Abstract
Recent work has shown that the Constrained Minimal Supersymmetric Standard Model (CMSSM) can possess several distinct solutions for certain values of its parameters. The extra solutions were not previously found by public supersymmetric spectrum generators because fixed point iteration (the algorithm used by the generators) is unstable in the neighbourhood of these solutions. The existence of the additional solutions calls into question the robustness of exclusion limits derived from collider experiments and cosmological observations upon the CMSSM, because limits were only placed on one of the solutions. Here, we map the CMSSM by exploring its multi-dimensional parameter space using the shooting method, which is not subject to the stability issues which can plague fixed point iteration. We are able to find multiple solutions where in all previous literature only one was found. The multiple solutions are of two distinct classes. One class, close to the border of bad electroweak symmetry breaking, is disfavoured by LEP2 searches for neutralinos and charginos. The other class has sparticles that are heavy enough to evade the LEP2 bounds. Chargino masses may differ by up to around 10% between the different solutions, whereas other sparticle masses differ at the sub-percent level. The prediction for the dark matter relic density can vary by a hundred percent or more between the different solutions, so analyses employing the dark matter constraint are incomplete without their inclusion.
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References
P. Fayet, Supersymmetry and Weak, Electromagnetic and Strong Interactions, Phys. Lett. B 64 (1976) 159 [INSPIRE].
P. Fayet, Spontaneously Broken Supersymmetric Theories of Weak, Electromagnetic and Strong Interactions, Phys. Lett. B 69 (1977) 489 [INSPIRE].
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].
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].
S. Dimopoulos and H. Georgi, Softly Broken Supersymmetry and SU(5), Nucl. Phys. B 193 (1981) 150 [INSPIRE].
B. Allanach, D.P. George and B. Gripaios, The dark side of the μ: on multiple solutions to renormalisation group equations and why the CMSSM is not necessarily being ruled out, JHEP 07 (2013) 098 [arXiv:1304.5462] [INSPIRE].
N. Arkani-Hamed, G.L. Kane, J. Thaler and L.-T. Wang, Supersymmetry and the LHC inverse problem, JHEP 08 (2006) 070 [hep-ph/0512190] [INSPIRE].
B. Allanach and M.J. Dolan, Supersymmetry With Prejudice: Fitting the Wrong Model to LHC Data, Phys. Rev. D 86 (2012) 055022 [arXiv:1107.2856] [INSPIRE].
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].
B. Allanach, SOFTSUSY: a program for calculating supersymmetric spectra, Comput. Phys. Commun. 143 (2002) 305 [hep-ph/0104145] [INSPIRE].
H. Baer, F.E. Paige, S.D. Protopopescu and X. Tata, Simulating Supersymmetry with ISAJET 7.0/ISASUSY 1.0, hep-ph/9305342 [INSPIRE].
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].
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].
G. Teschl, Ordinary Differential Equations and Dynamical Systems, American Mathematical Society, (2012).
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].
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].
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].
R. Bellman, Dynamic programming, Princeton University Press, (1957).
W. Press, S. Teukolsky, W. Vetterling and B. Flannery, Numerical Recipes in C, second edition, Cambridge University Press, (1992).
C. Broyden, A Class of Methods for Solving Nonlinear Simultaneous Equations, Math. Comput. 19 (1965) 577.
ATLAS collaboration, Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum using 4.7 fb −1 of \( \sqrt{s} \) = 7 TeV proton-proton collision data, Phys. Rev. D 87 (2013) 012008 [arXiv:1208.0949] [INSPIRE].
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].
ATLAS collaboration, Search for squarks and gluinos with the ATLAS detector in final states with jets and missing transverse momentum and 20.3 fb −1 of \( \sqrt{s} \) = 8 TeV proton-proton collision data, ATLAS-CONF-2013-047 (2013).
LEPSUSYWG, ALEPH, DELPHI, L3 and OPAL experiments, note LEPSUSYWG/01-03.1, http://lepsusy.web.cern.ch/lepsusy/Welcome.html.
Particle Data Group collaboration, J. Beringer et al., Supersymmetry, Part I (theory), Phys. Rev. D 86 (2012) 010001 [INSPIRE].
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].
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].
B. Allanach et al., The physics benchmark processes for the detector performance studies used in CLIC CDR Volume 3, LCD-Note-2012-003.
P.Z. Skands et al., SUSY Les Houches accord: Interfacing SUSY spectrum calculators, decay packages and event generators, JHEP 07 (2004) 036 [hep-ph/0311123] [INSPIRE].
A. Djouadi, M. Muhlleitner and M. Spira, Decays of supersymmetric particles: The Program SUSY-HIT (SUspect-SdecaY-HDECAY-InTerface), Acta Phys. Polon. B 38 (2007) 635 [hep-ph/0609292] [INSPIRE].
G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs 2.0: A Program to calculate the relic density of dark matter in a generic model, Comput. Phys. Commun. 176 (2007) 367 [hep-ph/0607059] [INSPIRE].
G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, Dark matter direct detection rate in a generic model with MicrOMEGAs 2.2, Comput. Phys. Commun. 180 (2009) 747 [arXiv:0803.2360] [INSPIRE].
Y. Bai, H.-C. Cheng, J. Gallicchio and J. Gu, A Toolkit of the Stop Search via the Chargino Decay, JHEP 08 (2013) 085 [arXiv:1304.3148] [INSPIRE].
Planck collaboration, P. Ade et al., Planck 2013 results. XVI. Cosmological parameters, arXiv:1303.5076 [INSPIRE].
B. Allanach and C. Lester, Multi-dimensional mSUGRA likelihood maps, Phys. Rev. D 73 (2006) 015013 [hep-ph/0507283] [INSPIRE].
O. Buchmueller et al., Higgs and Supersymmetry, Eur. Phys. J. C 72 (2012) 2020 [arXiv:1112.3564] [INSPIRE].
C. Balázs, A. Buckley, D. Carter, B. Farmer and M. White, Should we still believe in constrained supersymmetry?, Eur. Phys. J. C 73 (2013) 2563 [arXiv:1205.1568] [INSPIRE].
M.E. Cabrera, J.A. Casas and R.R. de Austri, The health of SUSY after the Higgs discovery and the XENON100 data, JHEP 07 (2013) 182 [arXiv:1212.4821] [INSPIRE].
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].
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].
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Allanach, B.C., George, D.P. & Nachman, B. Investigating multiple solutions in the constrained minimal supersymmetric standard model. J. High Energ. Phys. 2014, 31 (2014). https://doi.org/10.1007/JHEP02(2014)031
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DOI: https://doi.org/10.1007/JHEP02(2014)031