这是indexloc提供的服务，不要输入任何密码
Skip to main content
Springer Nature Link
Account
Menu
Find a journal Publish with us Track your research
Search
Cart
  1. Home
  2. Journal of High Energy Physics
  3. Article

Investigating the near-criticality of the Higgs boson

  • Open access
  • Published: 20 December 2013
  • Volume 2013, article number 89, (2013)
  • Cite this article

You have full access to this open access article

Download PDF
Journal of High Energy Physics Aims and scope Submit manuscript
Investigating the near-criticality of the Higgs boson
Download PDF
  • Dario Buttazzo1,2,
  • Giuseppe Degrassi3,
  • Pier Paolo Giardino1,4,
  • Gian F. Giudice1,
  • Filippo Sala2,5,
  • Alberto Salvio2,6 &
  • …
  • Alessandro Strumia4 

  • 3431 Accesses

  • 970 Citations

  • 125 Altmetric

  • 20 Mentions

  • Explore all metrics

Abstract

We extract from data the parameters of the Higgs potential, the top Yukawa coupling and the electroweak gauge couplings with full 2-loop NNLO precision, and we extrapolate the SM parameters up to large energies with full 3-loop NNLO RGE precision. Then we study the phase diagram of the Standard Model in terms of high-energy parameters, finding that the measured Higgs mass roughly corresponds to the minimum values of the Higgs quartic and top Yukawa and the maximum value of the gauge couplings allowed by vacuum metastability. We discuss various theoretical interpretations of the near-criticality of the Higgs mass.

Article PDF

Download to read the full article text

Similar content being viewed by others

Higgs boson contribution to the leading two-loop Yukawa corrections to gg → HH

Article Open access 25 August 2022

Analytic next-to-leading order Yukawa and Higgs boson self-coupling corrections to gg → HH at high energies

Article Open access 24 April 2025

New scenario for aligned Higgs couplings originated from the twisted custodial symmetry at high energies

Article Open access 04 February 2021

Explore related subjects

Discover the latest articles, books and news in related subjects, suggested using machine learning.
  • Criticality
  • Nuclear Physics
  • Particle Physics
  • Phase Transition and Critical Phenomena
  • Physical Sciences
  • Theoretical Particle Physics
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

References

  1. ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].

    ADS  Google Scholar 

  2. CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].

    ADS  Google Scholar 

  3. CMS collaboration, Updated measurements of the Higgs boson at 125 GeV in the two photon decay channel, CMS-PAS-HIG-13-001, CERN, Geneva Switzerland (2013).

  4. ATLAS collaboration, Measurements of the properties of the Higgs-like boson in the two photon decay channel with the ATLAS detector using 25 fb−1 of proton-proton collision data, ATLAS-CONF-2013-012, CERN, Geneva Switzerland (2013).

  5. CMS collaboration, Properties of the Higgs-like boson in the decay H → ZZ → 4ℓ in pp collisions at \( \sqrt{s} \) = 7 and 8 TeV, CMS-PAS-HIG-13-002, CERN, Geneva Switzerland (2013).

  6. ATLAS collaboration, Measurements of the properties of the Higgs-like boson in the four lepton decay channel with the ATLAS detector using 25 fb−1 of proton-proton collision data, ATLAS-CONF-2013-013, CERN, Geneva Switzerland (2013).

  7. P.P. Giardino, K. Kannike, I. Masina, M. Raidal and A. Strumia, The universal Higgs fit, arXiv:1303.3570 [INSPIRE].

  8. G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].

    Article  ADS  Google Scholar 

  9. I. Krive and A.D. Linde, On the vacuum stability problem in gauge theories, Nucl. Phys. B 117 (1976) 265 [INSPIRE].

    Article  ADS  Google Scholar 

  10. N. Krasnikov, Restriction of the fermion mass in gauge theories of weak and electromagnetic interactions, Yad. Fiz. 28 (1978) 549 [INSPIRE].

    Google Scholar 

  11. L. Maiani, G. Parisi and R. Petronzio, Bounds on the number and masses of quarks and leptons, Nucl. Phys. B 136 (1978) 115 [INSPIRE].

    Article  ADS  Google Scholar 

  12. H.D. Politzer and S. Wolfram, Bounds on particle masses in the Weinberg-Salam model, Phys. Lett. B 82 (1979) 242 [Erratum ibid. B 83 (1979) 421] [INSPIRE].

  13. P.Q. Hung, Vacuum instability and new constraints on fermion masses, Phys. Rev. Lett. 42 (1979) 873 [INSPIRE].

    Article  ADS  Google Scholar 

  14. N. Cabibbo, L. Maiani, G. Parisi and R. Petronzio, Bounds on the fermions and Higgs boson masses in grand unified theories, Nucl. Phys. B 158 (1979) 295 [INSPIRE].

