Skip to main content
Download PDF

Vacuum stability and the MSSM Higgs mass

Journal of High Energy Physics volume 2014, Article number: 106 (2014) Cite this article

Abstract

In the Minimal Supersymmetric Standard Model (MSSM), a Higgs boson mass of 125 GeV can be obtained with moderately heavy scalar top superpartners provided they are highly mixed. The source of this mixing, a soft trilinear stop-stop-Higgs coupling, can result in the appearance of charge- and color-breaking minima in the scalar potential of the theory. If such a vacuum exists and is energetically favorable, the Standard Model-like vacuum can decay to it via quantum tunnelling. In this work we investigate the conditions under which such exotic vacua arise, and we compute the tunnelling rates to them. Our results provide new constraints on the scalar top quarks of the MSSM.

References

  1. S.P. Martin, A supersymmetry primer, in Perspectives on supersymmetry II, G.L. Kane ed., World Scientific, Singapore (2010), hep-ph/9709356 [INSPIRE].

  2. R. Barbieri and G. Giudice, Upper bounds on supersymmetric particle masses, Nucl. Phys. B 306 (1988) 63 [INSPIRE].

    ADS  Article  Google Scholar 

  3. C. Wymant, Optimising stop naturalness, Phys. Rev. D 86 (2012) 115023 [arXiv:1208.1737] [INSPIRE].

    ADS  Google Scholar 

  4. 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 

  5. 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 

  6. L.J. Hall, D. Pinner and J.T. Ruderman, A natural SUSY Higgs near 126 GeV, JHEP 04 (2012) 131 [arXiv:1112.2703] [INSPIRE].

    ADS  Article  Google Scholar 

  7. J.-J. Cao, Z.-X. Heng, J.M. Yang, Y.-M. Zhang and J.-Y. Zhu, A SM-like Higgs near 125 GeV in low energy SUSY: a comparative study for MSSM and NMSSM, JHEP 03 (2012) 086 [arXiv:1202.5821] [INSPIRE].

    ADS  Article  Google Scholar 

  8. J.R. Ellis, G. Ridolfi and F. Zwirner, Radiative corrections to the masses of supersymmetric Higgs bosons, Phys. Lett. B 257 (1991) 83 [INSPIRE].

    ADS  Article  Google Scholar 

  9. H.E. Haber and R. Hempfling, Can the mass of the lightest Higgs boson of the minimal supersymmetric model be larger than m(Z)?, Phys. Rev. Lett. 66 (1991) 1815 [INSPIRE].

    ADS  Article  Google Scholar 

  10. M.S. Carena et al., Reconciling the two loop diagrammatic and effective field theory computations of the mass of the lightest CP-even Higgs boson in the MSSM, Nucl. Phys. B 580 (2000) 29 [hep-ph/0001002] [INSPIRE].

    ADS  Article  Google Scholar 

  11. P. Draper, P. Meade, M. Reece and D. Shih, Implications of a 125 GeV Higgs for the MSSM and low-scale SUSY breaking, Phys. Rev. D 85 (2012) 095007 [arXiv:1112.3068] [INSPIRE].

    ADS  Google Scholar 

  12. J. Casas, J. Espinosa, M. Quirós and A. Riotto, The lightest Higgs boson mass in the minimal supersymmetric standard model, Nucl. Phys. B 436 (1995) 3 [Erratum ibid. B 439 (1995) 466] [hep-ph/9407389] [INSPIRE].

  13. R. Kitano and Y. Nomura, Supersymmetry, naturalness and signatures at the LHC, Phys. Rev. D 73 (2006) 095004 [hep-ph/0602096] [INSPIRE].

    ADS  Google Scholar 

  14. J.M. Frere, D.R.T. Jones and S. Raby, Fermion masses and induction of the weak scale by supergravity, Nucl. Phys. B 222 (1983) 11 [INSPIRE].

    ADS  Article  Google Scholar 

  15. M. Claudson, L.J. Hall and I. Hinchliffe, Low-energy supergravity: false vacua and vacuous predictions, Nucl. Phys. B 228 (1983) 501 [INSPIRE].

