The Search For Supersymmetry

Liam Malone and Matthew French

SupersymmetryA Theoretical View

Introduction

Why do we need a new theory? How does Supersymmetry work? Why is Supersymmetry so popular? What evidence has been found?

The Standard Model

6 Quarks and 6 Leptons.

Associated Anti-Particles.

4 Forces – but only successfully describes three.

Symmetries and Group Theory

Each force has an associated symmetry. This can be described by a group. The group SU(N) has N2-1 parameters. These parameters can be seen as the amount of

mass-less bosons required to mediate the force. Ideally the standard model is a

SU(3)×SU(2)×U(1) model.

Weak Force

Weak force is very short range due to its massive bosons.

Have difficulty adding massive bosons and keeping the gauge invariance of the theory.

Yet scalar bosons are proposed. Some other process is taking place.

The Higgs Mechanism

Higgs mechanism solves this problem. Uses SPONTANEOUS SYMMETRY

BREAKING. Mix the SU(2) and U(1) symmetry into one

theory. Creates three massive bosons for the weak

force, the Higgs and the mass-less photon.

Renormalisation

Used to calculate physical quantities like the coupling constants of each force or the mass of a particle.

Sum over all interactions. Have to use momentum cut-off. Results in the quantity being dependant on

the energy scale it is measured on.

The Hierarchy Problem

Renormalizing fermion masses gives contributions from:

Renormalising the Higgs mass gives contributions from:

2

2

ln4

3~

fff m

Lm

π

αdm

)4

(~ 22 Lπ

αOdm

H

Other Problems with the Standard Model

No one knows why the electroweak symmetry is broken at this scale.

Why are the three forces strengths so different?

Why the 21 seemingly arbitrary parameters?

History of Supersymmetry

First developed by two groups, one in USSR and one in USA.

Gol’fund and Likhtmann were investigating space-time symmetries in the USSR.

Pierre Ramond and John Schwarz were trying to add fermions to boson string theory in the USA.

Supersymmetry

In renormalisation fermion terms and boson terms have different signs.

Therefore a fermion with the same charge and mass a boson will have equal and opposite contributions.

The basis of supersymmetry – every particle has a super partner of the opposite type.

Supersymmetry

In Quantum Mechanics this could be written as:

The operator Q changes particle type. Q has to commute with the Hamiltonian because

of the symmetry involved:

| |

| |

Q fermion boson

Q boson fermion

[ , ] 0Q H

Supersymmetry

The renormalised scalar mass now has the contributions from two particles:

2 2 2 2 2 2 2~ ( )( ) - ( )( ) ( )( - )4 4 4H B F B Fdm O L m O L m O m m

The only thing that this requires is the stability of the weak scale:

222 1- TeVmm FB

Constraints on SUSY

124 parameters required for all SUSY models.

However some phenomenological constraints exist.

These mean some SUSY models are already ruled out.

Minimal Supersymmetric Standard Model

In supersymmetry no restrictions are placed on the amount of new particles.

Normally restrict the amount of particles to least amount required.

This is the Minimal Supersymmetric Standard Model (MSSM).

MSSM

All particles gain one partner.

Gauge bosons have Gauginos: E.g The Higgs has the Higgsinos.

Fermions have Sfermions: E.g Electron has Selectron and Up quark has the

Sup.

Constrained MSSM

A subset of the MSSM parameter space.

Assumes mass unification at a GUT scale.

This gives only five parameters to consider.

The Five Parameters

M1/2 the mass that the gauginos unify at.

M0 the mass at which the sfermions unify at. Tan β is the ratio of the vacuum values of the

two Higgs bosons. A0 is the scalar trilinear interaction strength. The sign of the Higgs doublet mixing

parameter.

Figure showing the mass unification at grand scales. The five parameters m1/2=250 GeV, m0 = 100 GeV, tan β= 3, A0=0 and μ>0.

Local or Global?

Supersymmetry could be local or global symmetry.

Local symmetries are like the current standard model.

If SUSY is global has implications on symmetry breaking mechanisms.

SUSY Breaking

SUSY has to be broken between current experiment scales and Planck scale.

Natural to try and add in Higgs mechanism but this reintroduces Hierarchy problem.

Two possible ways: Gravity Interactions of the current gauge fields and the

superpartners

Gravity mediated breaking

In super gravity get graviton and gravitino.

Gravitino acquires mass when SUSY is broken.

If gravity mediates the breaking, LSP is the neutalino or sneutrino.

Gauge Mediated Breaking

If SM gauge fields mediate the SUSY breaking then SUSY is broken a lower scale.

Gravitino therefore has a very small mass and is the LSP.

Other Models do exist.

R-Parity Conservation

R-parity is a new quantity defined by:

All SM particles have R-parity 1 but all super partners have -1.

It is this that makes the LSP stable.

SLBR 2)-(31-

Dark Matter

Cosmologists believe most matter is dark matter.

Inferred this from observing motions of galaxys.

No one’s sure what it is.

Dark Matter

If R-parity is conserved then the Lightest Super Partner (LSP) will be stable.

Could explain the Dark Matter in the universe.

Depends on SUSY parameters whether the LSP is a gaugino or a sfermion.

Which LSP?

Graph showing regions of different LSP’s.Tan β =2

Proton Decay

The best GUT prediction is 1028 years.

Current best guess is greater than 5.5×1032

years.

SUSY can be used to fix this problem.

Other Advantages of SUSY

Grand Unified Theories (GUTs). Current understanding is just a low energy

approximation to some grand theory. On a large energy scale all forces and

particles should essentially be the same. Coupling constants should equate at high

energy.

