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A coverage study of the CMSSM based on ATLAS sensitivity using fast neural networks techniques

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Abstract

We assess the coverage properties of confidence and credible intervals on the CMSSM parameter space inferred from a Bayesian posterior and the profile likelihood based on an ATLAS sensitivity study. In order to make those calculations feasible, we introduce a new method based on neural networks to approximate the mapping between CMSSM parameters and weak-scale particle masses. Our method reduces the computational effort needed to sample the CMSSM parameter space by a factor of ~ 104 with respect to conventional techniques. We find that both the Bayesian posterior and the profile likelihood intervals can significantly over-cover and identify the origin of this effect to physical boundaries in the parameter space. Finally, we point out that the effects intrinsic to the statistical procedure are conated with simplifications to the likelihood functions from the experiments themselves.

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References

  1. G.L. Kane, C.F. Kolda, L. Roszkowski and J.D. Wells, Study of constrained minimal supersymmetry, Phys. Rev. D 49 (1994) 6173 [hep-ph/9312272] [SPIRES].

    ADS  Google Scholar 

  2. A. Brignole, L.E. Ibáñez and C. Muñoz, Soft supersymmetry-breaking terms from supergravity and superstring models, hep-ph/9707209 [SPIRES].

  3. M. Drees and M.M. Nojiri, The Neutralino relic density in minimal N = 1 supergravity, Phys. Rev. D 47 (1993) 376 [hep-ph/9207234] [SPIRES].

    ADS  Google Scholar 

  4. H. Baer and M. Brhlik, Cosmological Relic Density from Minimal Supergravity with Implications for Collider Physics, Phys. Rev. D 53 (1996) 597 [hep-ph/9508321] [SPIRES].

    ADS  Google Scholar 

  5. J.R. Ellis, T. Falk, K.A. Olive and M. Srednicki, Calculations of neutralino stau coannihilation channels and the cosmologically relevant region of MSSM parameter space, Astropart. Phys. 13 (2000) 181 [hep-ph/9905481] [SPIRES].

    Article  ADS  Google Scholar 

  6. J.R. Ellis, T. Falk, G. Ganis, K.A. Olive and M. Srednicki, The CMSSM Parameter Space at Large tanβ, Phys. Lett. B 510 (2001) 236 [hep-ph/0102098] [SPIRES].

    ADS  Google Scholar 

  7. L. Roszkowski, R. Ruiz de Austri and T. Nihei, New cosmological and experimental constraints on the CMSSM, JHEP 08 (2001) 024 [hep-ph/0106334] [SPIRES].

    Article  ADS  Google Scholar 

  8. A.B. Lahanas and V.C. Spanos, Implications of the Pseudo-Scalar Higgs Boson in determining the Neutralino Dark Matter, Eur. Phys. J. C 23 (2002) 185 [hep-ph/0106345] [SPIRES].

    ADS  Google Scholar 

  9. E.A. Baltz and P. Gondolo, Markov chain Monte Carlo exploration of minimal supergravity with implications for dark matter, JHEP 10 (2004) 052 [hep-ph/0407039] [SPIRES].

    Article  ADS  Google Scholar 

  10. B.C. Allanach and C.G. Lester, Multi-Dimensional mSUGRA Likelihood Maps, Phys. Rev. D 73 (2006) 015013 [hep-ph/0507283] [SPIRES].

    ADS  Google Scholar 

  11. B.C. Allanach, Naturalness priors and fits to the constrained minimal supersymmetric standard model, Phys. Lett. B 635 (2006) 123 [hep-ph/0601089] [SPIRES].

    ADS  Google Scholar 

  12. R.R. de Austri, R. Trotta and L. Roszkowski, A Markov chain Monte Carlo analysis of the CMSSM, JHEP 05 (2006) 002 [hep-ph/0602028] [SPIRES].

    Article  Google Scholar 

  13. B.C. Allanach, C.G. Lester and A.M. Weber, The Dark Side of mSUGRA, JHEP 12 (2006) 065 [hep-ph/0609295] [SPIRES].

    Article  MathSciNet  ADS  Google Scholar 

  14. L. Roszkowski, R.R. de Austri and R. Trotta, On the detectability of the CMSSM light Higgs boson at the Tevatron, JHEP 04 (2007) 084 [hep-ph/0611173] [SPIRES].

    Article  ADS  Google Scholar 

  15. 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] [SPIRES].

    Article  ADS  Google Scholar 

  16. L. Roszkowski, R. Ruiz de Austri and R. Trotta, Implications for the Constrained MSSM from a new prediction for b → s, JHEP 07 (2007) 075 [arXiv:0705.2012] [SPIRES].

    Article  ADS  Google Scholar 

  17. L. Roszkowski, R.R. de Austri, J. Silk and R. Trotta, On prospects for dark matter indirect detection in the Constrained MSSM, Phys. Lett. B 671 (2009) 10 [arXiv:0707.0622] [SPIRES].

    ADS  Google Scholar 

  18. B.C. Allanach, M.J. Dolan and A.M. Weber, Global Fits of the Large Volume String Scenario to WMAP5 and Other Indirect Constraints Using Markov Chain Monte Carlo, JHEP 08 (2008) 105 [arXiv:0806.1184] [SPIRES].