    ADS  Article  Google Scholar 

  16. G. Gamberini, G. Ridolfi and F. Zwirner, On radiative gauge symmetry breaking in the minimal supersymmetric model, Nucl. Phys. B 331 (1990) 331 [INSPIRE].

    ADS  Article  Google Scholar 

  17. J.A. Casas, A. Lleyda and C. Muñoz, Strong constraints on the parameter space of the MSSM from charge and color breaking minima, Nucl. Phys. B 471 (1996) 3 [hep-ph/9507294] [INSPIRE].

    ADS  Article  Google Scholar 

  18. T. Falk, K.A. Olive, L. Roszkowski and M. Srednicki, New constraints on superpartner masses, Phys. Lett. B 367 (1996) 183 [hep-ph/9510308] [INSPIRE].

    ADS  Article  Google Scholar 

  19. A. Riotto and E. Roulet, Vacuum decay along supersymmetric flat directions, Phys. Lett. B 377 (1996) 60 [hep-ph/9512401] [INSPIRE].

    ADS  Article  MathSciNet  Google Scholar 

  20. A. Kusenko, P. Langacker and G. Segre, Phase transitions and vacuum tunneling into charge and color breaking minima in the MSSM, Phys. Rev. D 54 (1996) 5824 [hep-ph/9602414] [INSPIRE].

    ADS  Google Scholar 

  21. J. Casas, A. Lleyda and C. Muñoz, Some implications of charge and color breaking in the MSSM, Phys. Lett. B 389 (1996) 305 [hep-ph/9606212] [INSPIRE].

    ADS  Article  Google Scholar 

  22. C. Le Mouel, Optimal charge and color breaking conditions in the MSSM, Nucl. Phys. B 607 (2001) 38 [hep-ph/0101351] [INSPIRE].

    ADS  Article  Google Scholar 

  23. C. Le Mouel, Charge and color breaking conditions associated to the top quark Yukawa coupling, Phys. Rev. D 64 (2001) 075009 [hep-ph/0103341] [INSPIRE].

    ADS  Google Scholar 

  24. M.S. Carena, M. Quirós and C. Wagner, Opening the window for electroweak baryogenesis, Phys. Lett. B 380 (1996) 81 [hep-ph/9603420] [INSPIRE].

    ADS  Article  Google Scholar 

  25. J.M. Cline, G.D. Moore and G. Servant, Was the electroweak phase transition preceded by a color broken phase?, Phys. Rev. D 60 (1999) 105035 [hep-ph/9902220] [INSPIRE].

    ADS  Google Scholar 

  26. H.H. Patel, M.J. Ramsey-Musolf and M.B. Wise, Color breaking in the early universe, Phys. Rev. D 88 (2013) 015003 [arXiv:1303.1140] [INSPIRE].

    ADS  Google Scholar 

  27. B.M. Kastening, Renormalization group improvement of the effective potential in massive phi**4 theory, Phys. Lett. B 283 (1992) 287 [INSPIRE].

    ADS  Article  Google Scholar 

  28. C. Ford, D.R.T. Jones, P.W. Stephenson and M.B. Einhorn, The effective potential and the renormalization group, Nucl. Phys. B 395 (1993) 17 [hep-lat/9210033] [INSPIRE].

    ADS  Article  Google Scholar 

  29. R. Jackiw, Functional evaluation of the effective potential, Phys. Rev. D 9 (1974) 1686 [INSPIRE].

    ADS  Google Scholar 

  30. H.H. Patel and M.J. Ramsey-Musolf, Baryon washout, electroweak phase transition and perturbation theory, JHEP 07 (2011) 029 [arXiv:1101.4665] [INSPIRE].

    ADS  Article  Google Scholar 

  31. N.K. Nielsen, On the gauge dependence of spontaneous symmetry breaking in gauge theories, Nucl. Phys. B 101 (1975) 173 [INSPIRE].