    Article  ADS  Google Scholar 

  15. A.D. Linde, Vacuum instability, cosmology and constraints on particle masses in the Weinberg-Salam model, Phys. Lett. B 92 (1980) 119 [INSPIRE].

    Article  ADS  Google Scholar 

  16. M. Lindner, Implications of triviality for the Standard Model, Z. Phys. C 31 (1986) 295 [INSPIRE].

    ADS  Google Scholar 

  17. M. Lindner, M. Sher and H.W. Zaglauer, Probing vacuum stability bounds at the Fermilab collider, Phys. Lett. B 228 (1989) 139 [INSPIRE].

    Article  ADS  Google Scholar 

  18. M. Sher, Electroweak Higgs potentials and vacuum stability, Phys. Rept. 179 (1989) 273 [INSPIRE].

    Article  ADS  Google Scholar 

  19. P.B. Arnold, Can the electroweak vacuum be unstable?, Phys. Rev. D 40 (1989) 613 [INSPIRE].

    ADS  Google Scholar 

  20. P.B. Arnold and S. Vokos, Instability of hot electroweak theory: bounds on m H and M t , Phys. Rev. D 44 (1991) 3620 [INSPIRE].

    ADS  Google Scholar 

  21. M. Sher, Precise vacuum stability bound in the Standard Model, Phys. Lett. B 317 (1993) 159 [Addendum ibid. B 331 (1994) 448] [hep-ph/9307342] [INSPIRE].

  22. G. Altarelli and G. Isidori, Lower limit on the Higgs mass in the Standard Model: an update, Phys. Lett. B 337 (1994) 141 [INSPIRE].

    Article  ADS  Google Scholar 

  23. J.A. Casas, J.R. Espinosa and M. Quirós, Improved Higgs mass stability bound in the Standard Model and implications for supersymmetry, Phys. Lett. B 342 (1995) 171 [hep-ph/9409458] [INSPIRE].

    Article  ADS  Google Scholar 

  24. J.R. Espinosa and M. Quirós, Improved metastability bounds on the Standard Model Higgs mass, Phys. Lett. B 353 (1995) 257 [hep-ph/9504241] [INSPIRE].

    Article  ADS  Google Scholar 

  25. J. Casas, J. Espinosa and M. Quirós, Standard Model stability bounds for new physics within LHC reach, Phys. Lett. B 382 (1996) 374 [hep-ph/9603227] [INSPIRE].

    Article  ADS  Google Scholar 

  26. B. Schrempp and M. Wimmer, Top quark and Higgs boson masses: interplay between infrared and ultraviolet physics, Prog. Part. Nucl. Phys. 37 (1996) 1 [hep-ph/9606386] [INSPIRE].

    Article  ADS  Google Scholar 

  27. T. Hambye and K. Riesselmann, Matching conditions and Higgs mass upper bounds revisited, Phys. Rev. D 55 (1997) 7255 [hep-ph/9610272] [INSPIRE].

    ADS  Google Scholar 

  28. G. Isidori, G. Ridolfi and A. Strumia, On the metastability of the Standard Model vacuum, Nucl. Phys. B 609 (2001) 387 [hep-ph/0104016] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  29. J. Espinosa, G. Giudice and A. Riotto, Cosmological implications of the Higgs mass measurement, JCAP 05 (2008) 002 [arXiv:0710.2484] [INSPIRE].

    Article  ADS  Google Scholar 

  30. J. Ellis, J. Espinosa, G. Giudice, A. Hoecker and A. Riotto, The probable fate of the Standard Model, Phys. Lett. B 679 (2009) 369 [arXiv:0906.0954] [INSPIRE].

    Article  ADS  Google Scholar 

  31. B. Feldstein, L.J. Hall and T. Watari, Landscape prediction for the Higgs boson and top quark masses, Phys. Rev. D 74 (2006) 095011 [hep-ph/0608121] [INSPIRE].

    ADS  Google Scholar 

  32. M. Holthausen, K.S. Lim and M. Lindner, Planck scale boundary conditions and the Higgs mass, JHEP 02 (2012) 037 [arXiv:1112.2415] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  33. J. Elias-Miro et al., Higgs mass implications on the stability of the electroweak vacuum, Phys. Lett. B 709 (2012) 222 [arXiv:1112.3022] [INSPIRE].

    Article  ADS  Google Scholar 

  34. C.-S. Chen and Y. Tang, Vacuum stability, neutrinos and dark matter, JHEP 04 (2012) 019 [arXiv:1202.5717] [INSPIRE].

    Article  ADS  Google Scholar 

  35. O. Lebedev, On stability of the electroweak vacuum and the Higgs portal, Eur. Phys. J. C 72 (2012) 2058 [arXiv:1203.0156] [INSPIRE].