    Article  ADS  Google Scholar 

  19. B.C. Allanach and D. Hooper, Panglossian Prospects for Detecting Neutralino Dark Matter in Light of Natural Priors, JHEP 10 (2008) 071 [arXiv:0806.1923] [SPIRES].

    Article  ADS  Google Scholar 

  20. G.D. Martinez, J.S. Bullock, M. Kaplinghat, L.E. Strigari and R. Trotta, Indirect Dark Matter Detection from Dwarf Satellites: Joint Expectations from Astrophysics and Supersymmetry, JCAP 06 (2009) 014 [arXiv:0902.4715] [SPIRES].

    ADS  Google Scholar 

  21. F. Feroz and M.P. Hobson, Multimodal nested sampling: an efficient and robust alternative to MCMC methods for astronomical data analysis, arXiv:0704.3704 [SPIRES].

  22. F. Feroz, M.P. Hobson and M. Bridges, MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics, arXiv:0809.3437 [SPIRES].

  23. R. Trotta, F. Feroz, M.P. Hobson, L. Roszkowski and R. Ruiz de Austri, The Impact of priors and observables on parameter inferences in the Constrained MSSM, JHEP 12 (2008) 024 [arXiv:0809.3792] [SPIRES].

    Article  ADS  Google Scholar 

  24. J. Skilling, Nested Sampling for Bayesian Computations, proceedings of Valencia/ISBA 8 th World Meeting on Bayesian Statistics, Valencia Spain (2006).

  25. F. Feroz et al., Bayesian Selection of sign(mu) within mSUGRA in Global Fits Including WMAP5 Results, JHEP 10 (2008) 064 [arXiv:0807.4512] [SPIRES].

    Article  ADS  Google Scholar 

  26. F. Feroz, M.P. Hobson, L. Roszkowski, R. Ruiz de Austri and R. Trotta, Are BR(b → s) and (g − 2) μ consistent within the Constrained MSSM?, arXiv:0903.2487 [SPIRES].

  27. 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] [SPIRES].

    ADS  Google Scholar 

  28. R. Trotta, R.R. de Austri and C.P. d.l. Heros, Prospects for dark matter detection with IceCube in the context of the CMSSM, JCAP 08 (2009) 034 [arXiv:0906.0366] [SPIRES].

    ADS  Google Scholar 

  29. S.S. AbdusSalam, B.C. Allanach, M.J. Dolan, F. Feroz and M.P. Hobson, Selecting a Model of Supersymmetry Breaking Mediation, Phys. Rev. D 80 (2009) 035017 [arXiv:0906.0957] [SPIRES].

    ADS  Google Scholar 

  30. M.E. Cabrera, J.A. Casas and R. Ruiz d Austri, MSSM Forecast for the LHC, JHEP 05 (2010) 043 [arXiv:0911.4686] [SPIRES].

    Article  ADS  Google Scholar 

  31. G. Bertone, D.G. Cerdeno, M. Fornasa, R.R. de Austri and R. Trotta, Identification of Dark Matter particles with LHC and direct detection data, Phys. Rev. D 82 (2010) 055008 [arXiv:1005.4280] [SPIRES].

    ADS  Google Scholar 

  32. P. Scott et al., Direct Constraints on Minimal Supersymmetry from Fermi-LAT Observations of the Dwarf Galaxy Segue 1, JCAP 01 (2010) 031 [arXiv:0909.3300] [SPIRES].

    ADS  Google Scholar 

  33. D.E. Lopez-Fogliani, L. Roszkowski, R.R. de Austri and T.A. Varley, A Bayesian Analysis of the Constrained NMSSM, Phys. Rev. D 80 (2009) 095013 [arXiv:0906.4911] [SPIRES].

    ADS  Google Scholar 

  34. L. Roszkowski, R. Ruiz de Austri and R. Trotta, Efficient reconstruction of CMSSM parameters from LHC data: A case study, Phys. Rev. D 82 (2010) 055003 [arXiv:0907.0594] [SPIRES].

    ADS  Google Scholar 

  35. R. Lafaye, T. Plehn, M. Rauch and D. Zerwas, Measuring Supersymmetry, Eur. Phys. J. C 54 (2008) 617 [arXiv:0709.3985] [SPIRES].

    Article  ADS  Google Scholar 

  36. Y. Akrami, P. Scott, J. Edsjo, J. Conrad and L. Bergstrom, A Profile Likelihood Analysis of the Constrained MSSM with Genetic Algorithms, JHEP 04 (2010) 057 [arXiv:0910.3950] [SPIRES].

    Article  ADS  Google Scholar 

  37. N. Reid, R. Mukerjee and D.A.S. Fraser, Some aspects of matching priors, in Mathematical statistics and applications: Festschrift for Constance van Eeden, M. Moore, S. Froda and C. Léger eds., Beachwood U.S.A. (2003), pp. 31–43, http://projecteuclid.org/euclid.lnms/1215091929.

