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Peter Athron

Quantifying Fine Tuning ( arXiv:0705.2241, Phys.Rev.D76:075010, 2007. arXiv:0707.1255 [hep-ph], AIP Conf.Proc.903:373-376,2007 . arXiv:0710.2486  [hep-ph] ). Peter Athron. In collaboration with. David Miller. Outline. Motivations for supersymmetry Hierarchy problem

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Peter Athron

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  1. Quantifying Fine Tuning (arXiv:0705.2241, Phys.Rev.D76:075010, 2007. arXiv:0707.1255 [hep-ph], AIP Conf.Proc.903:373-376,2007. arXiv:0710.2486 [hep-ph] ) Peter Athron In collaboration with David Miller

  2. Outline • Motivations for supersymmetry • Hierarchy problem • Little Hierarchy Problem (of Susy) • Traditional Tuning Measure • New tuning measure • Applications • SM • Toy model • MSSM

  3. Supersymmetry • Only possible extension to Poincare symmetry • Unifies gauge couplings • Provides Dark Matter candidates • Leptogenesis in the early universe • Essential ingredient for M-Theory • Elegant solution to the Hierarchy Problem!

  4. Hierarchy Problem • Standard Model (SM) of particle physics • Beautiful description of Electromagnetic, Weak and Strong forces • Neglects gravitation, very weak at low energies (large distances) • Expect New Physics at Planck Energy (Mass) • Higgs mass sensitive to this scale Enormous Fine tuning! • Supersymmetry (SUSY) removes quadratic dependence • Eliminates fine tuning SUSY?

  5. Little Hierarchy Problem • Constrained Minimal Supersymmetric Standard Model (CMSSM) • Z boson mass predicted from CMSSM parameters Fine tuning?

  6. Solutions? • Superymmetry Models with extended Higgs sectors • NMSSM • nMSSM • E6SSM • Supersymmetry Plus • Little Higgs • Twin Higgs • Alternative solutions to the Hierarchy Problem • Technicolor • Large Extra Dimensions • Little Higgs • Twin Higgs • Need a reliable, quantitative measure of fine tuning to judge the success of these approaches.

  7. Traditional Measure Observable • J.R. Ellis, K. Enqvist, D.V. Nanopoulas, & F.Zwirner (1986) • R. Barbieri & G.F. Giudice, (1988) DefineTuning Parameter % change in from 1% change in is fine tuned • J. A. Casas, J. R. Espinosa and I. Hidalgo (2004)

  8. Limitations of the Traditional Measure • Considers each parameter separately • Fine tuning is about cancellations between parameters . • A good fine tuning measure considers all parameters together. • Considers only one observable • Theories may contain tunings in several observables • Takes infinitesimal variations in the parameters • Observables may look stable (unstable) locally, but unstable (stable) over finite variations in the parameters. • Implicitly assumes a uniform distribution of parameters • Parameters in LGUT may be different to those in LSUSY • parameters drawn from a different probability distribution • Global Sensitivity (discussed later)

  9. New Measure Parameter space point, parameter spacevolume restricted by, `` `` Compare dimensionless variations in ALL parameters With dimensionless variations in ALL observables Unnormalised Tuning:

  10. G. W. Anderson & D.J Castano (1995) Consider: • Global Sensitivity All values of appear equally tuned! All are atypical? responds sensitively to throughout the whole parameter space (globally) Only relative sensitivity between different points indicates atypical values of True tuning must be quantified with a normalised measure

  11. New Measure Parameter space point, parameter spacevolume restricted by, `` `` `` `` AND Unnormalised Tunings Normalised Tunings mean value

  12. New Measure volume with physical scenarios qualitatively “similar” to point P Probability of random point lying in : Probability of a point lying in a “typical” volume: Define: We can associate our tuning measure with relative improbability!

  13. Standard Model Obtain over whole parameter range:

  14. Four observables, three parameters Large cancellations ) fine tuning

  15. Fine Tuning in the CMSSM • Choose a point P in the parameter space at GUT scale • Take random fluctuations about this point. • Using a modified version of Softsusy (B.C. Allanach) • Run to Electro-Weak Symmetry Breaking scale. • Predict Mz and sparticle masses • Count how many points are in F and in G. • Apply fine tuning measure

  16. Tuning in

  17. Tuning in

  18. Tuning

  19. Tuning

  20. m1/2(GeV)

  21. m1/2(GeV)

  22. “Natural” Point 1

  23. “Natural” Point 2

  24. If we normalise with NP1 If we normalise with NP2 Tunings for the points shown in plots are:

  25. Fine Tuning Summary • Probability dist. of parameters; • Naturalness comparisons of BSM models need a reliable tuning measure, but the traditional measure neglects: • Many parameter nature of fine tuning; • Tunings in other observables; • Behaviour over finite variations; • Global Sensitivity. • New measure addresses these issues and: • Demonstrates and increase with . • Naïve interpretation: tuning worse than thought. • Normalisation may dramatically change this. • If we can explain the Little hierarchy Problem. • Alternatively a large may be reduced by changing parameterisation. • Could provide a hint for a GUT.

  26. Technical Aside For our study of tuning in the CMSSM we chose a grid of points: To reduce statistical errors: Plots showing tuning variation in m1/2 were obtained by taking the average tuning for each m1/2 over all m0. Plots showing tuning variation in m0 were obtained by taking the average tuning for each m0 over all m1/2.

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