Abstract
We discuss aspects of the hierarchy problem in effective theories with light scalars and a large, physical ultraviolet (UV) cutoff. We make two main points: (1) The (naive) fine-tuning observed in an effective theory does not automatically imply that the UV completion is fine tuned. Instead, it gives a type of upper bound on the severity of the actual tuning in the UV completion; the actual tuning can be less severe than the naive tuning or even non-existent. (2) Within an effective theory, there appear to be two types of parameter relations that can alleviate the sensitivity of the scalar mass to the cutoff — relationships among dimensionless couplings or relationships among dimensionful parameters. Supersymmetric models provide symmetry-motivated examples of the former, while scale-invariant models give symmetry-motivated examples of the latter.
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References
K.G. Wilson, The Renormalization Group and Strong Interactions, Phys. Rev. D 3 (1971) 1818 [INSPIRE].
L. Susskind, Dynamics of Spontaneous Symmetry Breaking in the Weinberg-Salam Theory, Phys. Rev. D 20 (1979) 2619 [INSPIRE].
S. Weinberg, Phenomenological Lagrangians, Physica A 96 (1979) 327 [INSPIRE].
S. Dubovsky, V. Gorbenko and M. Mirbabayi, Natural Tuning: Towards A Proof of Concept, JHEP 09 (2013) 045 [arXiv:1305.6939] [INSPIRE].
R. Barbieri, Electroweak theory after the first Large Hadron Collider phase, Phys. Scripta T 158 (2013) 014006 [arXiv:1309.3473] [INSPIRE].
A. de Gouvêa, D. Hernández and T.M.P. Tait, Criteria for Natural Hierarchies, Phys. Rev. D 89 (2014) 115005 [arXiv:1402.2658] [INSPIRE].
M. Farina, D. Pappadopulo and A. Strumia, A modified naturalness principle and its experimental tests, JHEP 08 (2013) 022 [arXiv:1303.7244] [INSPIRE].
G.F. Giudice, Naturalness after LHC8, PoS(EPS-HEP 2013)163 [arXiv:1307.7879] [INSPIRE].
R. Foot, A. Kobakhidze, K.L. McDonald and R.R. Volkas, Poincaré Protection for a Natural Electroweak Scale, Phys. Rev. D 89 (2014) 115018 [arXiv:1310.0223] [INSPIRE].
W.A. Bardeen, On naturalness in the standard model, FERMILAB-CONF-95-391 [INSPIRE].
C. Wetterich, Fine Tuning Problem and the Renormalization Group, Phys. Lett. B 140 (1984) 215 [INSPIRE].
C. Wetterich, The Mass Of The Higgs Particle, DESY-87-154 [INSPIRE].
F. Vissani, Do experiments suggest a hierarchy problem?, Phys. Rev. D 57 (1998) 7027 [hep-ph/9709409] [INSPIRE].
J.A. Casas, J.R. Espinosa and I. Hidalgo, Implications for new physics from fine-tuning arguments. 1. Application to SUSY and seesaw cases, JHEP 11 (2004) 057 [hep-ph/0410298] [INSPIRE].
J.A. Casas, J.R. Espinosa and I. Hidalgo, Expectations for LHC from naturalness: modified versus SM Higgs sector, Nucl. Phys. B 777 (2007) 226 [hep-ph/0607279] [INSPIRE].
R.R. Volkas, A.J. Davies and G.C. Joshi, Naturalness Of The Invisible Axion Model, Phys. Lett. B 215 (1988) 133 [INSPIRE].
M.J.G. Veltman, The Infrared-Ultraviolet Connection, Acta Phys. Polon. B 12 (1981) 437 [INSPIRE].
I. Jack and D.R.T. Jones, Naturalness Without Supersymmetry?, Phys. Lett. B 234 (1990) 321 [INSPIRE].
M.S. Al-sarhi, I. Jack and D.R.T. Jones, Quadratic divergences in gauge theories, Z. Phys. C 55 (1992) 283 [INSPIRE].