    Article  ADS  Google Scholar 

  36. J. Elias-Miro, J.R. Espinosa, G.F. Giudice, H.M. Lee and A. Strumia, Stabilization of the electroweak vacuum by a scalar threshold effect, JHEP 06 (2012) 031 [arXiv:1203.0237] [INSPIRE].

    Article  ADS  Google Scholar 

  37. W. Rodejohann and H. Zhang, Impact of massive neutrinos on the Higgs self-coupling and electroweak vacuum stability, JHEP 06 (2012) 022 [arXiv:1203.3825] [INSPIRE].

    Article  ADS  Google Scholar 

  38. F. Bezrukov, M.Y. Kalmykov, B.A. Kniehl and M. Shaposhnikov, Higgs boson mass and new physics, JHEP 10 (2012) 140 [arXiv:1205.2893] [INSPIRE].

    Article  ADS  Google Scholar 

  39. A. Datta and S. Raychaudhuri, Vacuum stability constraints and LHC searches for a model with a universal extra dimension, Phys. Rev. D 87 (2013) 035018 [arXiv:1207.0476] [INSPIRE].

    ADS  Google Scholar 

  40. S. Alekhin, A. Djouadi and S. Moch, The top quark and Higgs boson masses and the stability of the electroweak vacuum, Phys. Lett. B 716 (2012) 214 [arXiv:1207.0980] [INSPIRE].

    Article  ADS  Google Scholar 

  41. J. Chakrabortty, M. Das and S. Mohanty, Constraints on TeV scale Majorana neutrino phenomenology from the vacuum stability of the Higgs, Mod. Phys. Lett. A 28 (2013) 1350032 [arXiv:1207.2027] [INSPIRE].

    Article  ADS  Google Scholar 

  42. L.A. Anchordoqui et al., Vacuum stability of Standard Model ++, JHEP 02 (2013) 074 [arXiv:1208.2821] [INSPIRE].

    Article  ADS  Google Scholar 

  43. I. Masina, Higgs boson and top quark masses as tests of electroweak vacuum stability, Phys. Rev. D 87 (2013) 053001 [arXiv:1209.0393] [INSPIRE].

    ADS  Google Scholar 

  44. E.J. Chun, H.M. Lee and P. Sharma, Vacuum stability, perturbativity, EWPD and Higgs-to-diphoton rate in type II seesaw models, JHEP 11 (2012) 106 [arXiv:1209.1303] [INSPIRE].

    Article  ADS  Google Scholar 

  45. D.J. Chung, A.J. Long and L.-T. Wang, The 125 GeV Higgs and electroweak phase transition model classes, Phys. Rev. D 87 (2013) 023509 [arXiv:1209.1819] [INSPIRE].

    ADS  Google Scholar 

  46. W. Chao, M. Gonderinger and M.J. Ramsey-Musolf, Higgs vacuum stability, neutrino mass and dark matter, Phys. Rev. D 86 (2012) 113017 [arXiv:1210.0491] [INSPIRE].

    ADS  Google Scholar 

  47. P. Bhupal Dev, D.K. Ghosh, N. Okada and I. Saha, 125 GeV Higgs boson and the type-II seesaw model, JHEP 03 (2013) 150 [Erratum ibid. 05 (2013) 049] [arXiv:1301.3453] [INSPIRE].

  48. O. Lebedev and A. Westphal, Metastable electroweak vacuum: implications for inflation, Phys. Lett. B 719 (2013) 415 [arXiv:1210.6987] [INSPIRE].

    Article  ADS  Google Scholar 

  49. H.B. Nielsen, PREdicted the Higgs mass, arXiv:1212.5716 [INSPIRE].

  50. A. Kobakhidze and A. Spencer-Smith, Electroweak vacuum (in)stability in an inflationary universe, Phys. Lett. B 722 (2013) 130 [arXiv:1301.2846] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  51. Y. Tang, Vacuum stability in the Standard Model, Mod. Phys. Lett. A 28 (2013) 1330002 [arXiv:1301.5812] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  52. F. Klinkhamer, Standard Model Higgs field and energy scale of gravity, JETP Lett. 97 (2013) 297 [arXiv:1302.1496] [INSPIRE].

    Article  ADS  Google Scholar 

  53. X.-G. He, H. Phoon, Y. Tang and G. Valencia, Unitarity and vacuum stability constraints on the couplings of color octet scalars, JHEP 05 (2013) 026 [arXiv:1303.4848] [INSPIRE].

