1. Strategies to Search for Supersymmetry John Ellis Warsaw, May 18th, 2007

2. Outline Introduction to supersymmetry Standard search strategy: –Neutralino dark matter –Missing-energy signature –Hadronic sparticle decays? Gravitino dark matter –Stau NLSP Metastable charged particle Stau or stop?

3. Why Supersymmetry (Susy)? Hierarchy problem: why is m W << m P ? (m P ~ 10 19 GeV is scale of gravity) Alternatively, why is G F = 1/ m W 2 >> G N = 1/m P 2 ? Or, why is V Coulomb >> V Newton ? e 2 >> G m 2 = m 2 / m P 2 Set by hand? What about loop corrections? δm H,W 2 = O(α/π) Λ 2 Cancel boson loops  fermions Need | m B 2 – m F 2 | < 1 TeV 2

4. Loop Corrections to Higgs Mass 2 Consider generic fermion and boson loops: Each is quadratically divergent: ∫ Λ d 4 k/k 2 Leading divergence cancelled if Supersymmetry! 2 x 2

5. Astronomers say that most of the matter in the Universe is invisible Dark Matter ‘Supersymmetric’ particles ? We shall look for them with the LHC Dark Matter in the Universe

6. Lightest Supersymmetric Particle Stable in many models because of conservation of R parity: R = (-1) 2S –L + 3B where S = spin, L = lepton #, B = baryon # Particles have R = +1, sparticles R = -1: Sparticles produced in pairs Heavier sparticles  lighter sparticles Lightest supersymmetric particle (LSP) stable Fayet

7. Possible Nature of LSP No strong or electromagnetic interactions Otherwise would bind to matter Detectable as anomalous heavy nucleus Possible weakly-interacting scandidates Sneutrino (Excluded by LEP, direct searches) Lightest neutralino χ (partner of Z, H, γ) Gravitino (nightmare for astrophysical detection)

8. Constraints on Supersymmetry Absence of sparticles at LEP, Tevatron selectron, chargino > 100 GeV squarks, gluino > 250 GeV Indirect constraints Higgs > 114 GeV, b → s γ Density of dark matter lightest sparticle χ: 0.094 < Ω χ h 2 < 0.124 3.3 σ effect in g μ – 2?

9. Particles + spartners 2 Higgs doublets, coupling μ, ratio of v.e.v.’s = tan β Unknown supersymmetry-breaking parameters: Scalar masses m 0, gaugino masses m 1/2, trilinear soft couplings A λ, bilinear soft coupling B μ Often assume universality: Single m 0, single m 1/2, single A λ, B μ : not string? Called constrained MSSM = CMSSM Gravitino mass? Minimal supergravity (mSUGRA) Additional relations: m 3/2 = m 0, B μ = A λ – m 0 Minimal Supersymmetric Extension of Standard Model (MSSM)

10. Current Constraints on CMSSM WMAP constraint on relic density Excluded because stau LSP Excluded by b  s gamma Excluded (?) by latest g - 2 Assuming the lightest sparticle is a neutralino JE + Olive + Santoso + Spanos

11. Effects in Specific Regions Co-annihilation: –Important when two or more sparticles nearly degenerate –e.g., neutralino and stau Strip in (m 1/2, m 0 ) plane Rapid annihilation via direct-channel Higgs pole(s): –h important when m 1/2 small, m 0 large –H, A important when tan , m 1/2 large

12. Current Constraints on CMSSM Impact of Higgs constraint reduced if larger m t, focus-point region far up Different tan β sign of μ JE + Olive + Santoso + Spanos

13. Sparticles may not be very light Full Model samples Detectable @ LHC Provide Dark Matter Detectable Directly Lightest visible sparticle → ← Second lightest visible sparticle JE + Olive + Santoso + Spanos

14. How ‘Likely’ are Heavy Sparticles? Fine-tuning of EW scaleFine-tuning of relic density Larger masses require more fine-tuning: but how much is too much?