M. Chaichian, R. Gonzalez Felipe and K. Huitu, On quadratic divergences and the Higgs mass, Phys. Lett. B 363 (1995) 101 [hep-ph/9509223] [INSPIRE].
Y. Hamada, H. Kawai and K.-y. Oda, Bare Higgs mass at Planck scale, Phys. Rev. D 87 (2013) 053009 [arXiv:1210.2538] [INSPIRE].
F. Jegerlehner, The Standard model as a low-energy effective theory: what is triggering the Higgs mechanism?, Acta Phys. Polon. B 45 (2014) 1167 [arXiv:1304.7813] [INSPIRE].
F. Jegerlehner, The hierarchy problem of the electroweak Standard Model revisited, arXiv:1305.6652 [INSPIRE].
I. Masina and M. Quirós, On the Veltman Condition, the Hierarchy Problem and High-Scale Supersymmetry, Phys. Rev. D 88 (2013) 093003 [arXiv:1308.1242] [INSPIRE].
O. Antipin, M. Mojaza and F. Sannino, Conformal Extensions of the Standard Model with Veltman Conditions, Phys. Rev. D 89 (2014) 085015 [arXiv:1310.0957] [INSPIRE].
M.T. Grisaru, W. Siegel and M. Roček, Improved Methods for Supergraphs, Nucl. Phys. B 159 (1979) 429 [INSPIRE].
S.R. Coleman and E.J. Weinberg, Radiative Corrections as the Origin of Spontaneous Symmetry Breaking, Phys. Rev. D 7 (1973) 1888 [INSPIRE].
A. Kobakhidze, Scale invariance and the electroweak symmetry breaking, PoS(ICHEP2012)156 [arXiv:1303.5897] [INSPIRE].
K.A. Meissner and H. Nicolai, Conformal Symmetry and the Standard Model, Phys. Lett. B 648 (2007) 312 [hep-th/0612165] [INSPIRE].
R. Foot, A. Kobakhidze and R.R. Volkas, Electroweak Higgs as a pseudo-Goldstone boson of broken scale invariance, Phys. Lett. B 655 (2007) 156 [arXiv:0704.1165] [INSPIRE].
R. Foot, A. Kobakhidze, K.L. McDonald and R.R. Volkas, Neutrino mass in radiatively-broken scale-invariant models, Phys. Rev. D 76 (2007) 075014 [arXiv:0706.1829] [INSPIRE].
R. Foot, A. Kobakhidze, K.L. McDonald and R.R. Volkas, A Solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory, Phys. Rev. D 77 (2008) 035006 [arXiv:0709.2750] [INSPIRE].
R. Foot, A. Kobakhidze and R.R. Volkas, Stable mass hierarchies and dark matter from hidden sectors in the scale-invariant standard model, Phys. Rev. D 82 (2010) 035005 [arXiv:1006.0131] [INSPIRE].
S. Iso, N. Okada and Y. Orikasa, Classically conformal B − L extended Standard Model, Phys. Lett. B 676 (2009) 81 [arXiv:0902.4050] [INSPIRE].
S. Iso, N. Okada and Y. Orikasa, The minimal B − L model naturally realized at TeV scale, Phys. Rev. D 80 (2009) 115007 [arXiv:0909.0128] [INSPIRE].
M. Holthausen, M. Lindner and M.A. Schmidt, Radiative Symmetry Breaking of the Minimal Left-Right Symmetric Model, Phys. Rev. D 82 (2010) 055002 [arXiv:0911.0710] [INSPIRE].
T. Hur and P. Ko, Scale invariant extension of the standard model with strongly interacting hidden sector, Phys. Rev. Lett. 106 (2011) 141802 [arXiv:1103.2571] [INSPIRE].