    Article  ADS  Google Scholar 

  54. E.J. Chun, S. Jung and H.M. Lee, Radiative generation of the Higgs potential, Phys. Lett. B 725 (2013) 158 [arXiv:1304.5815] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  55. F. Jegerlehner, The Standard Model as a low-energy effective theory: what is triggering the Higgs mechanism?, arXiv:1304.7813 [INSPIRE].

  56. O. Antipin, M. Gillioz, J. Krog, E. Mølgaard and F. Sannino, Standard Model vacuum stability and Weyl consistency conditions, JHEP 08 (2013) 034 [arXiv:1306.3234] [INSPIRE].

    Article  ADS  Google Scholar 

  57. V. Branchina and E. Messina, Stability, Higgs boson mass and new physics, arXiv:1307.5193 [INSPIRE].

  58. D.J. Gross and F. Wilczek, Ultraviolet behavior of non-Abelian gauge theories, Phys. Rev. Lett. 30 (1973) 1343 [INSPIRE].

    Article  ADS  Google Scholar 

  59. H.D. Politzer, Reliable perturbative results for strong interactions?, Phys. Rev. Lett. 30 (1973) 1346 [INSPIRE].

    Article  ADS  Google Scholar 

  60. W.E. Caswell, Asymptotic behavior of non-Abelian gauge theories to two loop order, Phys. Rev. Lett. 33 (1974) 244 [INSPIRE].

    Article  ADS  Google Scholar 

  61. D. Jones, Two loop diagrams in Yang-Mills theory, Nucl. Phys. B 75 (1974) 531 [INSPIRE].

    Article  ADS  Google Scholar 

  62. O. Tarasov, A. Vladimirov and A.Y. Zharkov, The Gell-Mann-Low function of QCD in the three loop approximation, Phys. Lett. B 93 (1980) 429 [INSPIRE].

    Article  ADS  Google Scholar 

  63. S. Larin and J. Vermaseren, The three loop QCD β-function and anomalous dimensions, Phys. Lett. B 303 (1993) 334 [hep-ph/9302208] [INSPIRE].

    Article  ADS  Google Scholar 

  64. T. van Ritbergen, J. Vermaseren and S. Larin, The four loop β-function in quantum chromodynamics, Phys. Lett. B 400 (1997) 379 [hep-ph/9701390] [INSPIRE].

    Article  ADS  Google Scholar 

  65. M. Czakon, The four-loop QCD β-function and anomalous dimensions, Nucl. Phys. B 710 (2005) 485 [hep-ph/0411261] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  66. D. Jones, The two loop β-function for a G 1 × G 2 gauge theory, Phys. Rev. D 25 (1982) 581 [INSPIRE].

    ADS  Google Scholar 

  67. M. Steinhauser, Higgs decay into gluons up to \( O\left( {\alpha_s^3{G_F}m_t^2} \right) \), Phys. Rev. D 59 (1999) 054005 [hep-ph/9809507] [INSPIRE].

    ADS  Google Scholar 

  68. M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 1. Wave function renormalization, Nucl. Phys. B 222 (1983) 83 [INSPIRE].

    Article  ADS  Google Scholar 

  69. L.N. Mihaila, J. Salomon and M. Steinhauser, Gauge coupling β-functions in the Standard Model to three loops, Phys. Rev. Lett. 108 (2012) 151602 [arXiv:1201.5868] [INSPIRE].

    Article  ADS  Google Scholar 

  70. L.N. Mihaila, J. Salomon and M. Steinhauser, Renormalization constants and β-functions for the gauge couplings of the Standard Model to three-loop order, Phys. Rev. D 86 (2012) 096008 [arXiv:1208.3357] [INSPIRE].

    ADS  Google Scholar 

  71. T. Cheng, E. Eichten and L.-F. Li, Higgs phenomena in asymptotically free gauge theories, Phys. Rev. D 9 (1974) 2259 [INSPIRE].

    ADS  Google Scholar 

  72. M. Fischler and J. Oliensis, Two loop corrections to the evolution of the Higgs-Yukawa coupling constant, Phys. Lett. B 119 (1982) 385 [INSPIRE].

    Article  ADS  Google Scholar 

  73. K. Chetyrkin and M. Zoller, Three-loop β-functions for top-Yukawa and the Higgs self-interaction in the Standard Model, JHEP 06 (2012) 033 [arXiv:1205.2892] [INSPIRE].

    Article  ADS  Google Scholar 

  74. A. Bednyakov, A. Pikelner and V. Velizhanin, Yukawa coupling β-functions in the Standard Model at three loops, Phys. Lett. B 722 (2013) 336 [arXiv:1212.6829] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  75. M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 2. Yukawa couplings, Nucl. Phys. B 236 (1984) 221 [INSPIRE].