  38. H.P.L. Lyons and A. de Roeck, Some aspects of matching priors, in Proceedings of the PHYSTAT LHC Workshop on Statistical Issues for LHC Physics, CERN, Geneva Switzerland, 27-29 June 2007, CERN Yellow Report 2008-001, 2008.

  39. T. Auld, M. Bridges, M.P. Hobson and S.F. Gull, Fast cosmological parameter estimation using neural networks, Mon. Not. Roy. Astron. Soc. Lett. 376 (2007) L11 [astro-ph/0608174] [SPIRES].

    Article  ADS  Google Scholar 

  40. R. Trotta, Bayes in the sky: Bayesian inference and model selection in cosmology, Contemp. Phys. 49 (2008) 71 [arXiv:0803.4089] [SPIRES].

    Article  ADS  Google Scholar 

  41. B.C. Allanach, S. Kraml and W. Porod, Theoretical uncertainties in sparticle mass predictions from computational tools, JHEP 03 (2003) 016 [hep-ph/0302102] [SPIRES].

    Article  ADS  Google Scholar 

  42. B.C. Allanach, SOFTSUSY: a program for calculating supersymmetric spectra, Comput. Phys. Commun. 143 (2002) 305 [hep-ph/0104145] [SPIRES].

    Article  ADS  MATH  Google Scholar 

  43. D.E. Rumelhart, G.E. Hilton and R. Williams, Learning representations by backpropagating errors, Nature 323 (1986) 533.

    Article  ADS  Google Scholar 

  44. J.C. Mason and M.G. Cox, Radial basis functions for multivariate interpolation: a review, in In Algorithms for Approximation, Clarendon Press, U.K. (1987) pp. 143–167.

    Google Scholar 

  45. V. Vapnik, The Nature of Statistical Learning Theory, Springer, New York USA (1995).

    MATH  Google Scholar 

  46. R.O.L. Breiman, J.H. Friedman and C. Stone, Classification and Regression Trees, Wadsworth, Belmont U.S.A. (1983).

    Google Scholar 

  47. D.E. Rumelhart, G. Hilton and R. Williams, Learning representations by backpropagating errors, MIT Press, Cambridge MA U.S.A. (1986).

    Google Scholar 

  48. G. Cybenko, Approximations by superpositions of sigmoidal functions, Mathematics of Control, Signals, and Systems 4 (2001) 303.

    Google Scholar 

  49. A.P.M. Leshno, V.Ya. Lin, A. Pinkus and S. Schocken, Multilayer Feedforward Networks With a Nonpolynomial Activation Function Can Approximate Any Function, Neural Netw. 6 (1993) 861.

    Article  Google Scholar 

  50. A. Bryson and Y. Ho, Applied optimal control: optimization, estimation, and control, Blaisdell Publishing Company, New York U.S.A. (1969).

    Google Scholar 

  51. D. MacKay, Bayesian Methods for Adaptive Models, California Institute of Technology, Pasadena U.S.A. (1992).

    Google Scholar 

  52. M. Hobson and A. Lasenby, The entropic prior for distributions with positive and negative values, Mon. Not. R. Astr. Soc. 298 (1998) 905 [astro-ph/9810240] [SPIRES].

    Article  ADS  Google Scholar 

  53. S. Gull and J. Skilling, Quantified maximum entropy: MemSys 5 users’ manual, Maximum Entropy Data Consultants Ltd, Royston U.K. (1999).

    Google Scholar 

  54. The ATLAS collaboration, G. Aad et al., Expected Performance of the ATLAS Experiment - Detector, Trigger and Physics, arXiv:0901.0512 [SPIRES].

  55. S. Wilks, The large-sample distribution of the likelihood ratio for testing composite hypotheses, Ann. Math. Statist. 9 (1938) 60.

    Article  MATH  Google Scholar 

  56. Y. Akrami, C. Savage, P. Scott, J. Conrad and J. Edsjö, Statistical coverage for supersymmetric parameter estimation: a case study with direct detection of dark matter, private communication.

  57. L. Moneta et al., The RooStats Project, proceedings of the 13th International Workshop on Advanced Computing and Analysis Techniques in Physics Research, India Jaipur (2010) [arXiv:1009.1003] [SPIRES].

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Authors and Affiliations

  1. Astrophysics Group, Cavendish Laboratory, University of Cambridge, J.J. Thomson Avenue, Cambridge, CB3 0HE, U.K.

    Michael Bridges, Farhan Feroz & Mike Hobson

  2. Center for Cosmology and Particle Physics, New York University, Washington Place, New York, NY, 10003, U.S.A.

    Kyle Cranmer

  3. Instituto de Física Corpuscular, IFIC-UV/CSIC, Valencia, Spain

    Roberto Ruiz de Austri

  4. Astrophysics Group, Imperial College London, Blackett Laboratory, Prince Consort Rd, London, SW7 2AZ, U.K.

    Roberto Trotta

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  1. Michael Bridges
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Correspondence to Roberto Trotta.

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Bridges, M., Cranmer, K., Feroz, F. et al. A coverage study of the CMSSM based on ATLAS sensitivity using fast neural networks techniques. J. High Energ. Phys. 2011, 12 (2011). https://doi.org/10.1007/JHEP03(2011)012

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