Abstract
We provide a comparative study of the fine tuning amount (Δ) at the two-loop leading log level in supersymmetric models commonly used in SUSY searches at the LHC. These are the constrained MSSM (CMSSM), non-universal Higgs masses models (NUHM1, NUHM2), non-universal gaugino masses model (NUGM) and GUT related gaugino masses models (NUGMd). Two definitions of the fine tuning are used, the first (Δmax) measures maximal fine-tuning w.r.t. individual parameters while the second (Δ q ) adds their contribution in “quadrature”. As a direct consequence of two theoretical constraints (the EW minimum conditions), fine tuning (Δ q ) emerges at the mathematical level as a suppressing factor (effective prior) of the averaged likelihood (\( L \)) under the priors, under the integral of the global probability of measuring the data (Bayesian evidence p(D)). For each model, there is little difference between Δ q , Δmax in the region allowed by the data, with similar behaviour as functions of the Higgs, gluino, stop mass or SUSY scale (\( {m_{\text{SUSY}}} = {\left( {{m_{{\overline t 1}}}{m_{{\overline t 2}}}} \right)^{{{{1} \left/ {2} \right.}}}} \)) or dark matter and g − 2 constraints. The analysis has the advantage that by replacing any of these mass scales or constraints by their latest bounds one easily infers for each model the value of Δ q , Δmax or vice versa. For all models, minimal fine tuning is achieved for M higgs near 115 GeV with a Δ q ≈ Δmax ≈ 10 to 100 depending on the model, and in the CMSSM this is actually a global minimum. Due to a strong (≈ exponential) dependence of Δ on M higgs, for a Higgs mass near 125 GeV, the above values of Δ q ≈ Δmax increase to between 500 and 1000. Possible corrections to these values are briefly discussed.
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References
S. Cassel and D. Ghilencea, A Review of naturalness and dark matter prediction for the Higgs mass in MSSM and beyond, Mod. Phys. Lett. A 27 (2012) 1230003 [arXiv:1103.4793] [INSPIRE].
J.R. Ellis, K. Enqvist, D.V. Nanopoulos and F. Zwirner, Observables in Low-Energy Superstring Models, Mod. Phys. Lett. A 1 (1986) 57 [INSPIRE].
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].
M.E. Cabrera, J.A. Casas and R. Ruiz d Austri, MSSM Forecast for the LHC, JHEP 05 (2010) 043 [arXiv:0911.4686] [INSPIRE].
S.S. AbdusSalam, B.C. Allanach, F. Quevedo, F. Feroz and M. Hobson, Fitting the Phenomenological MSSM, Phys. Rev. D 81 (2010) 095012 [arXiv:0904.2548] [INSPIRE].
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].
B. Allanach, Naturalness priors and fits to the constrained minimal supersymmetric standard model, Phys. Lett. B 635 (2006) 123 [hep-ph/0601089] [INSPIRE].
S. Cassel, D. Ghilencea and G. Ross, Testing SUSY at the LHC: Electroweak and Dark matter fine tuning at two-loop order, Nucl. Phys. B 835 (2010) 110 [arXiv:1001.3884] [INSPIRE].
S. Cassel, D. Ghilencea and G. Ross, Testing SUSY, Phys. Lett. B 687 (2010) 214 [arXiv:0911.1134] [INSPIRE].
J.O. Berger, B. Liseo, R.L. Wolpert, Integrated likelihood methods for eliminating nuisance parameters, Stat. Sci. 14 (1999) 1.
P.H. Chankowski, J.R. Ellis and S. Pokorski, The Fine tuning price of LEP, Phys. Lett. B 423 (1998)327 [hep-ph/9712234] [INSPIRE].
P.H. Chankowski, J.R. Ellis, M. Olechowski and S. Pokorski, Haggling over the fine tuning price of LEP, Nucl. Phys. B 544 (1999) 39 [hep-ph/9808275] [INSPIRE].
G.L. Kane and S. King, Naturalness implications of LEP results, Phys. Lett. B 451 (1999) 113 [hep-ph/9810374] [INSPIRE].
R. Barbieri and A. Strumia, What is the limit on the Higgs mass?, Phys. Lett. B 462 (1999) 144 [hep-ph/9905281] [INSPIRE].
R. Barbieri and A. Strumia, About the fine tuning price of LEP, Phys. Lett. B 433 (1998) 63 [hep-ph/9801353] [INSPIRE].
R. Barbieri and G. Giudice, Upper Bounds on Supersymmetric Particle Masses, Nucl. Phys. B 306 (1988) 63 [INSPIRE].
D. Horton and G. Ross, Naturalness and Focus Points with Non-Universal Gaugino Masses, Nucl. Phys. B 830 (2010) 221 [arXiv:0908.0857] [INSPIRE].
ATLAS collaboration, F. Giannoti, Update on the Standard Model Higgs searches in ATLAS, talk given at CERN Public Seminar, CERN, 13 December 2011 [https://indico.cern.ch/conferenceDisplay.py?confId=164890].