L. Alexander-Nunneley and A. Pilaftsis, The Minimal Scale Invariant Extension of the Standard Model, JHEP 09 (2010) 021 [arXiv:1006.5916] [INSPIRE].
R. Foot, A. Kobakhidze and R.R. Volkas, Cosmological constant in scale-invariant theories, Phys. Rev. D 84 (2011) 075010 [arXiv:1012.4848] [INSPIRE].
R. Foot and A. Kobakhidze, Electroweak Scale Invariant Models with Small Cosmological Constant, arXiv:1112.0607 [INSPIRE].
K. Ishiwata, Dark Matter in Classically Scale-Invariant Two Singlets Standard Model, Phys. Lett. B 710 (2012) 134 [arXiv:1112.2696] [INSPIRE].
J.S. Lee and A. Pilaftsis, Radiative Corrections to Scalar Masses and Mixing in a Scale Invariant Two Higgs Doublet Model, Phys. Rev. D 86 (2012) 035004 [arXiv:1201.4891] [INSPIRE].
N. Okada and Y. Orikasa, Dark matter in the classically conformal B − L model, Phys. Rev. D 85 (2012) 115006 [arXiv:1202.1405] [INSPIRE].
S. Iso and Y. Orikasa, TeV Scale B − L model with a flat Higgs potential at the Planck scale: In view of the hierarchy problem, Prog. Theor. Exp. Phys. 2013 (2013) 023B08 [arXiv:1210.2848] [INSPIRE].
C. Englert, J. Jaeckel, V.V. Khoze and M. Spannowsky, Emergence of the Electroweak Scale through the Higgs Portal, JHEP 04 (2013) 060 [arXiv:1301.4224] [INSPIRE].
M. Heikinheimo, A. Racioppi, M. Raidal, C. Spethmann and K. Tuominen, Physical Naturalness and Dynamical Breaking of Classical Scale Invariance, Mod. Phys. Lett. A 29 (2014) 1450077 [arXiv:1304.7006] [INSPIRE].
M. Heikinheimo, A. Racioppi, M. Raidal, C. Spethmann and K. Tuominen, Dark Supersymmetry, Nucl. Phys. B 876 (2013) 201 [arXiv:1305.4182] [INSPIRE].
T. Hambye and A. Strumia, Dynamical generation of the weak and Dark Matter scale, Phys. Rev. D 88 (2013) 055022 [arXiv:1306.2329] [INSPIRE].
I. Bars, P. Steinhardt and N. Turok, Local Conformal Symmetry in Physics and Cosmology, Phys. Rev. D 89 (2014) 043515 [arXiv:1307.1848] [INSPIRE].
M. Heikinheimo, A. Racioppi, M. Raidal and C. Spethmann, Twin Peak Higgs, Phys. Lett. B 726 (2013) 781 [arXiv:1307.7146] [INSPIRE].
C.D. Carone and R. Ramos, Classical scale-invariance, the electroweak scale and vector dark matter, Phys. Rev. D 88 (2013) 055020 [arXiv:1307.8428] [INSPIRE].
G. Marques Tavares, M. Schmaltz and W. Skiba, Higgs mass naturalness and scale invariance in the UV, Phys. Rev. D 89 (2014) 015009 [arXiv:1308.0025] [INSPIRE].
A. Farzinnia, H.-J. He and J. Ren, Natural Electroweak Symmetry Breaking from Scale Invariant Higgs Mechanism, Phys. Lett. B 727 (2013) 141 [arXiv:1308.0295] [INSPIRE].
Y. Kawamura, Naturalness, Conformal Symmetry and Duality, Prog. Theor. Exp. Phys. 2013 (2013) 113B04 [arXiv:1308.5069] [INSPIRE].
V.V. Khoze, Inflation and Dark Matter in the Higgs Portal of Classically Scale Invariant Standard Model, JHEP 11 (2013) 215 [arXiv:1308.6338] [INSPIRE].