    Article  ADS  Google Scholar 

  76. M.E. Machacek and M.T. Vaughn, Two loop renormalization group equations in a general quantum field theory. 3. Scalar quartic couplings, Nucl. Phys. B 249 (1985) 70 [INSPIRE].

    Article  ADS  Google Scholar 

  77. M.-X. Luo and Y. Xiao, Two loop renormalization group equations in the Standard Model, Phys. Rev. Lett. 90 (2003) 011601 [hep-ph/0207271] [INSPIRE].

    Article  ADS  Google Scholar 

  78. K. Chetyrkin and M. Zoller, β-function for the Higgs self-interaction in the Standard Model at three-loop level, JHEP 04 (2013) 091 [Erratum ibid. 09 (2013) 155] [arXiv:1303.2890] [INSPIRE].

  79. A. Bednyakov, A. Pikelner and V. Velizhanin, Higgs self-coupling β-function in the Standard Model at three loops, Nucl. Phys. B 875 (2013) 552 [arXiv:1303.4364] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  80. A. Sirlin, Radiative corrections in the SU(2) L × U(1) theory: a simple renormalization framework, Phys. Rev. D 22 (1980) 971 [INSPIRE].

    ADS  Google Scholar 

  81. W. Marciano and A. Sirlin, Radiative corrections to neutrino induced neutral current phenomena in the SU(2) L × U(1) theory, Phys. Rev. D 22 (1980) 2695 [Erratum ibid. D 31 (1985) 213] [INSPIRE].

  82. R. Tarrach, The pole mass in perturbative QCD, Nucl. Phys. B 183 (1981) 384 [INSPIRE].

    Article  ADS  Google Scholar 

  83. K. Chetyrkin and M. Steinhauser, Short distance mass of a heavy quark at order \( \alpha_s^3 \), Phys. Rev. Lett. 83 (1999) 4001 [hep-ph/9907509] [INSPIRE].

    Article  ADS  Google Scholar 

  84. K. Chetyrkin and M. Steinhauser, The relation between the MS-bar and the on-shell quark mass at order \( \alpha_s^3 \), Nucl. Phys. B 573 (2000) 617 [hep-ph/9911434] [INSPIRE].

    Article  ADS  Google Scholar 

  85. K. Melnikov and T.v. Ritbergen, The three loop relation between the MS-bar and the pole quark masses, Phys. Lett. B 482 (2000) 99 [hep-ph/9912391] [INSPIRE].

    Article  ADS  Google Scholar 

  86. R. Hempfling and B.A. Kniehl, On the relation between the fermion pole mass and MS Yukawa coupling in the Standard Model, Phys. Rev. D 51 (1995) 1386 [hep-ph/9408313] [INSPIRE].

    ADS  Google Scholar 

  87. A. Sirlin and R. Zucchini, Dependence of the quartic coupling H m on M H and the possible onset of new physics in the Higgs sector of the Standard Model, Nucl. Phys. B 266 (1986) 389 [INSPIRE].

    Article  ADS  Google Scholar 

  88. W.E. Caswell and F. Wilczek, On the gauge dependence of renormalization group parameters, Phys. Lett. B 49 (1974) 291 [INSPIRE].

    Article  ADS  Google Scholar 

  89. T. Muta, Foundations of quantum chromodynamics, World Scientific, Singapore (2010), pg. 192.

    MATH  Google Scholar 

  90. D. Atkinson and M. Fry, Should one truncate the electron selfenergy?, Nucl. Phys. B 156 (1979) 301 [INSPIRE].

    Article  ADS  Google Scholar 

  91. J. Breckenridge, M. Lavelle and T.G. Steele, The Nielsen identities for the two point functions of QED and QCD, Z. Phys. C 65 (1995) 155 [hep-th/9407028] [INSPIRE].

    ADS  Google Scholar 

  92. A.S. Kronfeld, The perturbative pole mass in QCD, Phys. Rev. D 58 (1998) 051501 [hep-ph/9805215] [INSPIRE].

    ADS  Google Scholar 

  93. Tevatron Electroweak Working Group, CDF and D0 collaborations, 2012 update of the combination of CDF and D0 results for the mass of the W boson, FERMILAB-TM-2532-E, Fermilab, Batavia U.S.A. (2012) [arXiv:1204.0042] [INSPIRE].

  94. ALEPH, DELPHI, L3, OPAL and LEP Electroweak Working Group collaborations, A combination of preliminary electroweak measurements and constraints on the Standard Model, 2006, CERN-PH-EP-2006-042, CERN, Geneva Switzerland (2006) [hep-ex/0612034] [INSPIRE].

