1. Amitava Datta Department of Physics Jadavpur University Kolkata

2. INTRODUCTION AND BASIC FACTS

3. DARK MATTER Wilkinson Microwave Anisotropy Probe (WMAP) Data : Most popular Candidate

4. EVOLUTION OF THE UNIVERSE AND DARK MATTER Early Universe: particles and sparticles in thermal equilibrium. Universe Cools and Expands : Too little thermal energy to produce heavy Sparticles. They annihilate and decay into particles and the LSP LSP and particles in equilibrium

5. The Expansion Continues: LSP density decreases, annihilation rate becomes small compared to the expansion rate of the universe, EQUILIBRIUM IS LOST AND THE LSP EXPERIENCES FREEZE OUT The LSP density today is determined by this small rate and further dilution due to expansion of the universe. Compute using MICROMEGAS, DARKSUSY…………

6. Important parameters: LSP mass and annihilation x-sec (depends on other SUSY parameters) Co-annihilation: Slightly heavier sparticles may exist longer in equilibrium with the LSP with comparable numbers and annihilate each other. This co-annihilation x-sec (depends on other SUSY parameters) is also important for the LSP relic density.

7. The Generic Scenarios LSP Annihilation and Co-annihilation

8. LSP Annihilation Diagram Bino-like LSP and light sfermion (R-type) gives reasonably high x-sec and not too large density ( The Bulk Region )

9. Resonant annihilation into Higgses

10. LSP Co-annihilation Examples

11. Annihilation into Gauge Bosons The LSP has significant a)Higgsino components ( e.g., The Focus Point/Hyperbolic Branch region in mSUGRA)(J. Feng et al hep-ph/9909334; K.Chan et al hep-ph/ 9710473 ). b)Wino component ( e.g., The AMSB model) See, e.g., Utpal Chattopadhyaya et al hep-ph/0610077

12. Plan of The Talk Realization of various scenarios in mSUGRA Tests at LHC Beyond mSUGRA Conclusions Ref1: Tevatron-for-LHC Report, S. Abdullin et al, hep-ph/0608322

13. Realization of various scenarios in mSUGRA

14. H. Baer et al in Ref 1 mSUGRA low tan  Focus Point Region ???

15. A. Belyaev : Hunting for SUSY……(2005) Allowed Regions in mSUGRA

16. LHC REACH Tip of the Higgs funnel? FP region?

17. Tests at LHC Distinctive features of the signal for each region of the parameter space (circumstantial evidences) Quantitative or semi-quantitative tests (determination of masses and mass differences –certainly ILC will do a better job if the sparticles are accessible)

18. Gluino pair-production Parton level simulation ( U. Chattopadhyay et al hep-ph/000822 ) :large number of b-jets in the signal. Electroweak gaugino production and decay H. Baer et al hep-ph/0507282 Very heavy squark, sleptons ; relatively light gauginos LHC SIGNALS OF FOCUS POINT SUPERSYMMETRY

19. Further works on gluino pair-production Simulation at the generator level ( P. G. Mercadante et al hep-ph/0506142 ) b-tagging improves the discovery reach. Inclusion of hitherto neglected but potentially dangerous backgrounds ( S.P. Das, A. D., M. Maity and M. Guchait – in preparation )

20. Handling the New Backgrounds tttt, ttbb, bbbb, ttqq, bbqq,…………… Events generated with CompHEP, ALPGEN, MADGRAPH Events interfaced with Pythia for simulation

21. Signal Features Cut Background removed

23. New backgrounds under control

24. The stau coannihilation Distinctive feature: large number of low energy  -pairs in the signal. Detection efficiency of low P T taus ? ( assume detection efficiency >50% for P T visible > 20 GEV) Measurement of  M ( approximately 15 GeV or smaller) ( 3 –10 fb -1 of data) Recent work:R.Arnowitt et al hep-ph /0603128

25. Invariant mass distribution (VISIBLE)

26. Shift of the peak with  M

27. The (“disfavoured”)Bulk Region Disfavoured in mSUGRA for A 0 = 0

28. LEP constraints A 0 =0 (LEP-SUSY WG)

29. Weaker constraints for large A 0

30. The BULK revisited Light sleptons Light stop: discovery at Tevatron ? Potential constraints (for large A 0 )

31. Allowed Region Large A 0 L. S. Stark et al hepph/0502197

32. Allowed Region Large A 0 with CCB Constraint

33. A Point in the WMAP Allowed Bulk Region m0 m1/2 A0 sign(  ) tan  80 200 -500 + 10 Key features BR(chi_1 +  stau_1 + neutrino) = 90% (ISAJET) BR(chi_2 0  stau_1 + neutrino) = 86% Lots of  s in the final state; very few isolated e or .