15. Precision Observables in Susy mWmW sin 2 θ W Present & possible future errors Sensitivity to m 1/2 in CMSSM along WMAP lines for different A Can one estimate the scale of supersymmetry? tan β = 50 tan β = 10 JE + Heinemeyer + Olive + Weber + Weiglein: 2007

16. More Observables b → sγ tan β = 10tan β = 50 g μ - 2 JE + Heinemeyer + Olive + Weber + Weiglein: 2007

17. B s → μμ More Observables tan β = 10tan β = 50 JE + Heinemeyer + Olive + Weber + Weiglein: 2007 Bu → Bu → 

18. Likelihood for m 1/2 Global Fit to all Observables tan β = 10tan β = 50 JE + Heinemeyer + Olive + Weber + Weiglein: 2007 Likelihood for M h

19. Classic Supersymmetric Signature Missing transverse energy carried away by dark matter particles

21. Supersymmetric Benchmark Studies Specific benchmark Points along WMAP lines Lines in susy space allowed by accelerators, WMAP data Sparticle detectability Along one WMAP line Calculation of relic density at a benchmark point Battaglia, De Roeck, Gianotti, JE, Olive, Pape

22. Summary of LHC Scapabilities … and Other Accelerators LHC almost `guaranteed’ to discover supersymmetry if it is relevant to the mass problem Battaglia, De Roeck, Gianotti, JE, Olive, Pape

23. Non-Universal Higgs Masses (NUHM) Generalize CMSSM (+) m Hi 2 = m 0 2 (1 + δ i ) Free Higgs mixing μ, pseudoscalar mass m A Larger parameter space Constrained by vacuum stability

24. Regions Allowed in Different Scenarios for Supersymmetry Breaking CMSSM Benchmarks NUHM Benchmarks GDM Benchmarks with stau NLSP with neutralino NLSP De Roeck, JE, Gianotti, Moortgat, Olive + Pape

25. Trapezoidal shape for quark-dijet combinations Endpoints related to squark mass Spectra in Squark  W,Z,H  Hadron Decays Butterworth + JE + Raklev: 2007

26. Search for Squark  W  Hadron Decays Use k T algorithm to define jets Cut on W mass W and QCD jets have different subjet splitting scales Corresponding to y cut Butterworth + JE + Raklev: 2007

27. Signals for Squark  W,Z Decays Butterworth + JE + Raklev: 2007 qW with subjet cuts qW without subjet cuts q + leptonic W qZ with subjet cuts

28. Background- subtracted qW mass combinations in benchmark scenarios Constrain sparticle mass spectra Search for Hadronic W, Z Decays Butterworth + JE + Raklev: 2007

29. Information on Sparticle Spectra Reconstructed sparticle masses as functions of LSP mass in scenarios  and  Butterworth + JE + Raklev: 2007 chargino Chargino/neutralino squark

30. A Light Heavy SUSY Higgs @ CDF? Excess seen in  spectrum Apparently also in bb CDF unable to exclude all sensitive region BUT: not see by D0

31. Is this possible within NUHM? YES: for limited ranges of tan , m 1/2, m 0,  and A 0 JE + Heinemeyer + Olive + Weiglein PREDICT: M h, b  s , B s  , B  , g  - 2 all close to experimental limits

32. Possible Nature of SUSY Dark Matter No strong or electromagnetic interactions Otherwise would bind to matter Detectable as anomalous heavy nucleus Possible weakly-interacting scandidates Sneutrino (Excluded by LEP, direct searches) Lightest neutralino χ (partner of Z, H, γ) Gravitino (nightmare for astrophysical detection) GDM: a bonanza for the LHC!

