1. Measurement of Dark Matter Content at the LHC Bhaskar Dutta Collaborators: R. Arnowitt, A. Gurrola, T. Kamon, A. Krislock, D. Toback Texas A&M University Measurement of Dark Matter Content at the LHC118 th August’ 08

2. OUTLINE  DM Relic Density (  h 2 ) in SUSY  mSUGRA Co-annihilation (CA) Region at the LHC  Prediction of DM Relic Density (  h 2 )  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, Phys. Rev. Lett. 100, (2008) 231802 Crockett, Dutta, Flanagan, Gurrola, Kamon, Kolev, VanDyke, ‘08; 2Measurement of Dark Matter Content at the LHC

3. 3 + …. + Co-annihilation (CA) Process Griest, Seckel ’91 A near degeneracy occurs naturally for light stau in mSUGRA. Anatomy of  ann Precision Cosmology at the LHC

4. In mSUGRA model the lightest stau seems to be naturally close to the lightest neutralino mass especially for large tan  For example, the lightest selectron mass is related to the lightest neutralino mass in terms of GUT scale parameters: For larger m 1/2 the degeneracy is maintained by increasing m 0 and we get a corridor in the m 0 - m 1/2 plane. The coannihilation channel occurs in most SUGRA models with non-universal soft breaking, Thus for m 0 = 0, becomes degenerate with at m 1/2 = 370 GeV, i.e. the coannihilation region begins at m 1/2 = (370-400) GeV Coannihilation, GUT Scale Arnowitt, Dutta, Santoso’ 01 Measurement of Dark Matter Content at the LHC 4

5. DM Allowed Regions in mSUGRA 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 5 Measurement of Dark Matter Content at the LHC

6. CA Region at tan  = 40 Can we measure  M at colliders? 6 Measurement of Dark Matter Content at the LHC

7. Smoking Gun of CA Region 100% 97% SUSY Masses (CDM) 2 quarks+2  ’s +missing energy Unique kinematics 7 Low energy taus exist in the CA region However, one needs to measure the model Parameters to predict the Dark matter content in this scenario Measurement of Dark Matter Content at the LHC

8. 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 Measurement of Dark Matter Content at the LHC8

9. 9 We use ISAJET + PGS4 PLB 639 (2006) 46 Measurement of Dark Matter Content at the LHC

10. M  Distribution Clean peak even for low  M We choose the peak position as an observable. 10 Measurement of Dark Matter Content at the LHC

11. SUSY Anatomy M j  M  p T(  ) 100% 97% SUSY Masses (CDM) Measuring Relic Density at the LHC11 M eff

12. 4 j+E T miss : 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 ] 12 Measurement of Dark Matter Content at the LHC

13. 3 j+1b+E T miss :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 ] M eff (b) M eff (b) can be used to determine A 0 and tan  even without measuring stop and sbottom masses 13 Phys. Rev. Lett. 100, (2008) 231802 Measurement of Dark Matter Content at the LHC

14. Observables SM+SUSY Background gets reduced Ditau invariant mass: M  Jet-  -  invariant mass: M j  Jet-  invariant mass: M j  P T of the low energy  M eff : 4 jets +missing energy M eff (b) : 4 jets +missing energy Since we are using 7 variables, we can measure the model parameters and the grand unified scale symmetry (a major ingredient of this model) 1.Sort  ’s by E T (E T 1 > E T 2 > …) Use OS  LS method to extract  pairs from the decays All these variables depend on masses => model parameters Measurement of Dark Matter Content at the LHC 14

15. 7 Eqs (as functions of SUSY parameters) Invert the equations to determine the masses Determining SUSY Masses (10 fb  1 ) 1  ellipse 10 fb -1 15 Phys. Rev. Lett. 100, (2008) 231802 M eff (b) = f 7 (g, q L, t, b) ~~~~ Measurement of Dark Matter Content at the LHC

16. [1] Established the CA region by detecting low energy  ’s (p T vis > 20 GeV) [2] Determined SUSY masses using: M , Slope, M j , M j , M eff e.g., Peak(M  ) = f (M gluino, M stau, M, M ) [3] Measure the dark matter relic density by determining m 0, m 1/2, tan , and A 0 DM Relic Density in mSUGRA 0 1  ~ 0 2  ~ 16 Measurement of Dark Matter Content at the LHC

17. Determining mSUGRA Parameters 17 Measurement of Dark Matter Content at the LHC

18. Mass Measurements  mSUGRA M  peak, M eff (b)peak …. Sensitive to A 0, tan  m   and  m 1/2 M j  peak, M eff peak …. Sensitive to m 0, m 1/2 18 Measurement of Dark Matter Content at the LHC

19. Determining mSUGRA Parameters Solved by inverting the following functions: 10 fb -1 19 Phys. Rev. Lett. 100, (2008) 231802 Measurement of Dark Matter Content at the LHC

20. Focus Point (FP) m 0 is large, m 1/2 can be small, e.g., m 0 = 3550 GeV, m 1/2 =314 GeV, tan  =10, A0=0 20 Measurement of Dark Matter Content at the LHC M(gluino) = 889 GeV, ΔM(χ 3 0 - χ 1 0 ) = 81 GeV, ΔM(χ 2 0 - χ 1 0 ) = 59 GeV, ΔM(χ 3 0 - χ 2 0 ) = 22 GeV Br(g → χ 2 0 tt) = 10.2% Br(g → χ 2 0 uu) = 0.8% Br(g → χ 3 0 tt) = 11.1% Br(g → χ 3 0 uu) = 0.009% ~ ~ ~ ~ - - - -

21. M(ll) (GeV) Events/GeV Measurement of Dark Matter Content at the LHC 21 Dilepton Mass at FP Baer, Barger, Salughnessy, Summy, Wang, PRD, 75, 095010 (2007), Crockett, Dutta, Flanagan, Gurrola, Kamon, Kolev, VanDyke, 08;

22. Measurement of Dark Matter Content at the LHC 22 Determination of masses: FP Relic density calculation depends on , tan  and m 1/2 All other masses are heavy m 1/2  and tan  can be solved from M(gluino), ΔM (χ 3 0 - χ 1 0 ) and ΔM (χ 2 0 - χ 1 0 ) M(gluino), ΔM (χ 3 0 - χ 1 0 ) and ΔM (χ 2 0 - χ 1 0 ) can be measured with an accuracy of ~ 10% Higher jet, b-jet, lepton multiplicity requirement increase the signal over background rate

23. [1] Established the CA region by detecting low energy  ’s (p T vis > 20 GeV) [2] Determined SUSY masses using: M , Slope, M j , M j , M eff e.g., Peak(M  ) = f (M gluino, M stau, M, M ) Gaugino universality test at ~15% (10 fb -1 ) [3] Measured the dark matter relic density by determining m 0, m 1/2, tan , and A 0 using M j , M eff, M , and M eff (b)Summary 0 1  ~ 0 2  ~ 23 Measurement of Dark Matter Content at the LHC

24. Summary… [4] For large m 0, when staus are not present, the mSUGRA parameters can still be extracted, but with less accuracy [6] It will be interesting to determine nonuniversal model Parameters, e.g.,  (Higgs sector nonuniversality) work in progress… [5] This analysis can be applied to any SUSY model Measurement of Dark Matter Content at the LHC