1. Supersymmetry at HERA Motivation for SUSY Basic SUSY facts Different SUSY models Current limits Sparticle creation at HERA SUSY analyses at ZEUS Future prospects DESY Student Seminar, 14.Nov.2005 Claus Horn

2. SUSY at HERA, 14.Nov.2005 Claus Horn Shortcomings of the Standard Model SM is only low energy approximation, In a fundamental theory all interactions should be unified GUT + gravity What is the origin of mass, Introduction of Higgs boson runs into problems. Cosmological problems 21 parameters – too many! Why three generations ? Why |Q el | = |Q p | ?...

3. SUSY at HERA, 14.Nov.2005 Claus Horn Motivation for Supersymmetry Coleman-Mandula theorem Unification of the forces Solution of the Hierarchy problem Candidates for dark matter Necessary for quantum-gravity

4. SUSY at HERA, 14.Nov.2005 Claus Horn Coleman-Mandula Theorem „In a theory with non-trivial scattering in more than 1+1 dimensions, the only possible conserved quantities that transform as tensors under the Lorentz group are the generators of the Poincare group and scalar quantum numbers.“ SUSY is the only possibel extension of the Poincare group. Our last chance to discover a fundamental space-time symmetry! Tensors fulfill comutation relations Add anti-commutators Graded Lie-algebras „super algebra“ P  : Energy-momentum operator Q: Supercharge

5. SUSY at HERA, 14.Nov.2005 Claus Horn Unification of the Forces Renormalisation Group Equations describe running of the coupling constants due to screening / antiscreening SM MSSM Example: Slope depends on number and masses of particles in the model Miracle!

6. SUSY at HERA, 14.Nov.2005 Claus Horn Solution of the Hierarchy Problem Corrections to the Higgs mass: Contributions of particles are canceled by contribution of their superpartners. SM: MSSM: Cancelation requires fine tuning to 17 orders of magnitude!

7. SUSY at HERA, 14.Nov.2005 Claus Horn For unbroken SUSY: No quantum correction to the Higgs mass (  m H =0). Broken SUSY: “running” Higgs mass superpartners have to be lighter than 1 TeV SUSY exact Q²Q² SUSY particles No SUSY mHmH mhmh SUSY Higgs sector very restricted: m h < 150 GeV Q2Q2

8. SUSY at HERA, 14.Nov.2005 Claus Horn Basic Facts about SUSY Symmetry between fermions and bosons Q|boson> = |fermion> Q + |fermion> = |boson> No superpartners with same masses are observed. SUSY is a borken symmetry. Spontaneous SUSY breaking in SM sector not possible supertrace theorem sum rules between particle and sparticle masses, e.g.: excluded! Hidden sector models

9. SUSY at HERA, 14.Nov.2005 Claus Horn Supermultiplets Chiral supermultiplets: (fermion,sfermion) = (spin ½, spin 0) Vectorial supermultiplet: (gauge boson, gauginos) = (spin 1, spin ½)

10. SUSY at HERA, 14.Nov.2005 Claus Horn Sparticles of the MSSM Neutral gauginos mix to form four neutralinos. Charged gauginos mix to form two charginos. M depends on M 2, tan(  ) and . BRs of  0 and  

11. SUSY at HERA, 14.Nov.2005 Claus Horn Parameters of the MSSM m A : pseudoscalar Higgs boson mass tan(  ) : ratio of VEV of two Higgs doublets  : Higgs mixing parameter M 1, M 2, M 3 : gaugino mass terms All sfermion masses A i : all mixing parameters of squark and slepton sector

12. SUSY at HERA, 14.Nov.2005 Claus Horn SUSY Breaking MSSM does not explain origin of SUSY breaking soft breaking terms are introduced „by hand“ more than 100 free parameters Hidden sector models: mSUGRA, GMSB Flavour problem solved in GMSB model.

13. SUSY at HERA, 14.Nov.2005 Claus Horn minimal SUperGRavity (mSUGRA) Parameter: m 0, m 1/2, A 0, tan(  ), sign(  ) Unified masses at the GUT scale m 0 : common scalar mass m 1/2 : common gaugino mass Unified trilinear couplings = A 0 Radiative EW symmetry breaking Constraints: M(G~)  1 TeV (in AMSB  10 TeV)

14. SUSY at HERA, 14.Nov.2005 Claus Horn Gauge Mediated SUSY Breaking (GMSB) Possible NLSPs: neutralino, stau LSP (in not-yet excluded parameter space) is always gravitino Distinct event signature: photon/tau + missing energy Gravitino might be candidate for dark matter even in RPV models. Gravitino can be very light: Parameter: , sqrt(F), M mess, N, tan(  ), sign(  ) Very predictive mass spectrum, easy to distinguish from SUGRA.