33. Possible Nature of NLSP if GDM NLSP = next-to-lightest sparticle Very long lifetime due to gravitational decay, e.g.: Could be hours, days, weeks, months or years! Generic possibilities: lightest neutralino χ lightest slepton, probably lighter stau lighter stop Constrained by astrophysics/cosmology

34. Density below WMAP limit Decays do not affect BBN/CMB agreement Different Regions of Sparticle Parameter Space if Gravitino LSP JE + Olive + Santoso + Spanos χ NLSP stau NLSP

35. Minimal Supergravity Model (mSUGRA) Excluded by b  s γ LEP constraints On m h, chargino Neutralino LSP region stau LSP (excluded) Gravitino LSP region JE + Olive + Santoso + Spanos More constrained than CMSSM: m 3/2 = m 0, B λ = A λ – 1

36. Regions Allowed in Different Scenarios for Supersymmetry Breaking CMSSM Benchmarks NUHM Benchmarks GDM Benchmarks with stau NLSP with neutralino NLSP De Roeck, JE, Gianotti, Moortgat, Olive + Pape

37. Spectra in NUHM and GDM Benchmark Scenarios Typical example of non-universal Higgs masses: Models with stau NLSP Models with gravitino LSP De Roeck, JE, Gianotti, Moortgat, Olive + Pape

38. Properties of NUHM and GDM Models Relic density ~ WMAP in NUHM models Generally < WMAP in GDM models Need extra source of gravitinos at high temperatures, after inflation? NLSP lifetime: 10 4 s < τ < few X 10 6 s De Roeck, JE, Gianotti, Moortgat, Olive + Pape

39. Final States in GDM Models with Stau NLSP All decay chains end with lighter stau Generally via χ Often via heavier sleptons Final states contain 2 staus, 2 τ, often other leptons De Roeck, JE, Gianotti, Moortgat, Olive + Pape

40. Triggering on GDM Events Will be selected by many separate triggers via combinations of μ, E energy, jets, τ JE, Raklev, Øye: 2007

41. Efficiency for Detecting Metastable Staus Good efficiency for reconstructing stau tracks JE + Raklev + Oye

42. ATLAS Momentum resolution Good momentum resolution JE + Raklev + Oye

43. Stau Mass Determination Good mass resolution JE + Raklev + Oye

44. Reconstructing Sparticle Masses JE + Raklev + Oye Neutralino  stau + tau Squark R  q + 

45. Reconstructing GDM Events JE, Raklev, Øye: 2006 Gluino → qq χ Slepton → l χ χ 2 → slepton l Sneutrino → stau W Chargino

46. Sparticle Mass Spectra JE + Raklev + Oye

47. Numbers of Visible Sparticle Species At different colliders De Roeck, JE, Gianotti, Moortgat, Olive + Pape

48. Slepton Trapping at LHC? βγ typically peaked ~ 2 Staus with βγ < 1 leave central tracker after next beam crossing Staus with βγ < ¼ trapped inside calorimeter Staus with βγ < ½ stopped within 10m Can they be dug out? De Roeck, JE, Gianotti, Moortgat, Olive + Pape Feng + Smith Hamaguchi + Kuno + Nakaya + Nojiri

49. Extract Cores from Surrounding Rock? Use muon system to locate impact point on cavern wall with uncertainty < 1cm Fix impact angle with accuracy 10 -3 Bore into cavern wall and remove core of size 1cm × 1cm × 10m = 10 -3 m 3 ~ 100 times/year Can this be done before staus decay? Caveat radioactivity induced by collisions! 2-day technical stop ~ 1/month Not possible if lifetime ~10 4 s, possible if ~10 6 s? Very little room for water tank in LHC caverns, only in forward directions where few staus De Roeck, JE, Gianotti, Moortgat, Olive + Pape

50. Potential Measurement Accuracies Measure stau mass to 1% Measure m ½ to 1% via cross section, other masses? Distinguish points ζ, η De Roeck, JE, Gianotti, Moortgat, Olive + Pape Gravitino Dark Matter even more interesting than Neutralino Dark Matter!

51. Stop NLSP in GDM Scenario? Not possible within CMSSM Diaz-Cruz, JE, Olive + Santoso: 2007

52. Stop NLSP possible within NUHM Tightly-constrained scenario with distinctive signature Diaz-Cruz, JE, Olive + Santoso: 2007

53. Summary Supersymmetry the most ‘expected’ surprise at the LHC ‘Expected’ signature missing energy Sparticle masses not necessarily universal Not the only possibility –Metastable charged particle? –Strongly interacting? Expect the unexpected!