ATLAS collaboration, G. Aad et al., Combined search for the Standard Model Higgs boson using up to 4.9 fb −1 of pp collision data at \( \sqrt {s} = 7 \) TeV with the ATLAS detector at the LHC, Phys. Lett. B 710 (2012) 49 [arXiv:1202.1408] [INSPIRE].
ATLAS collaboration, G. Aad et al., Search for the Standard Model Higgs boson in the diphoton decay channel with 4.9 fb −1 of pp collisions at \( \sqrt {s} = 7 \) TeV with ATLAS, Phys. Rev. Lett. 108 (2012) 111803 [arXiv:1202.1414] [INSPIRE].
ATLAS collaboration, G. Aad et al., Search for the Standard Model Higgs boson in the decay channel H → ZZ(∗) → 4l with 4.8 fb −1 of pp collision data at \( \sqrt {s} = 7 \) TeV with ATLAS, Phys. Lett. B 710 (2012) 383 [arXiv:1202.1415] [INSPIRE].
CMS collaboration, G. Tonelli, Update on the Standard Model Higgs searches in CMS, talk given at CERN Public Seminar, CERN, 13 December 2011 [https://indico.cern.ch/conferenceDisplay.py?confId=164890].
CMS collaboration, S. Chatrchyan et al., Search for the standard model Higgs boson decaying to bottom quarks in pp collisions at \( \sqrt {s} = 7 \) TeV, Phys. Lett. B 710 (2012) 284 [arXiv:1202.4195] [INSPIRE].
CMS collaboration, S. Chatrchyan et al., Search for neutral Higgs bosons decaying to tau pairs in pp collisions at \( \sqrt {s} = 7 \) TeV, Phys. Lett. B 713 (2012) 68 [arXiv:1202.4083] [INSPIRE].
CMS collaboration, S. Chatrchyan et al., Search for the standard model Higgs boson decaying into two photons in pp collisions at \( \sqrt {s} = 7 \) TeV, Phys. Lett. B 710 (2012) 403 [arXiv:1202.1487] [INSPIRE].
CMS collaboration, S. Chatrchyan et al., Combined results of searches for the standard model Higgs boson in pp collisions at \( \sqrt {s} = 7 \) TeV, Phys. Lett. B 710 (2012) 26 [arXiv:1202.1488] [INSPIRE].
S. Cassel, D. Ghilencea and G. Ross, Fine tuning as an indication of physics beyond the MSSM, Nucl. Phys. B 825 (2010) 203 [arXiv:0903.1115] [INSPIRE].
G.G. Ross, K. Schmidt-Hoberg and F. Staub, The generalised NMSSM at one loop: fine tuning and phenomenology, arXiv:1205.1509 [INSPIRE].
G.G. Ross and K. Schmidt-Hoberg, The fine-tuning of the generalised NMSSM, Nucl. Phys. B 862 (2012) 710 [arXiv:1108.1284] [INSPIRE].
M. Carena, K. Kong, E. Ponton and J. Zurita, Supersymmetric Higgs Bosons and Beyond, Phys. Rev. D 81 (2010) 015001 [arXiv:0909.5434] [INSPIRE].
I. Antoniadis, E. Dudas, D. Ghilencea and P. Tziveloglou, MSSM Higgs with dimension-six operators, Nucl. Phys. B 831 (2010) 133 [arXiv:0910.1100] [INSPIRE].
I. Antoniadis, E. Dudas, D. Ghilencea and P. Tziveloglou, Beyond the MSSM Higgs with D = 6 effective operators, Nucl. Phys. B 848(2011) 1 [arXiv:1012.5310] [INSPIRE].
I. Antoniadis, E. Dudas, D. Ghilencea and P. Tziveloglou, Non-linear MSSM, Nucl. Phys. B 841 (2010)157 [arXiv:1006.1662] [INSPIRE].
M. Carena, E. Ponton and J. Zurita, BMSSM Higgs Bosons at the Tevatron and the LHC, Phys. Rev. D 82 (2010) 055025 [arXiv:1005.4887] [INSPIRE].
M. Carena, E. Ponton and J. Zurita, BMSSM Higgs Bosons at the 7 TeV LHC, Phys. Rev. D 85 (2012) 035007 [arXiv:1111.2049] [INSPIRE].
A. Brignole, J. Casas, J. Espinosa and I. Navarro, Low scale supersymmetry breaking: Effective description, electroweak breaking and phenomenology, Nucl. Phys. B 666 (2003) 105 [hep-ph/0301121] [INSPIRE].
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].
M.S. Carena, J. Espinosa, M. Quirós and C. Wagner, Analytical expressions for radiatively corrected Higgs masses and couplings in the MSSM, Phys. Lett. B 355 (1995) 209 [hep-ph/9504316] [INSPIRE].
T. Sjöstrand, S. Mrenna and P.Z. Skands, A Brief Introduction to PYTHIA 8.1, Comput. Phys. Commun. 178 (2008) 852 [arXiv:0710.3820] [INSPIRE].