  95. 2012 Particle Data Group average, http://pdg.lbl.gov/.

  96. Tevatron Electroweak Working Group, CDF and D0 collaborations, Combination of CDF and D0 results on the mass of the top quark using up to 5.8 fb−1 of data, arXiv:1107.5255 [INSPIRE].

  97. CMS collaboration, CMS top physics website, https://twiki.cern.ch/twiki/bin/view/CMSPublic/PhysicsResultsTOP.

  98. CMS collaboration, talks at the Moriond 2013 conference, La Thuile Italy March 9-16 2013.

  99. ATLAS collaboration, ATLAS top physics website, https://twiki.cern.ch/twiki/bin/view/AtlasPublic/TopPublicResults.

  100. MuLan collaboration, V. Tishchenko et al., Detailed report of the MuLan measurement of the positive muon lifetime and determination of the Fermi constant, Phys. Rev. D 87 (2013) 052003 [arXiv:1211.0960] [INSPIRE].

    Google Scholar 

  101. S. Bethke, World summary of α s (2012), Nucl. Phys. Proc. Suppl. 234 (2013) 229 [arXiv:1210.0325] [INSPIRE].

    Article  ADS  Google Scholar 

  102. T. Kinoshita and A. Sirlin, Radiative corrections to Fermi interactions, Phys. Rev. 113 (1959) 1652 [INSPIRE].

    Article  ADS  Google Scholar 

  103. T. van Ritbergen and R.G. Stuart, On the precise determination of the Fermi coupling constant from the muon lifetime, Nucl. Phys. B 564 (2000) 343 [hep-ph/9904240] [INSPIRE].

    Article  ADS  Google Scholar 

  104. T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  105. R. Mertig and R. Scharf, TARCER: a Mathematica program for the reduction of two loop propagator integrals, Comput. Phys. Commun. 111 (1998) 265 [hep-ph/9801383] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  106. O. Tarasov, Generalized recurrence relations for two loop propagator integrals with arbitrary masses, Nucl. Phys. B 502 (1997) 455 [hep-ph/9703319] [INSPIRE].

    Article  ADS  Google Scholar 

  107. R. Mertig, M. Böhm and A. Denner, FEYN CALC: computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  108. M. Awramik, M. Czakon, A. Onishchenko and O. Veretin, Bosonic corrections to Δr at the two loop level, Phys. Rev. D 68 (2003) 053004 [hep-ph/0209084] [INSPIRE].

    ADS  Google Scholar 

  109. S.P. Martin, Evaluation of two loop selfenergy basis integrals using differential equations, Phys. Rev. D 68 (2003) 075002 [hep-ph/0307101] [INSPIRE].

    ADS  Google Scholar 

  110. S.P. Martin and D.G. Robertson, TSIL: a program for the calculation of two-loop self-energy integrals, Comput. Phys. Commun. 174 (2006) 133 [hep-ph/0501132] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  111. B.A. Kniehl and A. Sirlin, Pole mass, width and propagators of unstable Fermions, Phys. Rev. D 77 (2008) 116012 [arXiv:0801.0669] [INSPIRE].

    ADS  Google Scholar 

  112. F. Jegerlehner, M.Y. Kalmykov and B.A. Kniehl, On the difference between the pole and the MS-bar masses of the top quark at the electroweak scale, Phys. Lett. B 722 (2013) 123 [arXiv:1212.4319] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  113. S.P. Martin, Three-loop Standard Model effective potential at leading order in strong and top Yukawa couplings, arXiv:1310.7553 [INSPIRE].

  114. Particle Data Group collaboration, K. Nakamura et al., Review of particle physics, J. Phys. G 37 (2010) 075021 [INSPIRE].

    ADS  Google Scholar 

  115. LEP Electroweak Working Group webpage, http://lepewwg.web.cern.ch/.

  116. C. Froggatt and H.B. Nielsen, Standard Model criticality prediction: top mass 173 ± 5 GeV and Higgs mass 135 ± 9 GeV, Phys. Lett. B 368 (1996) 96 [hep-ph/9511371] [INSPIRE].

    Article  ADS  Google Scholar 

  117. C. Froggatt, H.B. Nielsen and Y. Takanishi, Standard Model Higgs boson mass from borderline metastability of the vacuum, Phys. Rev. D 64 (2001) 113014 [hep-ph/0104161] [INSPIRE].

    ADS  Google Scholar 

  118. C. Burgess, V. Di Clemente and J. Espinosa, Effective operators and vacuum instability as heralds of new physics, JHEP 01 (2002) 041 [hep-ph/0201160] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  119. G. Isidori, V.S. Rychkov, A. Strumia and N. Tetradis, Gravitational corrections to Standard Model vacuum decay, Phys. Rev. D 77 (2008) 025034 [arXiv:0712.0242] [INSPIRE].

