Abstract
We study theories which naturally select a vacuum with parametrically small Electroweak Scale due to finite temperature effects in the early universe. In particular, there is a scalar with an approximate shift symmetry broken by a technically natural small coupling to the Higgs, and a temperature dependent potential. As the temperature of the universe drops, the scalar follows the minimum of its potential altering the Higgs mass squared parameter. The scalar also has a periodic potential with amplitude proportional to the Higgs expectation value, which traps it in a vacuum with a small Electroweak Scale. The required temperature dependence of the potential can occur through strong coupling effects in a hidden sector that are suppressed at high temperatures. Alternatively, it can be generated perturbatively from a one-loop thermal potential. In both cases, for the scalar to be displaced, a hidden sector must be reheated to temperatures significantly higher than the visible sector. However this does not violate observational constraints provided the hidden sector energy density is transferred to the visible sector without disrupting big bang nucleosynthesis. We also study how the mechanism can be implemented when the visible sector is completed to the Minimal Supersymmetric Standard Model at a high scale. Models with a UV cutoff of 10 TeV and no fields taking values over a range greater than 1012 GeV are possible, although the scalar must have a range of order 108 times the effective decay constant in the periodic part of its potential.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P.W. Graham, D.E. Kaplan and S. Rajendran, Cosmological Relaxation of the Electroweak Scale, arXiv:1504.07551 [INSPIRE].
L.F. Abbott, A Mechanism for Reducing the Value of the Cosmological Constant, Phys. Lett. B 150 (1985) 427 [INSPIRE].
S.A. Abel, C.-S. Chu, J. Jaeckel and V.V. Khoze, SUSY breaking by a metastable ground state: Why the early universe preferred the non-supersymmetric vacuum, JHEP 01 (2007) 089 [hep-th/0610334] [INSPIRE].
N.J. Craig, P.J. Fox and J.G. Wacker, Reheating Metastable O’Raifeartaigh Models, Phys. Rev. D 75 (2007) 085006 [hep-th/0611006] [INSPIRE].
W. Fischler, V. Kaplunovsky, C. Krishnan, L. Mannelli and M.A.C. Torres, Meta-Stable Supersymmetry Breaking in a Cooling Universe, JHEP 03 (2007) 107 [hep-th/0611018] [INSPIRE].
S.A. Abel, J. Jaeckel and V.V. Khoze, Why the early universe preferred the non-supersymmetric vacuum: Part II, JHEP 01 (2007) 015 [hep-th/0611130] [INSPIRE].
E.F. Moreno and F.A. Schaposnik, R-symmetry and Supersymmetry Breaking at Finite Temperature, JHEP 10 (2009) 007 [arXiv:0908.2770] [INSPIRE].
J.R. Espinosa, G.F. Giudice and A. Riotto, Cosmological implications of the Higgs mass measurement, JCAP 05 (2008) 002 [arXiv:0710.2484] [INSPIRE].
D.J. Gross, R.D. Pisarski and L.G. Yaffe, QCD and Instantons at Finite Temperature, Rev. Mod. Phys. 53 (1981) 43 [INSPIRE].
E. Witten, Large-N Chiral Dynamics, Annals Phys. 128 (1980) 363 [INSPIRE].
N. Kaloper, A. Lawrence and L. Sorbo, An Ignoble Approach to Large Field Inflation, JCAP 03 (2011) 023 [arXiv:1101.0026] [INSPIRE].
J.R. Espinosa, C. Grojean, G. Panico, A. Pomarol, O. Pujolás and G. Servant, Cosmological Higgs-Axion Interplay for a Naturally Small Electroweak Scale, arXiv:1506.09217 [INSPIRE].
J.L. Feng, H. Tu and H.-B. Yu, Thermal Relics in Hidden Sectors, JCAP 10 (2008) 043 [arXiv:0808.2318] [INSPIRE].
S.R. Coleman, The Fate of the False Vacuum. 1. Semiclassical Theory, Phys. Rev. D 15 (1977) 2929 [Erratum ibid. D 16 (1977) 1248] [INSPIRE].
S. Coleman, Aspects of Symmetry: Selected Erice Lectures, Cambridge University Press, Cambridge U.K. (1988).
J. Kapusta and C. Gale, Finite-temperature field theory: Principles and applications, Cambridge University Press, Cambridge U.K. (2006).
N. Seiberg, Naturalness versus supersymmetric nonrenormalization theorems, Phys. Lett. B 318 (1993) 469 [hep-ph/9309335] [INSPIRE].
D. Boyanovsky, Supersymmetry Breaking at Finite Temperature: The Goldstone Fermion, Phys. Rev. D 29 (1984) 743 [INSPIRE].
A.K. Das and M. Kaku, Supersymmetry at high temperatures, Phys. Rev. D 18 (1978) 4540 [INSPIRE].
L. Girardello, M.T. Grisaru and P. Salomonson, Temperature and Supersymmetry, Nucl. Phys. B 178 (1981) 331 [INSPIRE].
K. Cheung and C.-W. Chiang, Splitting split supersymmetry, Phys. Rev. D 71 (2005) 095003 [hep-ph/0501265] [INSPIRE].
A. Arvanitaki, N. Craig, S. Dimopoulos and G. Villadoro, Mini-Split, JHEP 02 (2013) 126 [arXiv:1210.0555] [INSPIRE].
U. Ellwanger, C. Hugonie and A.M. Teixeira, The Next-to-Minimal Supersymmetric Standard Model, Phys. Rept. 496 (2010) 1 [arXiv:0910.1785] [INSPIRE].
S.P. Martin, A Supersymmetry primer, hep-ph/9709356 [INSPIRE].
J.P. Vega and G. Villadoro, SusyHD: Higgs mass Determination in Supersymmetry, JHEP 07 (2015) 159 [arXiv:1504.05200] [INSPIRE].
P. Sikivie, Axion Cosmology, Lect. Notes Phys. 741 (2008) 19 [astro-ph/0610440] [INSPIRE].
L. Kofman, A.D. Linde and A.A. Starobinsky, Reheating after inflation, Phys. Rev. Lett. 73 (1994) 3195 [hep-th/9405187] [INSPIRE].
L. Kofman, A.D. Linde and A.A. Starobinsky, Towards the theory of reheating after inflation, Phys. Rev. D 56 (1997) 3258 [hep-ph/9704452] [INSPIRE].
E. Hardy and J. Unwin, Preferential Reheating, forthcoming.
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1507.07525
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Hardy, E. Electroweak relaxation from finite temperature. J. High Energ. Phys. 2015, 77 (2015). https://doi.org/10.1007/JHEP11(2015)077
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2015)077