fine tuning

Fine Tuning Standard Model and Beyond

Peter Athron

Dr David MillerIn collaboration with

+

physical mass = “bare mass” + “loops”

= +

divergent Cut off integral at Planck Scale

Fine tuning

Hierarchy Problem

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

Peter Athron

Do i mention Coleman-Mandula theorem on slide?Think carefully about phrasing.

Peter Athron

Do i really mean this. Might sound like I'm claiming susy is a gut. Susy allows running gauge couplings to intersect at at a single point. Could add graph showing couplings unifying

Peter Athron

Is this still true??

Bosonic degrees of freedom = Fermionic degrees of freedom.

) Two scalar superpartners for each fermion

In Susy

No Fine Tuning?

Quadratic divergences cancelled!

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

Peter Athron

Phrase better!!Maybe too long for slide?Just say some of this and display Key Words??

R. Barbieri & G.F. Giudice, (1988)

Define Tuning

is fine tuned

% change in from 1% change in

Observable

Parameter

Traditional Measure

Peter Athron

Actually I've completely forgotten what this means!I should find out and then explain!!

Criticisms of 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.

Peter Athron

Shouldn't I be calling them definitions?

New Measure

the volume of parameter space,

the subspace of s.t. the observable

Tuning occurs when variations in dimensionless parameters ) larger variations in dimensionless observables.

Parameter space point,

Tuning is defined as:

Peter Athron

I think another key difference between our measure and Barbieri and Giudice's is that they take the limit where the variations go to zero. We don't want to do that!. We want the variations to be large so that cancellations are included! If our variations were too large in extent then we might not pick up finetuning as the Observable would move out of the region where experimental cuts in the space lead to the requirement of fine tuning. I.e m_h = 10TeV will be naturally produced by p_i of that scale which are not ruled out!

Peter Athron

Should I keep 'natural' in there

Peter Athron

B&G defined tuning as a function of the observable and a parameter. It was the level of tuning needed for in that parameter, with all others fixed, in order to get the observered value. we define tuning only as a function of the observable and consider how it responds to (uncorrelated) fluctuation in all the parameters

Fine tuning as a function of Higgs Mass Fine tuning as a function of the New Physics scale

SM Revisited

Peter Athron

Edit these so that:You can see them!, The axis are labled clearlyAdd comments explaining them.

Fine Tuning in the MSSM

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 is ok Apply fine tuning measure

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 minimises tuning? Is there a GUT with this distribution?

Also contains tunings

S.F. King, S. Moretti, R. Nevzarov,

hep-ph/0510419, hep-ph/0511256

Conclusions

Fine Tuning in the SM SUSY

Broken SUSY appears fine tuned Little Hierarchy Problem

Current measures of tuning neglect: Probability distribution of parameters. Many parameter nature of fine tuning Cancellations a finite distance from point

New measure addresses these issues Results for MSSM coming soon

Ruled out by experiment

Fine tuning as a function of Higgs Mass

Fine tuning as a function of the New Physics scale

Peter Athron

Edit these so that:You can see them!, The axis are labled clearlyAdd comments explaining them

Numerical Approximation

Where is the number of points in space

Is the Tuning Fine?

Aesthetic question. How much tuning are we prepared to tolerate?

Intuitive physical notion. How do we measure tuning?

fine tuning

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