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Peter Athron
David Miller
In collaboration with
Fine Tuning In Supersymmetric Models
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Overview
Little Hierarchy Problem
Traditional Measure
Define New Measure
Illustrate with SM Hierarchy Problem
Application to MSSM
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MSSM EWSB constraint (Tree Level) :
Sparticle mass limits ) Parameters
But
Little Hierarchy Problem
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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
The fine tuning is about cancellations between parameters . A good fine tuning measure considers all parameters together.
Implicitly assumes a uniform distribution of parameters
Parameters in LGUT may be different to those in LSUSY Corresponds to choosing parameters from a different probability distribution
Takes infinitesimal perturbations about the point
MSSM observables are complicated functions of many parameters. Many small isolated regions of parameter space may give the same value of the observable.
Considers only one observable
Theories may contain tunings in more than one observable
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the volume of parameter space,
the subspace of s.t. the observables
Tuning occurs when variations in dimensionless parameters ) larger variations in dimensionless observables.
Parameter space point,
Tuning is defined as:
New Measure
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SM Revisited
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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 often Mz (and sparticle masses) is ok Apply fine tuning measure
Fine Tuning in the MSSM
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For example . . .
MSUGRA benchmark point SPS1a:
ALL
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If the tuning in the MSSM is fine for flat probability distributions:
Nature is fine tuned.
EWSB by some other mechanism than the Higgs
e.g. Technicolor
The Hierarchy problem is solved other new physics
e.g. Little Higgs, Large Extra Dimensions
Extended Higgs sector SSM’s are favoured e.g. NMSSM, nMSSM, ESSM
The MSSM parameters are not all equally likely.
What probability distribution ameliorates this tuning?
Is there a GUT with this distribution?
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Fine Tuning in the SM SUSY
Broken SUSY appears fine tuned Little Hierarchy Problem Hint for a GUT theory?
Current measures of tuning neglect: Probability distribution of parameters. Many parameter nature of fine tuning Additional tunings in other observables Cancellations a finite distance from point
New measure addresses these issues Demonstrates an increase in tuning with the susy
scale.
Conclusions
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Numerical Approximation
Where is the number of points in space
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+
physical mass = “bare mass” + “loops”
= +
divergent Cut off integral at Planck Scale
Fine tuning
Hierarchy Problem
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Supersymmetry The only possible extension to space-time
Unifies gauge couplings
Provides Dark Matter candidates
Baryogenesis in the early universe
Elegant solution to the Hierarchy Problem!
Essential ingredient for M-Theory
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Bosonic degrees of freedom = Fermionic degrees of freedom.
) Two scalar superpartners for each fermion
In Susy
No Fine Tuning?
Quadratic divergences cancelled!
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MSSM At Tree Level:
Sparticle mass limits ) Parameters
But
Exact Susy Softly Broken Susy
LEP search fruitless!! Lower bounds on sparticles
Fine Tuning reintroduced?
Little Hierarchy Problem