15. SUSY at HERA, 14.Nov.2005 Claus Horn Typical Mass Spectra Neutralino 1 is light(est) Next: right-handed slepton (stau) & chargino 1 Squarks are relatively heavy

16. SUSY at HERA, 14.Nov.2005 Claus Horn R-parity Multiplicative discrete symmetry: R P =(-1) 3B+L+2S +1 for SM particles -1 for sparticles Most general Lagrangian contains additional trilinear terms in superpotential which violate R P : HERA is the ideal place to look for ‘ ! (Proton decay only if ‘ and ‘‘ are  0 at the same time.) RPC: sparticles pair-produced, LSP stable

17. SUSY at HERA, 14.Nov.2005 Claus Horn Overview of current best Limits Neutralinos / Charginos RPC and RPV Sleptons RPC and RPV Squarks RPC and RPV Huge multidimensional parameter spaces Comparison between different analysis difficult. Results only valid under restricted conditions.

18. SUSY at HERA, 14.Nov.2005 Claus Horn Current best Limits Neutralinos / Charginos Parameter region: LEP m(    > 92  GeV RPC MSSM m(  > 103  GeV tan(  )=2,  =-200 D0 m(   ) > 84 GeV RPV mSUGRA m(  ) > 160 GeV tan(  )=1.5 LEP m(    > 40  GeV RPV MSSM m(  > 103  GeV tan(  )=1.5

19. SUSY at HERA, 14.Nov.2005 Claus Horn Current best Limits - sleptons selectron R > 100 GeV smuon R > 95 GeV stau R > 86 GeV LEP:  RPC MSSM  = -200 tan(  ) = 1.5 D0: m( ~) > 460 GeV 132 =0.05 & ‘ 311 =0.16 selectron R > 100 GeV smuon R > 98 GeV stau R > 97 GeV LEP:  RPV MSSM  = -200 tan(  ) = 1.5

20. SUSY at HERA, 14.Nov.2005 Claus Horn Current best Limits - squarks D0: m(g~) > 232 GeV D0: m(q~) > 320 GeV RPC mSUGRA m 0 = 25 GeV mSUGRA m 0 = 500 GeV

21. SUSY at HERA, 14.Nov.2005 Claus Horn Current best Limits - squarks RPV CDF m(t~) > 155 GeV ‘ 333  0 HERA m(t~) > 275 GeV ‘ 1j1 =0.3

22. SUSY at HERA, 14.Nov.2005 Claus Horn Sparticle Creation at HERA Systematic approach needed to filter all interesting channels. Particles are produced on-shell (same for all SUSY models). Decay depends on sparticle spectra of SUSY model. HERA topologies Abstract notation SUSY-flow graphs Fundamental vertices } Abstract diagrams Approach:

23. SUSY at HERA, 14.Nov.2005 Claus Horn HERA Topologies All topologically distinct graphs with up to three outgoing (s)particle lines Initial state is fixed to electron+quark (g and  from proton are only considered with 2 outgoing lines)

24. SUSY at HERA, 14.Nov.2005 Claus Horn SUSY-flow Graphs Number of SUSY propagators Number of SUSY particles discarded Choos RPV vertices Mark sparticle lines with a „~“. In the case of RPC: C-like loops result. F, RPC:

25. SUSY at HERA, 14.Nov.2005 Claus Horn Abstract Notation & Fundamental Vertices Physics description on an abstract level to reduce complexity. All vertices of the MSSM ! (neglecting pure bosonic SM vertices)

26. SUSY at HERA, 14.Nov.2005 Claus Horn Restrictions diagrams with > 3 on-shell produced (s)particles are neglected diagrams with outgoing , g, Z 0 are not discussed diagrams with initial g/  and 3 outgoing particles are discarded u-channel diagrams are not stated expicetly diagrams with > 1 sparticle propagator are discarded interactions of Higgs bosons are not considered vertices with only SM bosons are neglected diagrams with three RPV vertices are discarded

