Renormalization-scale uncertainty in the decay rate of false vacuum

  • Motoi Endo
  • Takeo Moroi
  • Mihoko M. Nojiri
  • Yutaro ShojiEmail author
Open Access
Regular Article - Theoretical Physics


We study radiative corrections to the decay rate of false vacua, paying particular attention to the renormalization-scale dependence of the decay rate. The decay rate exponentially depends on the bounce action. The bounce action itself is renormalization-scale dependent. To make the decay rate scale-independent, radiative corrections, which are due to the field fluctuations around the bounce, have to be included. We show quantitatively that the inclusion of the fluctuations suppresses the scale dependence, and hence is important for the precise calculation of the decay rate. We also apply our analysis to a supersymmetric model and show that the radiative corrections are important for the Higgs-stau system with charge breaking minima.


Supersymmetry Phenomenology 


Open Access

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  1. [1]
    G. Degrassi et al., Higgs mass and vacuum stability in the Standard Model at NNLO, JHEP 08 (2012) 098 [arXiv:1205.6497] [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    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].ADSCrossRefGoogle Scholar
  3. [3]
    J.F. Gunion, H.E. Haber and M. Sher, Charge/color breaking minima and a-parameter bounds in supersymmetric models, Nucl. Phys. B 306 (1988) 1 [INSPIRE].ADSCrossRefGoogle Scholar
  4. [4]
    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].ADSCrossRefGoogle Scholar
  5. [5]
    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].ADSGoogle Scholar
  6. [6]
    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].
  7. [7]
    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].ADSGoogle Scholar
  8. [8]
    J. Avan and H.J. De Vega, Inverse scattering transform and instantons of four-dimensional Yukawa and ϕ 4 theories, Nucl. Phys. B 269 (1986) 621 [INSPIRE].ADSCrossRefGoogle Scholar
  9. [9]
    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].ADSCrossRefGoogle Scholar
  10. [10]
    J. Baacke and G. Lavrelashvili, One loop corrections to the metastable vacuum decay, Phys. Rev. D 69 (2004) 025009 [hep-th/0307202] [INSPIRE].ADSGoogle Scholar
  11. [11]
    G.V. Dunne, Functional determinants in quantum field theory, J. Phys. A 41 (2008) 304006 [arXiv:0711.1178] [INSPIRE].MathSciNetGoogle Scholar
  12. [12]
    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].ADSGoogle Scholar
  13. [13]
    J.H. Van Vleck, The correspondence principle in the statistical interpretation of quantum mechanics, Proc. Nat. Acad. Sci. 14 (1928) 178 [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  14. [14]
    R.H. Cameron and W.T. Martin, Evaluation of various Wiener integrals by use of certain Sturm-Liouville differential equations, Bull. Am. Math. Soc. 51 (1945) 73.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    I.M. Gelfand and A.M. Yaglom, Integration in functional spaces and it applications in quantum physics, J. Math. Phys. 1 (1960) 48 [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    R.F. Dashen, B. Hasslacher and A. Neveu, Nonperturbative methods and extended hadron models in field theory. 1. Semiclassical functional methods, Phys. Rev. D 10 (1974) 4114 [INSPIRE].ADSGoogle Scholar
  17. [17]
    S.R. Coleman, The uses of instantons, Subnucl. Ser. 15 (1979) 805 [INSPIRE].Google Scholar
  18. [18]
    K. Kirsten and A.J. McKane, Functional determinants by contour integration methods, Annals Phys. 308 (2003) 502 [math-ph/0305010] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  19. [19]
    K. Kirsten and A.J. McKane, Functional determinants for general Sturm-Liouville problems, J. Phys. A 37 (2004) 4649 [math-ph/0403050] [INSPIRE].ADSMathSciNetGoogle Scholar
  20. [20]
    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].ADSCrossRefGoogle Scholar
  21. [21]
    Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, arXiv:1502.01589 [INSPIRE].
  22. [22]
    J.E. 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].ADSCrossRefGoogle Scholar
  23. [23]
    A. Kusenko, K.-M. Lee and E.J. Weinberg, Vacuum decay and internal symmetries, Phys. Rev. D 55 (1997) 4903 [hep-th/9609100] [INSPIRE].ADSGoogle Scholar
  24. [24]
    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, JHEP 02 (2014) 110 [arXiv:1310.1932] [INSPIRE].ADSCrossRefGoogle Scholar
  25. [25]
    N. Blinov and D.E. Morrissey, Vacuum stability and the MSSM Higgs mass, JHEP 03 (2014) 106 [arXiv:1310.4174] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    J.E. Camargo-Molina, B. Garbrecht, B. O’Leary, W. Porod and F. Staub, Constraining the natural MSSM through tunneling to color-breaking vacua at zero and non-zero temperature, Phys. Lett. B 737 (2014) 156 [arXiv:1405.7376] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    M. Endo, T. Moroi and M.M. Nojiri, Footprints of supersymmetry on Higgs decay, JHEP 04 (2015) 176 [arXiv:1502.03959] [INSPIRE].ADSCrossRefGoogle Scholar
  28. [28]
    J.L. Lopez, D.V. Nanopoulos and X. Wang, Large (g − 2)μ in SU(5) × U(1) supergravity models, Phys. Rev. D 49 (1994) 366 [hep-ph/9308336] [INSPIRE].ADSGoogle Scholar
  29. [29]
    U. Chattopadhyay and P. Nath, Probing supergravity grand unification in the Brookhaven g − 2 experiment, Phys. Rev. D 53 (1996) 1648 [hep-ph/9507386] [INSPIRE].ADSGoogle Scholar
  30. [30]
    T. Moroi, The Muon anomalous magnetic dipole moment in the minimal supersymmetric standard model, Phys. Rev. D 53 (1996) 6565 [Erratum ibid. D 56 (1997) 4424] [hep-ph/9512396] [INSPIRE].
  31. [31]
    M. Endo, K. Hamaguchi, T. Kitahara and T. Yoshinaga, Probing bino contribution to muon g − 2, JHEP 11 (2013) 013 [arXiv:1309.3065] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    Particle Data Group collaboration, K.A. Olive et al., Review of particle physics, Chin. Phys. C 38 (2014) 090001 [INSPIRE].
  33. [33]
    Y. Okada, M. Yamaguchi and T. Yanagida, Renormalization group analysis on the Higgs mass in the softly broken supersymmetric standard model, Phys. Lett. B 262 (1991) 54 [INSPIRE].ADSCrossRefGoogle Scholar
  34. [34]
    M. Endo, T. Moroi, M. M. Nojiri and T. Shoji, work in progress.Google Scholar

Copyright information

© The Author(s) 2016

Authors and Affiliations

  • Motoi Endo
    • 1
    • 2
  • Takeo Moroi
    • 1
    • 2
  • Mihoko M. Nojiri
    • 2
    • 3
    • 4
  • Yutaro Shoji
    • 1
    Email author
  1. 1.Department of PhysicsUniversity of TokyoTokyoJapan
  2. 2.Kavli IPMU (WPI)University of TokyoKashiwaJapan
  3. 3.KEK Theory Center, IPNS, KEKTsukubaJapan
  4. 4.SOKENDAI (The Graduate University for Advanced Studies)TsukubaJapan

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