Figure (a): Coupling constants in the standard model

Figure (b): Coupling constants a GUT based on SUSY

Possible GUTs

The main competitor is a theory based on SU(5) symmetry.

Has 24 gauge bosons mediating a single force.

Others as well like one on SO(10) with 45 bosons!

Conclusions

The Standard Model has problems when considered above the electroweak scale.

Supersymmetry solves some of these problems.

Supersymmetry can also be used to explain cosmological phenomena.

SupersymmetryExperimental Issues and

Developments

Outline

Motivation for SUSY (continued) Detecting SUSY Current and future searches Results & constraints so far

Motivation for SUSY

Convergence of coupling constants Proton lifetime Dark matter (LSP) Anomalous muon magnetic moment Mass hierarchy problem

Convergence of Coupling Constants 1

In a GUT coupling constants meet at high energy

GUT gauge group must be able to contain SU(3)xSU(2)xU(1)

SU(5) best candidate Three constants:

21 5 /(3cos )W

22 / sin W

23 /(4 )sg

Convergence of Coupling Constants 2

Sou

rce:

Kaz

akov

, D I

; arx

iv.o

rg/h

ep-p

h/00

1228

8

Dark Matter

A leading candidate is the LSP SM has R=1 & SUSY has R=-1 Conservation of R-parity R-parity conservation ensures SUSY

particles only decay to other SUSY particles so LSP is stable

3( ) 2( 1) B L SR

WMAP 1

Sou

rce:

http

://m

ap.g

sfc.

nasa

.gov

WMAP 2

Sou

rce:

http

://m

ap.g

sfc.

nasa

.gov

WMAP 3

73% dark matter in universe Total matter density Improves prospect of discovery at LHC Within reach of 1TeV linear collider

2 0.01610.01810.1126CDMh

400 500m GeV

2

1

tan

WMAP 4

Adapted from: J. Ellis et al, Phys, Lett B 565, 176-182

Anomalous Muon Magnetic Moment

Experiment

Dirac theory:

QED corrections: virtual particles Deviation from SM of

1.00116592032muon

e

m

h

1.6 2.6

12muon

e

m

h

Anomalous Muon Magnetic Moment 2

Anomalous Muon Magnetic Moment 3

Sou

rce:

http

://ar

xiv.

org/

hep-

ex/0

4010

08

Who is looking for SUSY particles?

LEP Tevatron LHC – from 2007? ILC

Currently no experimental evidence found Can only constrain models

LEP

Sou

rce:

http

://in

tran

et.c

ern.

ch/P

ress

/Pho

toD

atab

ase/

LEP

Sou

rce:

http

://in

tran

et.c

ern.

ch/P

ress

/Pho

toD

atab

ase/

s-fermion searches

Production

Decay

Events with missing energy ~ 0

1fM m m

LEP Results 1

sleptons: selectron, smuon, stau Decay of sleptons Mass of s-lepton depends on mass of

neutralino

~

1R ll

LEP Results 2

Sou

rce:

LE

P2

SU

SY

Wor

king

Gro

up

LEP Results 3

s-lepton lower mass limit

neutralino mass

selectron 99.9 GeV 0 GeV

99.9 GeV 40 GeV

smuon 94.9 GeV 0 GeV

96.6 GeV 40 GeV

stau 86.6 GeV 0 GeV

92.6 GeV 40 Gev

Source: LEP2 SUSY Working Group

LEP Results 4

Sou

rce:

LE

P2

SU

SY

Wor

king

Gro

up

Tevatron

Sou

rce:

ww

w.f

nal.g

ov/p

ub/p

ress

pass

/vis

med

ia/in

dex.

htm

l

Tevatron

Sou

rce:

ww

w.f

nal.g

ov/p

ub/p

ress

pass

/vis

med

ia/in

dex.

htm

l

Tevatron Results 1

CDF & D0 Searches for bottom squarks

Photon + missing energy searches

Search for R-parity violation

NLSP LSP

01b b % %

Tevatron Results 2

Sou

rce:

htt

p://

ww

w.d

pf99

.libr

ary.

ucla

.edu

/ses

sion

7/H

ED

IN07

09.P

DF

LHC

Starting 2007 14TeV proton-proton collider ATLAS & CMS

ATLAS

Sou

rce:

http

://at

las.

ch

SUSY at ATLAS

Assuming MSSM & R-parity conservation SUSY production at LHC dominated by

gluino and squark production Decay signature is distinctive cf SM Large missing energy & multiple jets

SUSY at ATLAS 2

Sou

rce:

SU

SY

at A

TL

AS

talk

, Fra

nk P

aige

CMS

Source: http://cmsinfo.cern.ch

ILC

International linear collider Election-positron

Large electron polarisation Clean beams Beam energy can be tuned

Verifying SUSY at ILC

Pair production Precise study: mass, spin, coupling, mixing Look of SUSY breaking mechanism

Highly polarised source means background can be reduced to ~0

Mass and Spin

SUSY: and

Electron :: spin ½ :: light Selectron :: spin 0 :: heavy

Higgs :: spin 0 :: heavy Higgsino :: spin ½ :: light

0 0 0, , , ,h H H H A 0 0 0, , , ,h H H H A % %% % %

If SUSY is not Found

Summary SUSY Particle Masses

46m GeV01%02%03%

62.4m GeV

99.9m GeV

1 % 94m GeV

Source: Particle Date Group: http://pdg.lbl.gov/2004/tables/sxxx.pdf

e%%%

73m GeV

94m GeV

81.9m GeV

q%b%

t%

250m GeV

89m GeV

95.7m GeV

Summary

WMAP, LEP, Tevatron have placed limits If SUSY exists LHC expected to find it ILC – detailed examination of SUSY

particles