    ADS  Google Scholar 

  120. F. Bezrukov and M. Shaposhnikov, Standard Model Higgs boson mass from inflation: two loop analysis, JHEP 07 (2009) 089 [arXiv:0904.1537] [INSPIRE].

    Article  ADS  Google Scholar 

  121. M. Shaposhnikov and C. Wetterich, Asymptotic safety of gravity and the Higgs boson mass, Phys. Lett. B 683 (2010) 196 [arXiv:0912.0208] [INSPIRE].

    Article  ADS  Google Scholar 

  122. C. Ford, I. Jack and D. Jones, The Standard Model effective potential at two loops, Nucl. Phys. B 387 (1992) 373 [Erratum ibid. B 504 (1997) 551] [hep-ph/0111190] [INSPIRE].

  123. L.J. Hall and Y. Nomura, A finely-predicted Higgs boson mass from a finely-tuned weak scale, JHEP 03 (2010) 076 [arXiv:0910.2235] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  124. G.F. Giudice and A. Strumia, Probing high-scale and split supersymmetry with Higgs mass measurements, Nucl. Phys. B 858 (2012) 63 [arXiv:1108.6077] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  125. M. Cabrera, J. Casas and A. Delgado, Upper bounds on superpartner masses from upper bounds on the Higgs boson mass, Phys. Rev. Lett. 108 (2012) 021802 [arXiv:1108.3867] [INSPIRE].

    Article  ADS  Google Scholar 

  126. A. Arbey, M. Battaglia, A. Djouadi, F. Mahmoudi and J. Quevillon, Implications of a 125 GeV Higgs for supersymmetric models, Phys. Lett. B 708 (2012) 162 [arXiv:1112.3028] [INSPIRE].

    Article  ADS  Google Scholar 

  127. L.E. Ibánez and I. Valenzuela, The Higgs mass as a signature of heavy SUSY, JHEP 05 (2013) 064 [arXiv:1301.5167] [INSPIRE].

    Article  ADS  Google Scholar 

  128. A. Hebecker, A.K. Knochel and T. Weigand, The Higgs mass from a string-theoretic perspective, Nucl. Phys. B 874 (2013) 1 [arXiv:1304.2767] [INSPIRE].

    Article  ADS  MathSciNet  MATH  Google Scholar 

  129. P.J. Fox, A.E. Nelson and N. Weiner, Dirac gaugino masses and supersoft supersymmetry breaking, JHEP 08 (2002) 035 [hep-ph/0206096] [INSPIRE].

    Article  ADS  Google Scholar 

  130. K. Benakli, M.D. Goodsell and F. Staub, Dirac gauginos and the 125 GeV Higgs, JHEP 06 (2013) 073 [arXiv:1211.0552] [INSPIRE].

    Article  ADS  Google Scholar 

  131. A. Hebecker, A.K. Knochel and T. Weigand, A shift symmetry in the Higgs sector: experimental hints and stringy realizations, JHEP 06 (2012) 093 [arXiv:1204.2551] [INSPIRE].

    Article  ADS  Google Scholar 

  132. M. Redi and A. Strumia, Axion-Higgs unification, JHEP 11 (2012) 103 [arXiv:1208.6013] [INSPIRE].

    Article  ADS  MathSciNet  Google Scholar 

  133. G. Giudice and R. Rattazzi, Living dangerously with low-energy supersymmetry, Nucl. Phys. B 757 (2006) 19 [hep-ph/0606105] [INSPIRE].

    Article  ADS  MATH  Google Scholar 

  134. P. Bak, C. Tang and K. Wiesenfeld, Self-organized criticality: an explanation of 1/f noise, Phys. Rev. Lett. 59 (1987) 381 [INSPIRE].

    Article  ADS  Google Scholar 

  135. S. Weinberg, Anthropic bound on the cosmological constant, Phys. Rev. Lett. 59 (1987) 2607 [INSPIRE].

    Article  ADS  Google Scholar 

  136. J.F. Donoghue, K. Dutta and A. Ross, Quark and lepton masses and mixing in the landscape, Phys. Rev. D 73 (2006) 113002 [hep-ph/0511219] [INSPIRE].

    ADS  Google Scholar 

  137. L.J. Hall, M.P. Salem and T. Watari, Quark and lepton masses from Gaussian landscapes, Phys. Rev. Lett. 100 (2008) 141801 [arXiv:0707.3444] [INSPIRE].