    ADS  Article  Google Scholar 

  32. R. Fukuda and T. Kugo, Gauge invariance in the effective action and potential, Phys. Rev. D 13 (1976) 3469 [INSPIRE].

    ADS  Google Scholar 

  33. M. Garny and T. Konstandin, On the gauge dependence of vacuum transitions at finite temperature, JHEP 07 (2012) 189 [arXiv:1205.3392] [INSPIRE].

    ADS  Article  Google Scholar 

  34. D. Metaxas and E.J. Weinberg, Gauge independence of the bubble nucleation rate in theories with radiative symmetry breaking, Phys. Rev. D 53 (1996) 836 [hep-ph/9507381] [INSPIRE].

    ADS  Google Scholar 

  35. F. James and M. Roos, Minuit: a system for function minimization and analysis of the parameter errors and correlations, Comput. Phys. Commun. 10 (1975) 343 [INSPIRE]

    ADS  Article  Google Scholar 

  36. http://lcgapp.cern.ch/project/cls/work-packages/mathlibs/minuit/index.html.

  37. 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].

  38. 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 

  39. G.V. Dunne and H. Min, Beyond the thin-wall approximation: Precise numerical computation of prefactors in false vacuum decay, Phys. Rev. D 72 (2005) 125004 [hep-th/0511156] [INSPIRE].

    ADS  Google Scholar 

  40. H. Min, On the prefactor in false vacuum decay, J. Phys. A 39 (2006) 6551 [INSPIRE].

    ADS  Google Scholar 

  41. E.J. Weinberg, Vacuum decay in theories with symmetry breaking by radiative corrections, Phys. Rev. D 47 (1993) 4614 [hep-ph/9211314] [INSPIRE].

    ADS  Google Scholar 

  42. A. Kusenko, Improved action method for analyzing tunneling in quantum field theory, Phys. Lett. B 358 (1995) 51 [hep-ph/9504418] [INSPIRE].

    ADS  Article  MathSciNet  Google Scholar 

  43. T. Konstandin and S.J. Huber, Numerical approach to multi dimensional phase transitions, JCAP 06 (2006) 021 [hep-ph/0603081] [INSPIRE].

    ADS  Article  Google Scholar 

  44. J.-h. Park, Constrained potential method for false vacuum decays, JCAP 02 (2011) 023 [arXiv:1011.4936] [INSPIRE].

    ADS  Article  Google Scholar 

  45. C.L. Wainwright, CosmoTransitions: computing cosmological phase transition temperatures and bubble profiles with multiple fields, Comput. Phys. Commun. 183 (2012) 2006 [arXiv:1109.4189] [INSPIRE].

    ADS  Article  Google Scholar 

  46. J. Camargo-Molina, B. O’Leary, W. Porod and F. Staub, Vevacious: a tool for finding the global minima of one-loop effective potentials with many scalars, Eur. Phys. J. C 73 (2013) 2588 [arXiv:1307.1477] [INSPIRE].

    ADS  Article  Google Scholar 

  47. M. Reece, Vacuum instabilities with a wrong-sign Higgs-gluon-gluon amplitude, New J. Phys. 15 (2013) 043003 [arXiv:1208.1765] [INSPIRE].

    ADS  Article  Google Scholar 

  48. S. Heinemeyer, W. Hollik and G. Weiglein, FeynHiggs: a program for the calculation of the masses of the neutral CP even Higgs bosons in the MSSM, Comput. Phys. Commun. 124 (2000) 76 [hep-ph/9812320] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  49. A. Djouadi, J.-L. Kneur and G. Moultaka, SuSpect: a Fortran code for the supersymmetric and Higgs particle spectrum in the MSSM, Comput. Phys. Commun. 176 (2007) 426 [hep-ph/0211331] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  50. Particle Data Group collaboration, J. Beringer et al., Review of particle physics, Phys. Rev. D 86 (2012) 010001 [INSPIRE].

