The Search For Supersymmetry

1
The Search For Supersymmetry
Liam Malone and Matthew French
2
SupersymmetryA Theoretical View
3
Introduction

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

4
The Standard Model

• 6 Quarks and 6 Leptons.
• Associated Anti-Particles.
• 4 Forces but only successfully describes three.

5
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.

6
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.

7
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.

8
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.

9
The Hierarchy Problem

• Renormalizing fermion masses gives contributions
  from
• Renormalising the Higgs mass gives contributions
  from

10
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?

11
History of Supersymmetry

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

12
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.

13
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

14
Supersymmetry

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

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

15
Constraints on SUSY

• 124 parameters required for all SUSY models.
• However some phenomenological constraints exist.
• These mean some SUSY models are already ruled out.

16
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).

17
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.

18
Constrained MSSM

• A subset of the MSSM parameter space.
• Assumes mass unification at a GUT scale.
• This gives only five parameters to consider.

19
The Five Parameters

• M1/2 the mass that the gauginos unify at.
• M0 the mass at which the sfermions unify at.
• Tan ß 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.

20
Figure showing the mass unification at grand
scales. The five parameters m1/2250 GeV, m0
100 GeV, tan ß 3, A00 and µgt0.
21
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.

22
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

23
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.

24
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.

25
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.

26
Dark Matter

• Cosmologists believe most matter is dark matter.
• Inferred this from observing motions of galaxys.
• No ones sure what it is.

27
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.

28
Which LSP?
Graph showing regions of different LSPs. Tan ß 2
29
Proton Decay

• The best GUT prediction is 1028 years.
• Current best guess is greater than 5.51032
  years.
• SUSY can be used to fix this problem.

30
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.

31
Figure (a) Coupling constants in the standard
model
Figure (b) Coupling constants a GUT based on SUSY
32
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!

33
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.

34
SupersymmetryExperimental Issues and Developments
35
Outline

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

36
Motivation for SUSY

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

37
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

38
Convergence of Coupling Constants 2
Source Kazakov, D I arxiv.org/hep-ph/0012288
39
Dark Matter

• A leading candidate is the LSP
• SM has R1 SUSY has R-1
• Conservation of R-parity
• R-parity conservation ensures SUSY particles only
  decay to other SUSY particles so LSP is stable

40
WMAP 1
Source http//map.gsfc.nasa.gov
41
WMAP 2
Source http//map.gsfc.nasa.gov
42
WMAP 3

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

43
WMAP 4
Adapted from J. Ellis et al, Phys, Lett B 565,
176-182
44
Anomalous Muon Magnetic Moment

• Experiment
• Dirac theory
• QED corrections virtual particles
• Deviation from SM of

45
Anomalous Muon Magnetic Moment 2
46
Anomalous Muon Magnetic Moment 3
Source http//arxiv.org/hep-ex/0401008
47
Who is looking for SUSY particles?

• LEP
• Tevatron
• LHC from 2007?
• ILC
• Currently no experimental evidence found
• Can only constrain models

48
LEP
Source http//intranet.cern.ch/Press/PhotoDatabas
e/
49
LEP
Source http//intranet.cern.ch/Press/PhotoDatabas
e/
50
s-fermion searches

• Production
• Decay
• Events with missing energy

51
LEP Results 1

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

52
LEP Results 2
Source LEP2 SUSY Working Group
53
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
54
LEP Results 4
Source LEP2 SUSY Working Group
55
Tevatron
Source www.fnal.gov/pub/presspass/vismedia/index.
html
56
Tevatron
Source www.fnal.gov/pub/presspass/vismedia/index.
html
57
Tevatron Results 1

• CDF D0
• Searches for bottom squarks
• Photon missing energy searches
• Search for R-parity violation

58
Tevatron Results 2
Source http//www.dpf99.library.ucla.edu/session7
/HEDIN0709.PDF
59
LHC

• Starting 2007
• 14TeV proton-proton collider
• ATLAS CMS

60
ATLAS
Source http//atlas.ch
61
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

62
SUSY at ATLAS 2
Source SUSY at ATLAS talk, Frank Paige
63
CMS
Source http//cmsinfo.cern.ch
64
ILC

• International linear collider
• Election-positron
• Large electron polarisation
• Clean beams
• Beam energy can be tuned

65
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

66
Mass and Spin

• SUSY and
• Electron spin ½ light
• Selectron spin 0 heavy
• Higgs spin 0 heavy
• Higgsino spin ½ light

67
If SUSY is not Found
68
Summary SUSY Particle Masses






Source Particle Date Group http//pdg.lbl.gov/20
04/tables/sxxx.pdf
69
Summary

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