1. Measurement of Relic Density at the LHC1 Bhaskar Dutta Texas A&M University Bhaskar Dutta Texas A&M University Measurement of Relic Density at the LHC Collaborators: R. Arnowitt, A. Gurrola, T. Kamon, A. Krislock, D. Toback Arxiv: Phys. Lett.B: 649:73, 2007; 639:46, 2006

2. Measurement of Relic Density at the LHC 2 The signal to look for: 4 jet + missing E T SUSY in Early Stage at the LHC (or l + l -,  )

3. Measurement of Relic Density at the LHC 3 Kinematical Cuts and Event Selection  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 ] Hinchliffe et al. Phys. Rev. D 55 (1997) 5520 Example Analysis

4. Measurement of Relic Density at the LHC 4 SUSY scale is measured with an accuracy of 10-20%  This measurement does not tell us whether the model can generate the right amount of dark matter  The dark matter content is measured with an accuracy of around 6% at WMAP  Question: To what accuracy can we calculate the relic density based on the measurements at the LHC? Relic Density and M eff

5. Measurement of Relic Density at the LHC 5 We establish dark matter allowed regions from the detailed features of the signals. We accurately measure the masses and model parameters (all four mSUGRA parameters). We calculate the relic density and compare that with WMAP observation. Analysis Strategy

6. Measurement of Relic Density at the LHC6 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 couping 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 couping 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. 2.2x10  4 < Br (b  s  ) < 4.5x10  4 iii. iv. (g  2)  Experimental Constraints : 3  descripency

7. Measurement of Relic Density at the LHC 7 Dark Matter Allowed Regions We choose mSUGRA model. However, the results can be generalized. Neutralino-stau coannihilation region [In this talk] Focus point region – the lightest neutralino has a larger higgsino component A-annihilation funnel region – This appears for large values of m 1/2

8. Measurement of Relic Density at the LHC 8 +… In the stau-neutralino coannihilation region Griest, Seckel ’91 Relic Density Calculation

9. Measurement of Relic Density at the LHC9 Our Reference Point m 1/2 = 351, m 0 = 210, tan  = 40,  >0, A 0 = 0 [ISAJET version 7.69]

10. Measurement of Relic Density at the LHC10 SUSY Anatomy M eff (4 jets + E T miss ) M(j  ) M(  ) pT()pT() pT()pT() 100% 97% SUSY Masses (CDM) E T miss + jets + >2 

11. Measurement of Relic Density at the LHC11 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

12. Measurement of Relic Density at the LHC12 180 Measurement of Relic Density at the LHC12

13. Measurement of Relic Density at the LHC13 M  Distribution Clean peak even for low  M We choose the peak position as an observable.

14. Measurement of Relic Density at the LHC14 M  Distribution M peak  depends on m 0, m 1/2, A 0 and tan 

15. Measurement of Relic Density at the LHC15 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.

16. Measurement of Relic Density at the LHC16 M j  Distribution M peak depends on m 0, m 1/2 j 

17. Measurement of Relic Density at the LHC17 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 ]

18. Measurement of Relic Density at the LHC18 M eff peak vs. m 0, m 1/2 M eff peak …. insensitive to A 0 and tan . m 1/2 (GeV)m 0 (GeV)

19. Measurement of Relic Density at the LHC19 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

20. Measurement of Relic Density at the LHC20 M eff (b)peak vs. X M eff (b)peak …. sensitive to A 0 and tan . A0A0 tan  m 1/2 m0m0

21. Measurement of Relic Density at the LHC21 Determining Model Parameters The Model parameters are solved by inverting the following functions: m 0 =205 4; m 1/2 =350 4.2; A 0 =0 16; tan  = 40 0.8 (10 fb -1 ) We can also determine the sparticle masses using these observables and a few additional ones, e.g., M (peak) j  , etc Gaugino Universality can be checked (at 15% level)! =748 25; =831 21; =10.6 2; =141 19; = 260 15;

22. Measurement of Relic Density at the LHC22 Relic Density and Luminosity How does the uncertainty in the Dark Matter relic density change with Luminosity?  h 2 /  h 2 ~ 6% (30 fb -1 ) L= 50 fb -1 L= 10 fb -1

23. Measurement of Relic Density at the LHC23  h 2 /  h 2 ~ 6% (30 fb -1 ) Analysis with visible E T  > 20 GeV establishes stau- neutralino coannihilation region  M eff will establish the existence of SUSY Different observables are needed to establish the dark matter allowed regions in a SUSY model at the LHC  Squark, Gluino, stau, neutralino(1,2) can be determined without using mSUGRA assumptions Gaugino universality can be checked at 15% level Conclusion The mSUGRA parameters are determined using : 1) M eff peak 2)M j  peak 3)M  peak 4) M eff peak (b) m 0 =205 4; m 1/2 =350 4.2; A 0 =0 16; tan  = 40 0.8 (10 fb -1 )