The Search For Supersymmetry Liam Malone and Matthew French

Supersymmetry A 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 N 2 -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:

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:

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:

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  M 1/2 the mass that the gauginos unify at.  M 0 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 m 1/2 =250 GeV, m 0 = 100 GeV, tan β= 3, A 0 =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.

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 years.  Current best guess is greater than 5.5×10 32 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.

Supersymmetry Experimental 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: 

Convergence of Coupling Constants 2 Source: Kazakov, D I; arxiv.org/hep-ph/

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

WMAP 1 Source:

WMAP 2 Source:

WMAP 3  73% dark matter in universe  Total matter density   Improves prospect of discovery at LHC  Within reach of 1TeV linear collider 

WMAP 4 Adapted from: J. Ellis et al, Phys, Lett B 565,

Anomalous Muon Magnetic Moment  Experiment  Dirac theory:  QED corrections: virtual particles  Deviation from SM of

Anomalous Muon Magnetic Moment 2

Anomalous Muon Magnetic Moment 3 Source:

Who is looking for SUSY particles?  LEP  Tevatron  LHC – from 2007?  ILC  Currently no experimental evidence found  Can only constrain models

LEP Source:

LEP Source:

s-fermion searches  Production  Decay  Events with missing energy 

LEP Results 1  sleptons: selectron, smuon, stau  Decay of sleptons   Mass of s-lepton depends on mass of neutralino

LEP Results 2 Source: LEP2 SUSY Working Group

LEP Results 3 s-lepton lower mass limit neutralino mass selectron99.9 GeV0 GeV 99.9 GeV40 GeV smuon94.9 GeV0 GeV 96.6 GeV40 GeV stau86.6 GeV0 GeV 92.6 GeV40 Gev Source: LEP2 SUSY Working Group

LEP Results 4 Source: LEP2 SUSY Working Group

Tevatron Source:

Tevatron Source:

Tevatron Results 1  CDF & D0  Searches for bottom squarks  Photon + missing energy searches  Search for R-parity violation

Tevatron Results 2 Source:

LHC  Starting 2007  14TeV proton-proton collider  ATLAS & CMS

ATLAS Source:

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 Source: SUSY at ATLAS talk, Frank Paige

CMS Source:

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

If SUSY is not Found

Summary SUSY Particle Masses Source: Particle Date Group:

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