    Article  ADS  Google Scholar 

  138. G.W. Gibbons, S. Gielen, C. Pope and N. Turok, Measures on mixing angles, Phys. Rev. D 79 (2009) 013009 [arXiv:0810.4813] [INSPIRE].

    ADS  Google Scholar 

  139. G.F. Giudice, G. Perez and Y. Soreq, Flavor beyond the standard universe, arXiv:1207.4861 [INSPIRE].

  140. N. Arkani-Hamed, S. Dimopoulos and S. Kachru, Predictive landscapes and new physics at a TeV, hep-th/0501082 [INSPIRE].

  141. V. Agrawal, S.M. Barr, J.F. Donoghue and D. Seckel, The anthropic principle and the mass scale of the Standard Model, Phys. Rev. D 57 (1998) 5480 [hep-ph/9707380] [INSPIRE].

    ADS  Google Scholar 

  142. I.Y. Kobzarev, L. Okun and M. Voloshin, Bubbles in metastable vacuum, Sov. J. Nucl. Phys. 20 (1975) 644 [Yad. Fiz. 20 (1974) 1229] [INSPIRE].

  143. 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].

  144. C.G. Callan Jr. and S.R. Coleman, The fate of the false vacuum. 2. First quantum corrections, Phys. Rev. D 16 (1977) 1762 [INSPIRE].

    ADS  Google Scholar 

  145. S.R. Coleman and F. De Luccia, Gravitational effects on and of vacuum decay, Phys. Rev. D 21 (1980) 3305 [INSPIRE].

    ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CERN, Theory Division, CH-1211, Geneva 23, Switzerland

    Dario Buttazzo, Pier Paolo Giardino & Gian F. Giudice

  2. Scuola Normale Superiore and INFN, sezione di Pisa, Piazza dei Cavalieri 7, Pisa, Italy

    Dario Buttazzo, Filippo Sala & Alberto Salvio

  3. Dipartimento di Matematica e Fisica, Università di Roma Tre and INFN, sezione di Roma Tre, Via della Vasca Navale 84, Rome, Italy

    Giuseppe Degrassi

  4. Dipartimento di Fisica, Università di Pisa and INFN, sezione di Pisa, Largo Bruno Pontecorvo 3, Pisa, Italy

    Pier Paolo Giardino & Alessandro Strumia

  5. Theoretical Physics Group, Lawrence Berkeley National Laboratory, 1 Cyclotron Rd., Berkeley, CA, United States

    Filippo Sala

  6. Departamento de Física Teórica, Universidad Autónoma de Madrid and Instituto de Física Teórica IFT-UAM/CSIC, C/Nicolás Cabrera 13-15, Madrid, Spain

    Alberto Salvio

Authors
  1. Dario Buttazzo
    View author publications

    Search author on:PubMed Google Scholar

  2. Giuseppe Degrassi
    View author publications

    Search author on:PubMed Google Scholar

  3. Pier Paolo Giardino
    View author publications

    Search author on:PubMed Google Scholar

  4. Gian F. Giudice
    View author publications

    Search author on:PubMed Google Scholar

  5. Filippo Sala
    View author publications

    Search author on:PubMed Google Scholar

  6. Alberto Salvio
    View author publications

    Search author on:PubMed Google Scholar

  7. Alessandro Strumia
    View author publications

    Search author on:PubMed Google Scholar

Corresponding author

Correspondence to Alberto Salvio.

Additional information

ArXiv ePrint: 1307.3536

Rights and permissions

Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Reprints and permissions

About this article

Cite this article

Buttazzo, D., Degrassi, G., Giardino, P.P. et al. Investigating the near-criticality of the Higgs boson. J. High Energ. Phys. 2013, 89 (2013). https://doi.org/10.1007/JHEP12(2013)089

Download citation

  • Received: 14 November 2013

  • Accepted: 03 December 2013

  • Published: 20 December 2013

  • DOI: https://doi.org/10.1007/JHEP12(2013)089

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Higgs Physics
  • Standard Model
  • Renormalization Group
Use our pre-submission checklist

Avoid common mistakes on your manuscript.

Advertisement

Search

Navigation

  • Find a journal
  • Publish with us
  • Track your research

Discover content

  • Journals A-Z
  • Books A-Z

Publish with us

  • Journal finder
  • Publish your research
  • Language editing
  • Open access publishing

Products and services

  • Our products
  • Librarians
  • Societies
  • Partners and advertisers

Our brands

  • Springer
  • Nature Portfolio
  • BMC
  • Palgrave Macmillan
  • Apress
  • Discover
  • Your US state privacy rights
  • Accessibility statement
  • Terms and conditions
  • Privacy policy
  • Help and support
  • Legal notice
  • Cancel contracts here

Not affiliated

Springer Nature

© 2025 Springer Nature