Supersymmetry at HERA

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

2. 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 |Qel| = |Qp| ? ...

3. Motivation for Supersymmetry • Coleman-Mandula theorem • Unification of the forces • Solution of the Hierarchy problem • Candidates for dark matter • Necessary for quantum-gravity

4. 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.“ Graded Lie-algebras „super algebra“ Tensors fulfill comutation relations Add anti-commutators Pm: Energy-momentum operator Q: Supercharge SUSY is the only possibel extension of the Poincare group. Our last chance to discover a fundamental space-time symmetry!

5. SM MSSM Unification of the Forces Renormalisation Group Equations describe running of the coupling constants due to screening / antiscreening Example: Slope depends on number and masses of particles in the model Miracle!

6. Solution of the Hierarchy Problem Corrections to the Higgs mass: SM: Cancelation requires fine tuning to 17 orders of magnitude! MSSM: Contributions of particles are canceled by contribution of their superpartners.

7. For unbroken SUSY: No quantum correction to the Higgs mass (DmH=0). Broken SUSY: “running” Higgs mass mh No SUSY SUSY Higgs sector very restricted: mh < 150 GeV SUSY exact mH Q² Q2 SUSY particles superpartners have to be lighter than 1 TeV

8. 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. Supermultiplets Chiral supermultiplets: (fermion,sfermion) = (spin ½, spin 0) Vectorial supermultiplet: (gauge boson, gauginos) = (spin 1, spin ½)

10. Sparticles of the MSSM Charged gauginos mix to form two charginos. Neutral gauginos mix to form four neutralinos. M depends on M2, tan(b) and m. BRs of c0 and c

11. Parameters of the MSSM • mA : pseudoscalar Higgs boson mass • tan(b) : ratio of VEV of two Higgs doublets • m: Higgs mixing parameter • M1, M2, M3 : gaugino mass terms • All sfermion masses • Ai: all mixing parameters of squark and slepton sector

12. 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. minimal SUperGRavity (mSUGRA) Constraints: • Unified masses at the GUT scale • m0: common scalar mass • m1/2: common gaugino mass • Unified trilinear couplings = A0 • Radiative EW symmetry breaking Parameter: m0, m1/2, A0, tan(b), sign(m) M(G~)  1 TeV (in AMSB  10 TeV)

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

15. Typical Mass Spectra Neutralino1 is light(est) Next: right-handed slepton (stau) & chargino1 Squarks are relatively heavy

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

17. Overview of current best Limits • Neutralinos / Charginos • RPC and RPV • Sleptons • RPC and RPV • Squarks • RPC and RPV Huge multidimensional parameter spaces Results only valid under restricted conditions. Comparison between different analysis difficult.

18. Current best Limits Parameter region: Neutralinos / Charginos LEP m(c0) > 92GeV RPC MSSM m(c±) > 103GeV tan(b)=2, m=-200 LEP m(c0) > 40GeV RPV MSSM m(c±) > 103GeV tan(b)=1.5 D0 m(c0) > 84 GeV RPV mSUGRA m(c±) > 160 GeV tan(b)=1.5

19. Current best Limits - sleptons selectronR > 100 GeV smuonR > 95 GeV stauR > 86 GeV RPC MSSM m = -200 tan(b) = 1.5 LEP: RPV MSSM l0 m = -200 tan(b) = 1.5 LEP: selectronR > 100 GeV smuonR > 98 GeV stauR > 97 GeV D0: m(n~) > 460 GeV l132=0.05 & l‘311=0.16

20. Current best Limits - squarks RPC D0: m(q~) > 320 GeV mSUGRA m0 = 25 GeV D0: m(g~) > 232 GeV mSUGRA m0 = 500 GeV

21. Current best Limits - squarks RPV CDF m(t~) > 155 GeV l‘3330 HERA m(t~) > 275 GeV l‘1j1=0.3

22. Sparticle Creation at HERA Systematic approach needed to filter all interesting channels. Approach: 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

23. HERA Topologies • All topologically distinct graphs • with up to three outgoing (s)particle lines • Initial state is fixed to electron+quark • (g and g from proton are only considered with 2 outgoing lines)

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

25. Abstract Notation & Fundamental Vertices Physics description on an abstract level to reduce complexity. All vertices of the MSSM ! (neglecting pure bosonic SM vertices)

26. Restrictions • diagrams with > 3 on-shell produced (s)particles are neglected • diagrams with outgoing g, g, Z0 are not discussed • diagrams with initial g/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. Example: Application to type C Diagrams RPC: RPV: SUSY-flow graphs:

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

29. Sparticle Decays Neutralino: RPC MSSMRPV MSSMGMSB Stable LSP missing energy Chargino: RPCRPV

30. Sparticle Decays Sleptons: RPV: RPC: RPC MSSM: missing E, e / m / t RPV MSSM: 2 jets / 2 l / 2jets+2l GMSB: l + g + G~ Squarks decay in the same way.

31. Results Diagrams with squarks are neglected. Characteristic signatures for different models!

32. Results With two outgoing lines: C5 With three outgoing lines and one sparticle: F4-2 With three outgoing lines and two sparticles: D1

33. Interesting SUSY Diagram D1 • Only SM propagators • Production of two sparticles • with m100 GeV each Highest expected cross section for: Signature: RPC MSSM: E + e- RPC GMSB: e-+2(g+G~) • G = g • Low Q2 (PhP) Calculated cross section: 20 pb for mc=me~=120 GeV (no warrenty!)

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

35. ' Current Analyses at ZEUS Production via C5 Decay in MSSM: Gaugino analysis NC-like channel e- + jets CC-like channel Decay in GMSB: Gravitino analysis n + jets Signature: jet + g + missing energy

36. Gravitino Analysis

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

38. Gravitino Analysis No events in signal region

39. Limits – Gravitino Analysis

40. Limits – Gaugino Analysis Extended LEP limits in M2 - m plane:

41. Future: LHC and ILC

42. 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 Meff) SUSY signal and SM bkg. for tt- decay (m0=1TeV, m1/2=500 GeV)

43. SUSY at LHC LHC 5s discovery curves But: Complicated decay channels: g~ -> q~q -> cqq -> l~lqq -> cllqq Problem is to seperate different SUSY channels.

44. Future Prospects - ILC Higher luminosity at similar energy Precision measurements of SUSY parameters! LHC: ILC:

45. Future

46. 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 !