Advertisement

The dark side of the μ: on multiple solutions to renormalisation group equations, and why the CMSSM is not necessarily being ruled out

  • B. C. Allanach
  • Damien P. George
  • Ben Gripaios
Article

Abstract

When solving renormalisation group equations in a quantum field theory, one often specifies the boundary conditions at multiple renormalisation scales, such as the weak and grand-unified scales in a theory beyond the standard model. A point in the parameter space of such a model is usually specified by the values of couplings at these boundaries of the renormalisation group flow, but there is no theorem guaranteeing that such a point has a unique solution to the associated differential equations, and so there may exist multiple, phenomenologically distinct solutions, all corresponding to the same point in parameter space. We show that this is indeed the case in the constrained minimal supersymmetric standard model (CMSSM), and we exhibit such solutions, which cannot be obtained using out-of-the-box computer programs in the public domain. Some of the multiple solutions we exhibit have CP-even lightest Higgs mass predictions between 124 and 126 GeV. Without an exhaustive 11-dimensional MSSM parameter scan per CMSSM parameter point to capture all of the multiple solutions, CMSSM phenomenological analyses are incomplete.

Keywords

Supersymmetry Phenomenology 

References

  1. [1]
    E. Lindelöf, Sur lapplication de la méthode des approximations successives aux équations différentielles ordinaires du premier ordre, Comptes Rendus 114 (1894) 454.Google Scholar
  2. [2]
    M. Liu and P. Nath, Higgs boson mass, proton decay, naturalness and constraints of LHC and Planck data, arXiv:1303.7472 [INSPIRE].
  3. [3]
    V. Berezinsky, Destruction of long range order in one-dimensional and two-dimensional systems having a continuous symmetry group. 1. Classical systems, Sov. Phys. JETP 32 (1971) 493 [INSPIRE].ADSGoogle Scholar
  4. [4]
    J. Kosterlitz and D. Thouless, Ordering, metastability and phase transitions in two-dimensional systems, J. Phys. C 6 (1973) 1181 [INSPIRE].ADSGoogle Scholar
  5. [5]
    A.M. Polyakov, Quark confinement and topology of gauge groups, Nucl. Phys. B 120 (1977) 429 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  6. [6]
    B. Svetitsky and L.G. Yaffe, Critical behavior at finite temperature confinement transitions, Nucl. Phys. B 210 (1982) 423 [INSPIRE].ADSCrossRefGoogle Scholar
  7. [7]
    N.O. Agasian and K. Zarembo, Phase structure and nonperturbative states in three-dimensional adjoint Higgs model, Phys. Rev. D 57 (1998) 2475 [hep-th/9708030] [INSPIRE].ADSGoogle Scholar
  8. [8]
    B. Gripaios, Variational analysis of deconfinement in compact U(1) gauge theory, Phys. Rev. D 67 (2003) 025023 [hep-th/0211104] [INSPIRE].ADSGoogle Scholar
  9. [9]
    P. Fayet, Supersymmetry and weak, electromagnetic and strong interactions, Phys. Lett. B 64 (1976) 159 [INSPIRE].ADSGoogle Scholar
  10. [10]
    P. Fayet, Spontaneously broken supersymmetric theories of weak, electromagnetic and strong interactions, Phys. Lett. B 69 (1977) 489 [INSPIRE].ADSGoogle Scholar
  11. [11]
    G.R. Farrar and P. Fayet, Phenomenology of the production, decay and detection of new hadronic states associated with supersymmetry, Phys. Lett. B 76 (1978) 575 [INSPIRE].ADSGoogle Scholar
  12. [12]
    P. Fayet, Relations between the masses of the superpartners of leptons and quarks, the goldstino couplings and the neutral currents, Phys. Lett. B 84 (1979) 416 [INSPIRE].ADSGoogle Scholar
  13. [13]
    S. Dimopoulos and H. Georgi, Softly broken supersymmetry and SU(5), Nucl. Phys. B 193 (1981) 150 [INSPIRE].ADSCrossRefGoogle Scholar
  14. [14]
    E. Cremmer et al., SuperHiggs effect in supergravity with general scalar interactions, Phys. Lett. B 79 (1978) 231 [INSPIRE].ADSGoogle Scholar
  15. [15]
    E. Cremmer et al., Spontaneous symmetry breaking and Higgs effect in supergravity without cosmological constant, Nucl. Phys. B 147 (1979) 105 [INSPIRE].MathSciNetADSCrossRefGoogle Scholar
  16. [16]
    R. Barbieri, S. Ferrara and C.A. Savoy, Gauge models with spontaneously broken local supersymmetry, Phys. Lett. B 119 (1982) 343 [INSPIRE].ADSGoogle Scholar
  17. [17]
    M. Drees and M.M. Nojiri, Radiative symmetry breaking in minimal N = 1 supergravity with large Yukawa couplings, Nucl. Phys. B 369 (1992) 54 [INSPIRE].ADSCrossRefGoogle Scholar
  18. [18]
    Y. Yamada, SUSY and GUT threshold effects in SUSY SU(5) models, Z. Phys. C 60 (1993) 83 [INSPIRE].ADSGoogle Scholar
  19. [19]
    G. Altarelli, F. Feruglio and I. Masina, From minimal to realistic supersymmetric SU(5) grand unification, JHEP 11 (2000) 040 [hep-ph/0007254] [INSPIRE].ADSCrossRefGoogle Scholar
  20. [20]
