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. • 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.

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 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.

20. 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.

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 one’s 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 LSP’s. Tan β =2

29. 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.

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 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

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/PhotoDatabase/

49. LEP Source: http://intranet.cern.ch/Press/PhotoDatabase/

50. s-fermion searches • Production • Decay • Events with missing energy