27. SUSY at HERA, 14.Nov.2005 Claus Horn Example: Application to type C Diagrams RPC: RPV: SUSY-flow graphs:

28. SUSY at HERA, 14.Nov.2005 Claus Horn C3: disfavoured due to high limits on squark masses C7: - “ – C6: lepto-quark search / contact interaction C5: beeing analysed at the moment ! Possible abstract diagrams:

29. SUSY at HERA, 14.Nov.2005 Claus Horn Sparticle Decays Neutralino: RPC MSSM RPV MSSM GMSB Chargino: Stable LSP missing energy RPC RPV

30. SUSY at HERA, 14.Nov.2005 Claus Horn Sparticle Decays Sleptons: Squarks decay in the same way. RPC MSSM: missing E, e /  /  RPV MSSM: 2 jets / 2 l / 2jets+2l GMSB: l +  + G~ RPC: RPV:

31. SUSY at HERA, 14.Nov.2005 Claus Horn Results Diagrams with squarks are neglected. Characteristic signatures for different models!

32. SUSY at HERA, 14.Nov.2005 Claus Horn Results With two outgoing lines: C5 With three outgoing lines and one sparticle: F4-2 With three outgoing lines and two sparticles: D1

33. SUSY at HERA, 14.Nov.2005 Claus Horn Interesting SUSY Diagram D1 Highest expected cross section for:  =  Low Q 2 (PhP) Calculated cross section: 20 pb for m  =m e~ =120 GeV (no warrenty!) Only SM propagators Production of two sparticles with m  100 GeV each Signature: RPC MSSM: E + e - RPC GMSB: e - +2(  +G~)

34. SUSY at HERA, 14.Nov.2005 Claus Horn Interesting SUSY Diagram F4-2 Highest expected cross section for: resolved PhP Cross section: to be determined Signature: RPV MSSM: 2jets / 2jets+2l RPV GMSB: l+G~ / l+  +G~ Only SM propagators Only one sparticle Slepton production (first time at HERA)

35. SUSY at HERA, 14.Nov.2005 Claus Horn Current Analyses at ZEUS Decay in MSSM: Gaugino analysis Decay in GMSB: Gravitino analysis ' Production via C5 NC-like channel CC-like channel Signature: e - + jets  + jets jet +  + missing energy

36. SUSY at HERA, 14.Nov.2005 Claus Horn Gravitino Analysis

37. SUSY at HERA, 14.Nov.2005 Claus Horn Discriminant Method Box size All events get classified. Less statistics needed. Faster calculation. More accurate results. Generally better S/B seperation. Improvement: variable box size Multidimensional cuts generally result in a better S/B ratio, than one dimensional cuts. # events /box ~ (box_size) d

38. SUSY at HERA, 14.Nov.2005 Claus Horn Gravitino Analysis No events in signal region

39. SUSY at HERA, 14.Nov.2005 Claus Horn Limits – Gravitino Analysis

40. SUSY at HERA, 14.Nov.2005 Claus Horn Limits – Gaugino Analysis Extended LEP limits in M 2 -  plane:

41. SUSY at HERA, 14.Nov.2005 Claus Horn Future: LHC and ILC

42. SUSY at HERA, 14.Nov.2005 Claus Horn Future Prospects - LHC SUSY gauge couplings are the same as in SM. Cross sections only surpressed by mass terms. At high energies production rates should be similar to SM! Discovery is no problem. (reonstruct M eff ) SUSY signal and SM bkg. for tt- decay (m 0 =1TeV, m 1/2 =500 GeV)

43. SUSY at HERA, 14.Nov.2005 Claus Horn SUSY at LHC Complicated decay channels: g~ -> q~q ->  qq -> l~lqq ->  llqq Problem is to seperate different SUSY channels. But: LHC 5  discovery curves

44. SUSY at HERA, 14.Nov.2005 Claus Horn Future Prospects - ILC Higher luminosity at similar energy Precision measurements of SUSY parameters! LHC: ILC:

45. SUSY at HERA, 14.Nov.2005 Claus Horn Future

46. SUSY at HERA, 14.Nov.2005 Claus Horn Summary SUSY is a very interesting and promising theory. It is challenging, but there are SUSY channels were HERA is favoured compared to LEP and the Tevatron. If we do not find it before, then the LHC will give the final answer: Be prepared to discover a new world !