    ADS  Google Scholar 

  51. V. Barger, P. Huang, M. Ishida and W.-Y. Keung, Scalar-top masses from SUSY loops with 125 GeV mh and precise Mw, Phys. Lett. B 718 (2013) 1024 [arXiv:1206.1777] [INSPIRE].

    ADS  Article  Google Scholar 

  52. S. Heinemeyer, O. Stal and G. Weiglein, Interpreting the LHC Higgs search results in the MSSM, Phys. Lett. B 710 (2012) 201 [arXiv:1112.3026] [INSPIRE].

    ADS  Article  Google Scholar 

  53. J.R. Espinosa, C. Grojean, V. Sanz and M. Trott, NSUSY fits, JHEP 12 (2012) 077 [arXiv:1207.7355] [INSPIRE].

    ADS  Article  Google Scholar 

  54. M. Drees and K. Hagiwara, Supersymmetric contribution to the electroweak ρ parameter, Phys. Rev. D 42 (1990) 1709 [INSPIRE].

    ADS  Google Scholar 

  55. S. Heinemeyer, W. Hollik and G. Weiglein, Electroweak precision observables in the minimal supersymmetric standard model, Phys. Rept. 425 (2006) 265 [hep-ph/0412214] [INSPIRE].

    ADS  Article  Google Scholar 

  56. G. D’Ambrosio, G. Giudice, G. Isidori and A. Strumia, Minimal flavor violation: an effective field theory approach, Nucl. Phys. B 645 (2002) 155 [hep-ph/0207036] [INSPIRE].

    ADS  Article  Google Scholar 

  57. M. Ciuchini, G. Degrassi, P. Gambino and G. Giudice, Next-to-leading QCD corrections to B → X s γ in supersymmetry, Nucl. Phys. B 534 (1998) 3 [hep-ph/9806308] [INSPIRE].

    ADS  Google Scholar 

  58. B. Grzadkowski and M. Misiak, Anomalous Wtb coupling effects in the weak radiative B-meson decay, Phys. Rev. D 78 (2008) 077501 [Erratum ibid. D 84 (2011) 059903] [arXiv:0802.1413] [INSPIRE].

  59. Heavy Flavor Averaging Group collaboration, Y. Amhis et al., Averages of B-hadron, C-hadron and τ-lepton properties as of early 2012, arXiv:1207.1158 [INSPIRE].

  60. A. Arbey and F. Mahmoudi, SuperIso relic: a program for calculating relic density and flavor physics observables in Supersymmetry, Comput. Phys. Commun. 181 (2010) 1277 [arXiv:0906.0369] [INSPIRE].

    ADS  Article  MATH  Google Scholar 

  61. ATLAS collaboration, Search for direct third-generation squark pair production in final states with missing transverse momentum and two b-jets in \( \sqrt{s} \) = 8 TeV pp collisions with the ATLAS detector, JHEP 10 (2013) 189 [arXiv:1308.2631] [INSPIRE].

    ADS  Google Scholar 

  62. ATLAS collaboration, Search for pair-produced top squarks decaying into a charm quark and the lightest neutralinos with 20.3 fb −1 of pp collisions at \( \sqrt{s} \) = 8 TeV with the ATLAS detector at the LHC, ATLAS-CONF-2013-068 (2013).

  63. CMS collaboration, Search for top-squark pair production in the single-lepton final state in pp collisions at \( \sqrt{s} \) = 8 TeV, Eur. Phys. J. C 73 (2013) 2677 [arXiv:1308.1586] [INSPIRE].

    ADS  Google Scholar 

  64. CMS collaboration, Search for supersymmetry using razor variables in events with b-jets in pp collisions at 8 TeV, CMS-PAS-SUS-13-004 (2013).

  65. M. Carena, G. Nardini, M. Quirós and C.E.M. Wagner, The effective theory of the light stop scenario, JHEP 10 (2008) 062 [arXiv:0806.4297] [INSPIRE].

