energy theories. It arises in attempts to reconcile the Standard Model with candidates such as Grand Unified Theory, Supersymmetry, and scenarios invoking the Planck scale or string theory. The question motivates model building in particle physics and guides searches at facilities like the Large Hadron Collider and experiments at CERN.
Overview
The hierarchy problem (physics) concerns why the weak scale set by the Higgs field vacuum expectation value (~246 GeV) is so much smaller than the Planck scale (~1.22×10^19 GeV), the scale associated with gravity and quantum gravity proposals like string theory and M-theory. It also touches on scale separation in Grand Unified Theory frameworks such as SU(5), SO(10), and E6, and the sensitivity of scalar masses to ultraviolet physics in effective field theories rooted in Quantum field theory. Prominent figures who shaped the conceptual problem include Gerard 't Hooft, Leonard Susskind, Howard Georgi, and Steven Weinberg.
Formulation in Quantum Field Theory
In the language of Quantum field theory, the hierarchy problem (physics) appears as the quadratic sensitivity of a scalar mass parameter to high-energy cutoffs like the Planck scale or a Grand Unified Theory scale. Radiative corrections to the Higgs boson mass in perturbative calculations involve loops containing particles from the Standard Model—for example, the top quark, W boson, and Z boson—and hypothetical heavy states from Supersymmetry, Technicolor, or Extra dimensions constructions. Naturalness arguments advanced by Gerard 't Hooft and critiques by John Bell and Leonard Susskind frame fine-tuning as an aesthetic and technical problem in renormalization and regularization schemes such as those introduced by Kenneth Wilson and Gabriele Veneziano.
Proposed Solutions and Extensions
A variety of approaches address the hierarchy problem (physics). Supersymmetry (e.g., Minimal Supersymmetric Standard Model) introduces superpartners that cancel quadratic divergences; influential proponents include Savas Dimopoulos and Howard Georgi. Technicolor and composite-Higgs models invoke strong dynamics analogous to Quantum chromodynamics and were developed by researchers like Steven Weinberg and S. Dimopoulos. Extra-dimensional proposals such as the Randall–Sundrum model and Arkani-Hamed–Dimopoulos–Dvali model use warped or large extra dimensions to lower effective scales; key names include Lisa Randall and Nima Arkani-Hamed. Anthropic and landscape arguments derive from string theory vacua discussions by Leonard Susskind and involve the multiverse framing proposed by Andrei Linde and Alan Guth. Other ideas include relaxion mechanisms introduced by Graham, Kaplan, and Rajendran, asymptotic safety advocated by Steven Weinberg, and neutral naturalness exemplified by the Twin Higgs models associated with Zohar Komargodski and collaborators.
Experimental Tests and Constraints
Collider searches at the Large Hadron Collider and experiments like ATLAS and CMS have constrained simple implementations of Supersymmetry and many composite or extra-dimensional signatures, putting pressure on low-scale solutions to the hierarchy problem (physics). Precision measurements from LEP, flavor experiments at Belle II and LHCb, and electroweak fits conducted by groups connected to CERN and Fermilab have limited parameter space for models such as the Minimal Supersymmetric Standard Model and low-scale Grand Unified Theory variants like SO(10). Direct searches for resonances, missing energy signals, and exotic decays yield bounds feeding into global fits performed by collaborations including ATLAS and CMS. Cosmological probes from Planck and observations related to inflationary scenarios by Alan Guth and Andrei Linde inform anthropic and landscape considerations.
Related Theoretical Issues
The hierarchy problem (physics) intersects with several conceptual issues: the cosmological constant problem highlighted by Steven Weinberg; naturalness debates involving figures like Leonard Susskind and Giovanni Ridolfi; vacuum stability analyses tied to the measured Higgs boson and top quark masses; and ultraviolet completions in string theory and loop quantum gravity communities including Juan Maldacena and Carlo Rovelli. It also relates to model-building frameworks such as Effective field theory, renormalization group flow studied by Kenneth Wilson, and conjectures about quantum gravity from Edward Witten and Ashoke Sen.
Historical Development
Recognition of fine-tuning in scalar masses emerged in the 1970s amid the development of renormalization and Grand Unified Theory proposals; early contributors included Gerard 't Hooft, Kenneth Wilson, and Sidney Coleman. Throughout the 1980s and 1990s, influential work on Supersymmetry by Peter Fayet, Savas Dimopoulos, and Howard Georgi, and on Technicolor by Steven Weinberg and S. Dimopoulos, shaped the dominant paradigms. The discovery of the Higgs boson at CERN in 2012 intensified scrutiny, leading to renewed interest in alternatives such as anthropic reasoning promoted by Leonard Susskind and landscape ideas from Michael Douglas. Ongoing experimental results from LHC runs and theoretical developments in string theory and cosmology continue to drive the debate.