    S. AbdusSalam et al., Benchmark models, planes, lines and points for future SUSY searches at the LHC, Eur. Phys. J. C 71 (2011) 1835 [arXiv:1109.3859] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    S.P. Martin and M.T. Vaughn, Two loop renormalization group equations for soft supersymmetry breaking couplings, Phys. Rev. D 50 (1994) 2282 [Erratum ibid. D 78 (2008) 039903] [hep-ph/9311340] [INSPIRE].
  22. [22]
    D. Capper, D. Jones and P. van Nieuwenhuizen, Regularization by dimensional reduction of supersymmetric and nonsupersymmetric gauge theories, Nucl. Phys. B 167 (1980) 479 [INSPIRE].ADSCrossRefGoogle Scholar
  23. [23]
    B. Allanach, SOFTSUSY: a program for calculating supersymmetric spectra, Comput. Phys. Commun. 143 (2002) 305 [hep-ph/0104145] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  24. [24]
    H. Baer, F.E. Paige, S.D. Protopopescu and X. Tata, Simulating supersymmetry with ISAJET 7.0/ISASUSY 1.0, hep-ph/9305342 [INSPIRE].
  25. [25]
    W. Porod, SPheno, a program for calculating supersymmetric spectra, SUSY particle decays and SUSY particle production at e + e colliders, Comput. Phys. Commun. 153 (2003) 275 [hep-ph/0301101] [INSPIRE].ADSCrossRefGoogle Scholar
  26. [26]
    D. Chowdhury, R. Garani and S.K. Vempati, SUSEFLAV: program for supersymmetric mass spectra with seesaw mechanism and rare lepton flavor violating decays, Comput. Phys. Commun. 184 (2013) 899 [arXiv:1109.3551] [INSPIRE].ADSCrossRefGoogle Scholar
  27. [27]
    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].ADSzbMATHCrossRefGoogle Scholar
  28. [28]
    D.M. Pierce, J.A. Bagger, K.T. Matchev and R.-j. Zhang, Precision corrections in the minimal supersymmetric standard model, Nucl. Phys. B 491 (1997) 3 [hep-ph/9606211] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    ATLAS collaboration, A particle consistent with the Higgs boson observed with the ATLAS Detector at the Large Hadron Collider, Science 338 (2012) 1576 [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    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].ADSGoogle Scholar
  31. [31]
    B. Allanach, J. Hetherington, M.A. Parker and B. Webber, Naturalness reach of the large hadron collider in minimal supergravity, JHEP 08 (2000) 017 [hep-ph/0005186] [INSPIRE].ADSGoogle Scholar
  32. [32]
    B. Allanach and M. Parker, Uncertainty in electroweak symmetry breaking in the minimal supersymmetric standard model and its impact on searches for supersymmetric particles, JHEP 02 (2013) 064 [arXiv:1211.3231] [INSPIRE].ADSCrossRefGoogle Scholar
  33. [33]
    ATLAS collaboration, Search for squarks and gluinos with the ATLAS detector using final states with jets and missing transverse momentum and 5.8 fb −1 of \( \sqrt{s}=8 \) TeV proton-proton collision data, ATLAS-CONF-2012-109 (2012).
  34. [34]
    CMS collaboration, Search for new physics in the multijet and missing transverse momentum final state in proton-proton collisions at \( \sqrt{s}=7 \) TeV, Phys. Rev. Lett. 109 (2012) 171803 [arXiv:1207.1898] [INSPIRE].ADSCrossRefGoogle Scholar
  35. [35]
    B. Allanach and C. Lester, Multi-dimensional mSUGRA likelihood maps, Phys. Rev. D 73 (2006) 015013 [hep-ph/0507283] [INSPIRE].ADSGoogle Scholar
  36. [36]
    O. Buchmueller et al., Higgs and supersymmetry, Eur. Phys. J. C 72 (2012) 2020 [arXiv:1112.3564] [INSPIRE].ADSGoogle Scholar
  37. [37]
    C. Balázs, A. Buckley, D. Carter, B. Farmer and M. White, Should we still believe in constrained supersymmetry?, arXiv:1205.1568 [INSPIRE].
  38. [38]
    M.E. Cabrera, J.A. Casas and R.R. de Austri, The health of SUSY after the Higgs discovery and the XENON100 data, arXiv:1212.4821 [INSPIRE].
  39. [39]
    A. Fowlie et al., The CMSSM favoring new territories: the impact of new LHC limits and a 125 GeV Higgs, Phys. Rev. D 86 (2012) 075010 [arXiv:1206.0264] [INSPIRE].ADSGoogle Scholar
  40. [40]
    C. Strege et al., Global Fits of the CMSSM and NUHM including the LHC Higgs discovery and new XENON100 constraints, JCAP 04 (2013) 013 [arXiv:1212.2636] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    B.C. Allanach, K. Cranmer, C.G. Lester and A.M. Weber, Natural priors, CMSSM fits and LHC weather forecasts, JHEP 08 (2007) 023 [arXiv:0705.0487] [INSPIRE].ADSCrossRefGoogle Scholar
  42. [42]
    M. Cabrera, J. Casas and R. Ruiz de Austri, Bayesian approach and Naturalness in MSSM analyses for the LHC, JHEP 03 (2009) 075 [arXiv:0812.0536] [INSPIRE].ADSCrossRefGoogle Scholar
  43. [43]
    Particle Data Group collaboration, J. Beringer et al., Review of particle physics, Phys. Rev. D 86 (2012) 010001 [INSPIRE].ADSGoogle Scholar

Copyright information

© SISSA, Trieste, Italy 2013

Authors and Affiliations

  • B. C. Allanach
    • 1
  • Damien P. George
    • 1
    • 2
  • Ben Gripaios
    • 2
  1. 1.Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical SciencesUniversity of CambridgeCambridgeU.K.
  2. 2.Cavendish LaboratoryUniversity of CambridgeCambridgeU.K.

Personalised recommendations