    ADS  Article  Google Scholar 

  66. J. Fan and M. Reece, A new look at Higgs constraints on stops, arXiv:1401.7671 [INSPIRE].

  67. J. Hisano, K. Kawagoe, R. Kitano and M.M. Nojiri, Scenery from the top: study of the third generation squarks at CERN LHC, Phys. Rev. D 66 (2002) 115004 [hep-ph/0204078] [INSPIRE].

    ADS  Google Scholar 

  68. K. Rolbiecki, J. Tattersall and G. Moortgat-Pick, Towards measuring the stop mixing angle at the LHC, Eur. Phys. J. C 71 (2011) 1517 [arXiv:0909.3196] [INSPIRE].

    ADS  Google Scholar 

  69. M. Blanke, D. Curtin and M. Perelstein, SUSY-Yukawa sum rule at the LHC, Phys. Rev. D 82 (2010)035020 [arXiv:1004.5350] [INSPIRE].

    ADS  Google Scholar 

  70. M. Perelstein and M. Saelim, SUSY-Yukawa sum rule at the LHC and the ILC, arXiv:1201.5839 [INSPIRE].

  71. M. Berggren, R. Keranen, H. Kluge and A. Sopczak, Study of scalar top quarks at a future e + e − linear collider, hep-ph/9911345 [INSPIRE].

  72. E. Boos et al., Polarization in sfermion decays: determining tan β and trilinear couplings, Eur. Phys. J. C 30 (2003) 395 [hep-ph/0303110] [INSPIRE].

    ADS  Article  Google Scholar 

  73. G.F. Giudice and A. Kusenko, A strongly interacting phase of the minimal supersymmetric model, Phys. Lett. B 439 (1998) 55 [hep-ph/9805379] [INSPIRE].

    ADS  Article  Google Scholar 

  74. P. Hernández, N. Rius and V. Sanz, Trilinear couplings and scalar bound states in supersymmetric extensions of the standard model, Nucl. Phys. Proc. Suppl. 95 (2001) 272 [INSPIRE].

    ADS  Article  Google Scholar 

  75. J.M. Cornwall, A. Kusenko, L. Pearce and R. Peccei, Can supersymmetry breaking lead to electroweak symmetry breaking via formation of scalar bound states?, Phys. Lett. B 718 (2013)951 [arXiv:1210.6433] [INSPIRE].

    ADS  Article  Google Scholar 

  76. L. Pearce, A. Kusenko and R.D. Peccei, Phenomenology of supersymmetric models with a symmetry-breaking seesaw mechanism, Phys. Rev. D 88 (2013) 075011 [arXiv:1307.6157] [INSPIRE].

    ADS  Google Scholar 

  77. J. Camargo-Molina, B. O’Leary, W. Porod and F. Staub, Stability of the CMSSM against sfermion VEVs, JHEP 12 (2013) 103 [arXiv:1309.7212] [INSPIRE].

    ADS  Article  Google Scholar 

  78. D. Chowdhury, R.M. Godbole, K.A. Mohan and S.K. Vempati, Charge and color breaking constraints in MSSM after the Higgs discovery at LHC, arXiv:1310.1932 [INSPIRE].

  79. N. Blinov and D.E. Morrissey, Charge and color breaking constraints in the minimal supersymmetric standard model, arXiv:1309.7397 [INSPIRE].

Download references

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

  1. TRIUMF, 4004 Wesbrook Mall, Vancouver, BC, V6T 2A3, Canada

    Nikita Blinov & David E. Morrissey

  2. Department of Physics and Astronomy, University of British Columbia, Vancouver, BC, V6T 1Z1, Canada

    Nikita Blinov

Authors
  1. Nikita Blinov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David E. Morrissey
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikita Blinov.

Additional information

ArXiv ePrint: 1310.4174

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.

Reprints and Permissions

About this article

Cite this article

Blinov, N., Morrissey, D.E. Vacuum stability and the MSSM Higgs mass. J. High Energ. Phys. 2014, 106 (2014). https://doi.org/10.1007/JHEP03(2014)106

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/JHEP03(2014)106

Keywords

  • Beyond Standard Model
  • Supersymmetric Standard Model