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Peter Athron David Miller In collaboration with Fine Tuning

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

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Little Hierarchy Problem Constrained Minimal Supersymmetric Standard Model (CMSSM) Z boson mass predicted from CMSSM parameters Fine tuning? Only low mass SUSY avoids fine tuning SM masses sensitive to SUSY masses

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R. Barbieri & G.F. Giudice, (1988) Define Tuning is fine tuned % change in from 1% change in Observable Parameter Traditional Measure

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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 Global Sensitivity G. W. Anderson & D.J Castano (1995) Consider: All points are tuned?All points are special, atypical scenarios? True tuning must be quantified with a normalised measure No unnatural cancellation!

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

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parameter space volume restricted by, Parameter space point, Unnormalised Tuning: New Measure Tuning: mean value `` Compare dimensionless variations in ALL parameters With dimensionless variations in ALL observables Remove Global Sensitivity

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Probability of random point lying in : Probability of a point lying in a “typical” volume: New Measure Define: We measure the relative improbability! volume with physical scenarios qualitatively “similar” to point P

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Standard Model Obtain over whole parameter range:

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Large numbers of observables and parameters Numerical Approach Choose a point P in the parameter space. Take random fluctuations about this point. Count how many points are in and Apply tuning measure Fine Tuning in the CMSSM

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Tuning

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Tuning in

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“Natural” Point 1

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“Natural” Point 2

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If we normalise with NP1If we normalise with NP2 Tunings for the points shown in plots are:

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Fine Tuning in the SM SUSY CMSSM appears fine tuned in Little Hierarchy Problem New measure considers how: all observables restrict space formed by all parameters in comparison to “typical” (global sensitivity) CMSSM may not be fine tuned Conclusions

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Tuning in

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Tuning

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m 1/2 (GeV)

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For our study of tuning in the CMSSM we chose a grid of points: Plots showing tuning variation in m 1/2 were obtained by taking the average tuning for each m 1/2 over all m 0. Plots showing tuning variation in m 0 were obtained by taking the average tuning for each m 0 over all m 1/2. Technical Aside To reduce statistical errors:

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For example... MSUGRA benchmark point SPS1a: ALL

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Supersymmetry The only possible extension to space-time Unifies gauge couplings Provides Dark Matter candidates Leptogenesis in the early universe Elegant solution to the Hierarchy Problem! Essential ingredient for M-Theory

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Beyond the Standard Model Physics Technicolor Large Extra Dimensions Little Higgs Twin Higgs Supersymmetry

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Superymmetry Models with extended Higgs sectors NMSSM nMSSM ESSM 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. Solutions?

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

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