1. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case1 Cosmological Connection at the LHC : Stau Neutralino Co-annhilation Case R. Arnowitt, B. Dutta, A. Gurrola, T. Kamon, A. Krislock, D. Toback Department of Physics, Texas A&M University “Facing the LHC Data” Institute for Physics and Mathematics of the Universe The University of Tokyo, Japan December 17-21, 2007 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case1

2. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case2OUTLINE  Dark Matter (DM) in Universe  DM Particle in SUSY  Cosmological Connection (CC) at the LHC and  h 2 [Co-annihilation (CA) Case]  Summary Arnowitt, Dutta, Kamon, Kolev, Toback, PLB 639 (2006) 46 Arnowitt, Arusano, Dutta, Kamon, Kolev, Simeon, Toback, Wagner, PLB 649 (2007) 73 Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, in preparation 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case2

3. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case3 4321 splitting normal matter and dark matter apart – Another Clear Evidence of Dark Matter – (8/21/06) Dark Matter (Gravitational Lensing) Ordinary Matter (NASA’s Chandra X Observatory) time Approximately the same size as the Milky Way Dark Matter (DM) in Universe 12/17/073

4. Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case4 DM Particle I’m hungry. Can you make the DM sandwich with the elementary particles? No, sir. But with Neutrino?

5. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case5 DM Particle It sounds good. Extra charge? It sounds good. Extra charge? No, sir. Free of charge. No, sir. Free of charge.

6. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case6 DM Particle in SUSY SUSY is an interesting class of models to provide a weakly interacting massive neutral particle (M ~ 100 GeV). SUSY CDM = Neutralino ( ) Astrophysics 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case6

7. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case7 Cosmological Connection (CC) at the LHC and  h 2 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case7

8. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case8 + …. + Co-annihilation (CA) Process Griest, Seckel ’91 An accidental near degeneracy occurs naturally for light stau in mSUGRA. Anatomy of  ann

9. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case9 Minimal Supergravity (mSUGRA) 4 parameters + 1 sign m 1/2 Common gaugino mass at M G m 0 Common scalar mass at M G A 0 Trilinear coupling at M G tan  / at the electroweak scale sign(  ) Sign of Higgs mixing parameter (W (2) =  H u H d ) 4 parameters + 1 sign m 1/2 Common gaugino mass at M G m 0 Common scalar mass at M G A 0 Trilinear coupling at M G tan  / at the electroweak scale sign(  ) Sign of Higgs mixing parameter (W (2) =  H u H d ) i. M Higgs > 114 GeVM chargino > 104 GeV ii. 2.2 x 10  4 < Br (b  s  ) < 4.5 x 10  4 iii. iv. (g  2)  [~3  deviation from the SM calculation] Experimental Constraints

10. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case10 DM Allowed Regions Below is the case of mSUGRA model. However, the results can be generalized. [Stau-Neutralino CA region] [Focus point region] the lightest neutralino has a larger Higgsino component [A-annihilation funnel region] This appears for large values of m 1/2 [Bulk region] almost ruled out

11. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case11 Mass of Squarks and Sleptons Mass of Gauginos No CDM Candidate Excluded (Magnetic Moment of Muon) Excluded (Rare B Decay b  s  ) Excluded (Higgs mass) CDM allowed region Magnetic Moment of Muon Higgs Mass (M h ) Branching Ratio b  s  CA Regions - Illustration Co-annihilation Region

12. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case12 CA Region at tan  = 40 Can we measure  M at colliders?

13. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case13 CC at the LHC

14. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case14  Excess in E T miss + Jets  R-parity conserving SUSY  M eff  Measurement of the SUSY scale at 10-20%. Excess in E T miss + Jets Hinchliffe and Paige, Phys. Rev. D 55 (1997) 5520 q The heavy SUSY particle mass is measured by combining the final state particles q q q  E T j1 > 100 GeV, E T j2,3,4 > 50 GeV  M eff > 400 GeV (M eff  E T j1 +E T j2 +E T j3 +E T j4 + E T miss )  E T miss > max [100, 0.2 M eff ] HM1: High Mass Scenario 1 m 1/2 = 250, m 0 = 60;  = 45 fb M(gluino) = 1886; M(squark) = 1721 CMS

15. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case15  DM content  Measurements of the SUSY masses [e.g., M.M. Nojiri, G. Polesselo, D.R. Tovey, JHEP 0603 (2006) 063]  Key: Dilepton “edge” in the  2 0 decay in dilepton (ee, ,  ) channels for reconstruction of decay chain. Dilepton Endpoint Spiropoulou (SUSY2007) LM1: (Low Mass Case 1) m 1/2 = 180, m 0 = 850;  = 55 pb [post-WMAP benchmark point B ’ ] M(gluino) = 611 M(squark) = 559 gluino  squark+quark B(X02  slep_R lept) = 11.2% B(X02  stau_1 tau) = 46% B(X+1  sneut_L lept) = 36%

16. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case16  In the CA region, however, the ee and  channels are almost absent. We are in a different game: Br(  2 0  ee,  ) ~ 0% Br(  2 0   ) ~ 100%  M = 5-15 GeV Dilepton Endpoint in CA Region  Questions: (1) How can we establish the dark matter allowed regions? (2) To what accuracy can we calculate the relic density based on the measurements at the LHC?

17. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case17 Our Reference Point m 1/2 = 351, m 0 = 210, tan  = 40,  >0, A 0 = 0 [ISAJET version 7.69]

18. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case18 Smoking Gun of CA Region 100% 97% SUSY Masses (CDM) 2 quarks+2  ’s +CDM particle Unique kinematics

19. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case19 SUSY Anatomy M eff M(j  ) M(  ) pT()pT() pT()pT() 100% 97% SUSY Masses (CDM) E T miss + jets + >2 

20. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case20 Number of Counts / 1 GeV E T vis (true) > 20, 20 GeV E T vis (true) > 40, 20 GeV E T vis (true) > 40, 40 GeV Number of Counts / 2 GeV p T soft Slope and M  Slope of p T distribution of “soft  ” contains ΔM information Low energy  ’s are an enormous challenge for the detectors p T and M  distributions in true di-  pairs from neutralino decay with |  | < 2.5

21. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case21 Warming-up Quizzes I.Hadronic or leptonic?  Hadronic, because e or  does not tell us the evidence of tau leptons II.How low in p T ?  CDF : p T vis >15-20 GeV III.Worries about triggers?  E T miss + jet trigger for SUSY  Lepton+tau trigger for Z’s (calibration) [Assumption]   = 50%, fake rate 1%

22. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case22 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case22

23. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case23 M  Distribution Clean peak even for low  M We choose the peak position as an observable.

24. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case24 180 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case24

25. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case25 OS OS-LS LS OS  LS Slope(p T soft ) M  < M  end point p T vis (GeV)

26. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case26 We can still see the dependence of the p T slope on  M using OS  LS method.  M Dependence of Slope(p T soft )

27. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case27 M  peak vs. X Uncertainty Bands with 10 fb -1

28. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case28 Slope(p T soft ) vs. X Uncertainty Bands with 10 fb -1

29. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case29 SUSY Anatomy M eff M j  M  p T(  ) 100% 97% SUSY Masses (CDM)

30. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case30 M j  Distribution M  < M  endpoint Jets with E T > 100 GeV J  masses for each jet Choose the 2 nd large value gluino  squark + j “other” jet Peak value ~ True Value  We take the peak value as an observable.

31. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case31 M j  Distribution Squark Mass = 840 GeV Squark Mass = 660 GeV Peak value depends on squark mass M  < M  endpoint Jets with E T > 100 GeV J  masses for each jet Choose the 2 nd large value We choose the peak position as an observable.

32. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case32 M j  peak vs. X

33. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case33 4 observables defined as functions of 5 masses Invert the equations to determine the masses as functions of the observables 137  19 GeV 260  15 GeV 829  28 GeV Determining SUSY Masses (10 fb  1 ) 5 th observable ( ) is not ready for this talk. We assume: [This assumption will be removed once the M j  study is ready.]

34. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case34 Gaugino Universality (10 fb  1 ) We test a gaugino univesality. 1  ellipse

35. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case35 SUSY Anatomy M eff M j  M  p T(  ) 100% 97% SUSY Masses (CDM)

36. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case36 M eff Distribution At Reference Point M eff peak = 1274 GeV M eff peak = 1220 GeV (m 1/2 = 335 GeV) M eff peak = 1331 GeV (m 1/2 = 365 GeV)  E T j1 > 100 GeV, E T j2,3,4 > 50 GeV [No e ’s,  ’s with p T > 20 GeV]  M eff > 400 GeV (M eff  E T j1 +E T j2 +E T j3 +E T j4 + E T miss [No b jets;  b ~ 50%])  E T miss > max [100, 0.2 M eff ]

37. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case37 M eff peak vs. X M eff peak …. Very insensitive to A 0 and tan . m 1/2 (GeV)m 0 (GeV)

38. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case38 M eff (b) Distribution At Reference Point M eff (b)peak = 1026 GeV M eff (b)peak = 933 GeV (m 1/2 = 335 GeV) M eff (b)peak = 1122 GeV (m 1/2 = 365 GeV)  E T j1 > 100 GeV, E T j2,3,4 > 50 GeV [No e ’s,  ’s with p T > 20 GeV]  M eff (b) > 400 GeV (M eff (b)  E T j1=b +E T j2 +E T j3 +E T j4 + E T miss [j1 = b jet])  E T miss > max [100, 0.2 M eff ]

39. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case39 M eff (b)peak vs. X M eff (b)peak …. Sensitive to A 0 and tan . A0A0 tan  m 1/2 m0m0

40. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case40 DM Connection [1] Detection of low energy  ’s (p T > 20 GeV) in the stau-neutralino CA region. [2] Construction of observables: N OS-LS, M j , M , Slope, M eff, M eff (b) [3] Reconstruction of SUSY masses using: e.g., Peak(M  ) = f (M gluino, M stau, M, M ) [4] N OS-LS, M j , Slope, M eff, to solve for m 0 and m 1/2 e.g., Gaugino universality test [5] M , M eff (b) to solve tan  and A 0 [6] Dark matter content in mSUGRA 0 1  ~ 0 2  ~

41. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case41 We have made a determination of the masses The gaugino masses determine m 1/2 Writing  M as a function of the model parameters: Incorporating the M eff and M eff (b) observables  tan  / tan  ~ 7.8 %  A 0 ~ ± 25 GeV  m 0 / m 0 ~ 4.9 %  m 1/2 / m 1/2 ~ 3 % mSUGRA Parameters (10 fb  1 ) 1  ellipse

42. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case42 We have made a determination of the mSUGRA model parameters The Dark Matter relic density depends on the model parameters: DM Relic Density (10 fb  1 ) We can determine  M to ~ 17 % accuracy and  h 2 to ~ 35 %

43. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case43Summary This talk is about a cosmological connection at the LHC in the case of co- annihilation (CA). The LHC should be able to uncover the striking small  M signature (smoking gun in the CA region) with ~10 fb -1 of data in multi-  final states and make high quality measurements with the first few years of running. With the mSUGRA model in the CA region, the dark matter content can be measured with an accuracy of ~40%.

44. 12/17/07 Cosmological Connection at the LHC: Stau Neutralino Coannihilation Case44 The University of New Mexico Albuquerque, USA May 2008 TO HELP SOLVE THE PUZZLE OF THE UNIVERSE. 44