Peter Athron David Miller In collaboration with Fine Tuning

 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)

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

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

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!

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

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

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

Standard Model Obtain over whole parameter range:

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

Tuning

Tuning in

“Natural” Point 1

“Natural” Point 2

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

 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

Tuning in

Tuning

m 1/2 (GeV)

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:

For example... MSUGRA benchmark point SPS1a: ALL

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

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

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?

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