34. All squark gluino events generated by PYTHIA (parton level); tau abd b decays switched off. #of events with at least one tau : 81% # of events with one tau pair + 2b jets +missing energy =29% ( Signal?) Bonus: light stop (218).

35. The Potential Constraints The scalar potential in MSSM is a complicated object – function of many scalars including charged and coloured fields. Require: no minimum for a non-zero charged or coloured field deeper than the EWSB minimum

36. Example Minimization  Constraints on mSUGRA parameters A.D and A. Samanta hep-ph/0406129 Upper bounds on sparticle masses

37. What if we leave in a false vacuum with a life time larger than the age of the universe?

38. Conclusions (mSUGRA) Several interesting regions of WMAP allowed parameter space are within the striking range of the LHC. By and large third generation sfermions lead to characteristic signatures in all regions Detection efficiencies- important experimental issue.

39. In sptite of extensive analyses there are still open questions Focus point region: backgrounds from tttt, ttbb,ttgg,…….. seems to be manageable; gluino mass reach? Increase the reach in the tau co-annihilation region (high tan  ), Higgs funnel and focus point region. The bulk region for large A_0 has not been fully analyzed ; may lead to qualitatively new signatures.

40. Beyond mSUGRA Co-annihilation with light stop Electroweak baryogenesis - light stop once more! Discovery at Tevatron ? Nonuniversal scalar masses – the VLSPs revisited

41. Coannihilation with lighter stop Recent work C. Balazs et al in reference 1 Stop LSP mass difference < 30 GeV Beyond mSUGRA scenario Discovery at Tevatron? Confirmation at LHC? 2 b-jets+ 2 LS dilepton+ missing transverse energy from gluino pairs Production followed by gluino decays into top and stop ( Kraml and Rakhlev in ref 1)

42. Stop Co-annihilation

43. Baryogenesis and Light stop EWBG needs a boson with mass ~ EW scale and strongly coupled to the Higgs boson – stop is a viable candidate. Require Discovery at Tevatron ? CP Phase (EDM constraint?) Recent analysis C. Balazs et al ref 1. (MSSM)

44. Stop co-annihilation (with CP Phase)

45. Stop Search Prospect Tevatron Stop search at Tevatron R. Demina et al hep-ph/ 9910 275 (c-tagging?, 4-body decay?) Both CDM(stop co- annihilation and EW baryogeneis via light stop?

46. The 4-body decay of the stop C. Boehm et al hep-Ph/9907428 : May be the dominant mode. A strong Higgs mass bound reduces the allowed parameter space: S. P. Das hep-ph/0512011

47. The VLSP Scenario Right slepton heavier than left sleptons ( forbidden in mSUGRA; allowed in models with non-universal scalar mass) Large numder of e and  in the final state Invisible decay of sneutrino and the second lightest neutralino Many interesting signatures (Qualitatively different from the ones in mSUGRA) at LEP and Tevatron were proposed: S.Chakrabarty, AD, Asesh Datta, M. Drees, M. Guchait, B. Mukhopadhyaya and M. K. Parida. LHC??

48. WMAP Allowed VLSP Scenario MICROOMEGAS chi_1 + 173.6 Thanks to Utpal Chattopadhyaya, Debottam Das and Sujoy Poddar! Snuelec :102.0 (NLSP)

49. Decay BRs (SDECAY) BR(~chi_20 -> ~nu_eL nu_eb) 10% Sneutrino (NLSP)decay invisibly Six such invisible channels BR(~chi_20 -> ~e_L- e+) 5% BR(~chi_20 -> ~tau_1- tau+) 10% Lots of e and  in the final state (not allowed even in the resurrected bulk of mSUGRA

50. Can one rule out a model because of too little or too much dark matter? Too little: May be there are non-sparticle or even non-particle dark matter Too much: A little RPV (induced by physics at the high scale) will make the LSP cosmologically unstable but stable at colliders.

51. Slight departures from Msugra (not necessarily from SUGRA) may lead to qualitatively new signatures The VLSP scenario and other beyond mSUGRA models call for special attention; More acceptable naturalness parameters (S.F. King and J. P. Roberts……………) in models with non-universal scalar and/or gaugino masses? The very special light stop: a) mSUGRA with large A_0 (beware of potential constraints) b) stop coannihilation c) electroweak baryogenesis; discovery at Tevatron ? (Beware of 4-body decays) Conclusions (Beyond mSUGRA)

54. SIGNALS FROM GLUINO PAIR -PRODUCTION From U. Chattopadhyay et al hep-ph/0008228