E. Gabrielli, M. Heikinheimo, K. Kannike, A. Racioppi, M. Raidal and C. Spethmann, Towards Completing the Standard Model: Vacuum Stability, EWSB and Dark Matter, Phys. Rev. D 89 (2014) 015017 [arXiv:1309.6632] [INSPIRE].
T.G. Steele, Z.-W. Wang, D. Contreras and R.B. Mann, Viable dark matter via radiative symmetry breaking in a scalar singlet Higgs portal extension of the standard model, Phys. Rev. Lett. 112 (2014) 171602 [arXiv:1310.1960] [INSPIRE].
M. Hashimoto, S. Iso and Y. Orikasa, Radiative symmetry breaking at the Fermi scale and flat potential at the Planck scale, Phys. Rev. D 89 (2014) 016019 [arXiv:1310.4304] [INSPIRE].
M. Holthausen, J. Kubo, K.S. Lim and M. Lindner, Electroweak and Conformal Symmetry Breaking by a Strongly Coupled Hidden Sector, JHEP 12 (2013) 076 [arXiv:1310.4423] [INSPIRE].
S. Abel and A. Mariotti, Novel Higgs Potentials from Gauge Mediation of Exact Scale Breaking, Phys. Rev. D 89 (2014) 125018 [arXiv:1312.5335] [INSPIRE].
C.T. Hill, Is the Higgs Boson Associated with Coleman-Weinberg Dynamical Symmetry Breaking?, Phys. Rev. D 89 (2014) 073003 [arXiv:1401.4185] [INSPIRE].
J. Guo and Z. Kang, Higgs Naturalness and Dark Matter Stability by Scale Invariance, arXiv:1401.5609 [INSPIRE].
M. Hashimoto, S. Iso and Y. Orikasa, Radiative Symmetry Breaking from Flat Potential in various U(1)′ models, Phys. Rev. D 89 (2014) 056010 [arXiv:1401.5944] [INSPIRE].
S. Benić and B. Radovčić, Electroweak breaking and Dark Matter from the common scale, Phys. Lett. B 732 (2014) 91 [arXiv:1401.8183] [INSPIRE].
A. Salvio and A. Strumia, Agravity, JHEP 06 (2014) 080 [arXiv:1403.4226] [INSPIRE].
J. Kubo, K.S. Lim and M. Lindner, Electroweak Symmetry Breaking by QCD, arXiv:1403.4262 [INSPIRE].
V.V. Khoze, C. McCabe and G. Ro, Higgs vacuum stability from the dark matter portal, arXiv:1403.4953 [INSPIRE].
G.C. Dorsch, S.J. Huber and J.M. No, Cosmological Signatures of a UV-Conformal Standard Model, arXiv:1403.5583 [INSPIRE].
M. Shaposhnikov and D. Zenhausern, Quantum scale invariance, cosmological constant and hierarchy problem, Phys. Lett. B 671 (2009) 162 [arXiv:0809.3406] [INSPIRE].
F. Gretsch and A. Monin, Dilaton: Saving Conformal Symmetry, arXiv:1308.3863 [INSPIRE].
C. Tamarit, Running couplings with a vanishing scale anomaly, JHEP 12 (2013) 098 [arXiv:1309.0913] [INSPIRE].
K.A. Meissner and H. Nicolai, Effective action, conformal anomaly and the issue of quadratic divergences, Phys. Lett. B 660 (2008) 260 [arXiv:0710.2840] [INSPIRE].
H. Aoki and S. Iso, Revisiting the Naturalness Problem: Who is afraid of quadratic divergences?, Phys. Rev. D 86 (2012) 013001 [arXiv:1201.0857] [INSPIRE].
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Kobakhidze, A., McDonald, K.L. Comments on the hierarchy problem in effective theories. J. High Energ. Phys. 2014, 155 (2014). https://doi.org/10.1007/JHEP07(2014)155
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DOI: https://doi.org/10.1007/JHEP07(2014)155