G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs: A Program for calculating the relic density in the MSSM, Comput. Phys. Commun. 149 (2002) 103 [hep-ph/0112278] [INSPIRE].
G. Bélanger, F. Boudjema, A. Pukhov and A. Semenov, MicrOMEGAs: Version 1.3, Comput. Phys. Commun. 174 (2006) 577 [hep-ph/0405253] [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].
B. Allanach, SOFTSUSY: a program for calculating supersymmetric spectra, Comput. Phys. Commun. 143 (2002) 305 [hep-ph/0104145] [INSPIRE].
O. Buchmueller et al., Supersymmetry in Light of 1/fb of LHC Data, Eur. Phys. J. C 72 (2012)1878 [arXiv:1110.3568] [INSPIRE].
S. Sekmen et al., Interpreting LHC SUSY searches in the phenomenological MSSM, JHEP 02 (2012) 075 [arXiv:1109.5119] [INSPIRE].
S. Cassel, D. Ghilencea, S. Kraml, A. Lessa and G. Ross, Fine-tuning implications for complementary dark matter and LHC SUSY searches, JHEP 05 (2011) 120 [arXiv:1101.4664] [INSPIRE].
S. Akula, N. Chen, D. Feldman, M. Liu, Z. Liu, P. Nath and G. Peim, Interpreting the First CMS and ATLAS SUSY Results, Phys. Lett. B 699 (2011) 377 [arXiv:1103.1197] [INSPIRE].
D. Feldman, K. Freese, P. Nath, B.D. Nelson and G. Peim, Predictive Signatures of Supersymmetry: Measuring the Dark Matter Mass and Gluino Mass with Early LHC data, Phys. Rev. D 84 (2011) 015007 [arXiv:1102.2548] [INSPIRE].
P. Bechtle et al., What if the LHC does not find supersymmetry in the \( \sqrt {s} = 7 \) TeV run?, Phys. Rev. D 84 (2011) 011701 [arXiv:1102.4693] [INSPIRE].
S. Akula, D. Feldman, Z. Liu, P. Nath and G. Peim, New Constraints on Dark Matter from CMS and ATLAS Data, Mod. Phys. Lett. A 26 (2011) 1521 [arXiv:1103.5061] [INSPIRE].
M. Davier, A. Hoecker, B. Malaescu, C. Yuan and Z. Zhang, Reevaluation of the hadronic contribution to the muon magnetic anomaly using new e + e − → π+π− cross section data from BABAR, Eur. Phys. J. C 66 (2010) 1 [arXiv:0908.4300] [INSPIRE].
Heavy Flavor Averaging Group collaboration, D. Asner et al., Averages of b-hadron, c-hadron and τ -lepton Properties, arXiv:1010.1589 [INSPIRE].
CMS and LHCb ollaborations, Search for the rare decay B s → μ + μ − at the LHC with the CMS and LHCb experiments Combination of LHC results of the search for B s → μ + μ − decays, PAS-BPH-11-019 [LHCb-CONF-2011-047, CERN-LHCb-CONF-2011-047].
Particle Data Group, http://pdg.lbl.gov/.
WMAP collaboration, G. Hinshaw et al., Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps and Basic Results, Astrophys. J. Suppl. 180 (2009) 225 [arXiv:0803.0732] [INSPIRE].
LHCb collaboration, R. Aaij et al., Strong constraints on the rare decays B s → μ + μ − and B 0 → μ + μ −, Phys. Rev. Lett. 108, 231801 (2012) [arXiv:1203.4493] [INSPIRE].
ALEPH, DELPHI, L3, OPAL, LEP Working Group for Higgs Boson Searches collaborations, S. Schael et al., Search for neutral MSSM Higgs bosons at LEP, Eur. Phys. J. C 47 (2006) 547 [hep-ex/0602042] [INSPIRE].
LEP Working Group for Higgs boson searches, ALEPH, DELPHI, L3, OPAL collaborations, R. Barate et al., Search for the standard model Higgs boson at LEP, Phys. Lett. B 565 (2003) 61 [hep-ex/0306033] [INSPIRE].
G. Degrassi, S. Heinemeyer, W. Hollik, P. Slavich and G. Weiglein, Towards high precision predictions for the MSSM Higgs sector, Eur. Phys. J. C 28 (2003) 133 [hep-ph/0212020] [INSPIRE].
S. Heinemeyer, MSSM Higgs physics at higher orders, Int. J. Mod. Phys. A 21 (2006) 2659 [hep-ph/0407244] [INSPIRE].
ATLAS collaboration, Search for gluinos in events with two same-sign leptons, jets and missing transverse momentum with the ATLAS detector in pp collisions at \( \sqrt {s} = 7 \) TeV, ATLAS-CONF-2012-004 (2012).
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Ghilencea, D.M., Lee, H.M. & Park, M. Tuning supersymmetric models at the LHC: a comparative analysis at two-loop level.. J. High Energ. Phys. 2012, 46 (2012). https://doi.org/10.1007/JHEP07(2012)046
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DOI: https://doi.org/10.1007/JHEP07(2012)046