Peter Athron

David Miller

In collaboration with

Quantifying Fine Tuning (arXiv:0705.2241)

Outline

Motivations for supersymmetry Hierarchy problem

Little Hierarchy Problem Traditional Tuning Measure New tuning measure ESSM

EWSB in the ESSM

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

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?

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.

Solutions?

J.R. Ellis, K. Enqvist, D.V. Nanopoulas, & F.Zwirner (1986)

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.

Implicitly assumes a uniform distribution of parameters

Parameters in LGUT may be different to those in LSUSY

parameters drawn from a different probability distribution

Takes infinitesimal variations in the parameters

Observables may look stable (unstable) locally, but unstable (stable) over finite variations in the parameters.

Considers only one observable

Theories may contain tunings in several observables

Global Sensitivity (discussed later)

parameter space volume restricted by,

Parameter space point,

Unnormalised Tuning:

New Measure

`` ``

Compare dimensionless variations in ALL parameters

With dimensionless variations in ALL observables

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

parameter space volume restricted by,

Parameter space point,

Unnormalised Tunings

New Measure

Normalised Tunings

mean value

`` ``

`` `` AND

Probability of random point lying in :

Probability of a point lying in a “typical” volume:

New Measure

Define:

We can associate our tuning measure with relative improbability!

volume with physical scenarios qualitatively “similar” to point P

Standard Model

Obtain over whole parameter range:

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

Fine Tuning in the CMSSM

For our study of tuning in the CMSSM we chose a grid of points:

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.

Technical Aside

To reduce statistical errors:

Tuning in

Tuning in

Tuning

Tuning

m1/2(GeV)

m1/2(GeV)

“Natural” Point 1

“Natural” Point 2

If we normalise with NP1 If we normalise with NP2

Tunings for the points shown in plots are:

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;

Probability dist. of parameters;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.

Fine Tuning Summary

Electroweak Symmetry Breaking in the E6SSM

Peter AthronIn collaboration with

S.F. King, D.J. Miller, S. Moretti & R. Nevzorov.

Exceptional Supersymmetric Standard Model (Phys.Rev. D73 (2006) 035009 arXiv:hep-ph/0510419 , Phys.Lett. B634 (2006)

278-284 arXiv:hep-ph/0511256 S.F.King, S.Moretti & R. Nevzorov)

Exotic coloured matter

3 generations of Singlet fields

Ordinary matter

E6 inspired model with an extra gauged U(1) symmetry

Matter content based on 3 generations of complete 27plet representations of E6 ) anomalies automatically cancelled

Provides a low energy alternative to the MSSM and NMSSM

3 generations of Higgs like fields

Extra SU(2) doublets(for gauge coupling unification)

E6SSM Superpotential

S = S3 develops vev, hSi = s, giving mass to exotic coloured fields

Hu = H2,3 & Hd = H1,3 develop vevs, hH0ui=vu &

hH0di=vd Give mass to ordinary matter via Higgs

Mechanism

generates an effective term

Solves -problem of MSSM as in NMSSM without tadpoles/domain walls problems

ESSMNMSSMMSSM

Two Loop Upper Bounds on the Light Higgs

NUHESSM GUT-scale universality assumptions

Highscale mass for all other scalar fields

Highscale mass for three generations of Singlet fields

Highscale mass for three generations of H2 fields

Highscale mass for three generations of H1 fields

Universal Gaugino MassUniversal trilinear soft mass

Minimal supergravity inspired GUT-scale constraints on parameters

EWSB constraints

Scalar masses

Gaugino massesTrilinear soft masses

Solutions must possess symmetry

Obtain RGE solutions for soft masses at EW scale

Fix v2 = vu2 + vd

2 = (174 GeV)2

Choose Yukawas 3=0.6; 1,2=0.46; 1,2,3=0.162

Choose tan = vu/vd = 10, s = 3 TeV

EWSB constraintsAllowed

EW tachyons

GUT tachyons Experimentally ruled out

Sample Spectrum

Conclusions Solutions with all universal masses are hard to find. Allow non universal Higgs masses. Dramatic improvement! Many spectrums which could be seen at the LHC. RGE solutions ) Gluino often lighter than the squarks Further work:

Include two loop RGEs for gaugino masses Look for solutions with stronger universality assumptions

1 loop RGE solutions for fully universal benchmark point