Gauge hierarchy from electroweak vacuum metastability
Abstract
We consider the possibility that the gauge hierarchy is a byproduct of the metastability of the electroweak vacuum, i.e., that whatever mechanism is responsible for the latter also sets the running Higgs mass to a value smaller than its natural value by many orders of magnitude. We find that the metastability of the electroweak vacuum, together with the requirement that such a nontrivial vacuum exists, requires the Higgs mass to be smaller than the instability scale by around 1 order of magnitude. While this bound is quite weak in the Standard Model (SM), as the instability scale is ~1011 GeV, simple and well-motivated extensions of the SM significantly tighten the bound by lowering the instability scale. We first consider the effect of right-handed neutrinos in the vMSM with approximate B -$$\tilde{L}$$ symmetry, which allows for masses of order TeV for the right-handed neutrinos and $$\mathscr{O}$$(1) Yukawa couplings. We find that right-handed neutrinos cannot by themselves fully explain the gauge hierarchy, as the tightest upper bound compatible with current experimental constraints is ~ 108 GeV. As we demonstrate on the example of the minimal SU(4)/Sp(4) composite Higgs model, this bound can be lowered significantly through the interplay of the neutrinos and a dimension-six operator. In this scenario, the bound can be brought down considerably, with the smallest value accessible by our perturbative treatment being of order ≃ 10 TeV, and consistently several orders of magnitude below its natural value. While this is insufficient to fully solve the gauge hierarchy problem, our results imply that, assuming the SM symmetry-breaking pattern, small running Higgs masses are a universal property of theories giving rise to metastability, suggesting a common origin of the two underlying fine-tunings and providing a strong constraint on any attempt to explain metastability.
- Authors:
- Publication Date:
- Research Org.:
- Univ. of Pennsylvania, Philadelphia, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), High Energy Physics (HEP); Heinrich-Böll Foundation; National Aeronautics and Space Administration (NASA); Simons Foundation
- OSTI Identifier:
- 1860288
- Alternate Identifier(s):
- OSTI ID: 1980045
- Grant/Contract Number:
- SC0013528; 80NSSC18K0694
- Resource Type:
- Published Article
- Journal Name:
- Physical Review D
- Additional Journal Information:
- Journal Name: Physical Review D Journal Volume: 105 Journal Issue: 5; Journal ID: ISSN 2470-0010
- Publisher:
- American Physical Society
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 79 ASTRONOMY AND ASTROPHYSICS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; composite models; extension of fermion sector; hierarchy problem; vacuum stability
Citation Formats
Khoury, Justin, and Steingasser, Thomas. Gauge hierarchy from electroweak vacuum metastability. United States: N. p., 2022.
Web. doi:10.1103/PhysRevD.105.055031.
Khoury, Justin, & Steingasser, Thomas. Gauge hierarchy from electroweak vacuum metastability. United States. https://doi.org/10.1103/PhysRevD.105.055031
Khoury, Justin, and Steingasser, Thomas. Wed .
"Gauge hierarchy from electroweak vacuum metastability". United States. https://doi.org/10.1103/PhysRevD.105.055031.
@article{osti_1860288,
title = {Gauge hierarchy from electroweak vacuum metastability},
author = {Khoury, Justin and Steingasser, Thomas},
abstractNote = {We consider the possibility that the gauge hierarchy is a byproduct of the metastability of the electroweak vacuum, i.e., that whatever mechanism is responsible for the latter also sets the running Higgs mass to a value smaller than its natural value by many orders of magnitude. We find that the metastability of the electroweak vacuum, together with the requirement that such a nontrivial vacuum exists, requires the Higgs mass to be smaller than the instability scale by around 1 order of magnitude. While this bound is quite weak in the Standard Model (SM), as the instability scale is ~1011 GeV, simple and well-motivated extensions of the SM significantly tighten the bound by lowering the instability scale. We first consider the effect of right-handed neutrinos in the vMSM with approximate B -$\tilde{L}$ symmetry, which allows for masses of order TeV for the right-handed neutrinos and $\mathscr{O}$(1) Yukawa couplings. We find that right-handed neutrinos cannot by themselves fully explain the gauge hierarchy, as the tightest upper bound compatible with current experimental constraints is ~ 108 GeV. As we demonstrate on the example of the minimal SU(4)/Sp(4) composite Higgs model, this bound can be lowered significantly through the interplay of the neutrinos and a dimension-six operator. In this scenario, the bound can be brought down considerably, with the smallest value accessible by our perturbative treatment being of order ≃ 10 TeV, and consistently several orders of magnitude below its natural value. While this is insufficient to fully solve the gauge hierarchy problem, our results imply that, assuming the SM symmetry-breaking pattern, small running Higgs masses are a universal property of theories giving rise to metastability, suggesting a common origin of the two underlying fine-tunings and providing a strong constraint on any attempt to explain metastability.},
doi = {10.1103/PhysRevD.105.055031},
journal = {Physical Review D},
number = 5,
volume = 105,
place = {United States},
year = {Wed Mar 30 00:00:00 EDT 2022},
month = {Wed Mar 30 00:00:00 EDT 2022}
}
https://doi.org/10.1103/PhysRevD.105.055031
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