1. June 8, 2007DSU 2007, Minnesota Relic Density at the LHC B. Dutta In Collaboration With: R. Arnowitt, A. Gurrola, T. Kamon, A. Krislock, D. Toback Phys. Lett. B 639 (2006) 46; B 649 (2007) 73; To appear Texas A&M University

2. The signal to look for: 4 jet + missing E T SUSY in Early Stage 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 ] Phys. Rev. D 55 (1997) 5520 Example Analysis

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 to be 23% with an accuracy of around 5% 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. We establish the dark matter allowed regions from the detailed features of the signals. We accurately measure the masses. We calculate the relic density and compare with WMAP. Strategy

6. 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

7. Dark Matter Allowed Regions We choose mSUGRA model. However, the results can be generalized. Neutralino-stau coannihilation 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

8. +… In the stau neutralino coannihilation region Griest, Seckel ’91 Relic Density Calculation

9. 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

10. tan  = 40,  > 0, A 0 = 0 Can we measure  M at colliders? Coannihilation Region

11. SUSY Signals at the LHC In Coannihilation Region of SUSY Parameter Space: Soft  pppp Hard  Final state: 3/4  s+jets +missing energy Use hadronically decaying  Soft  Trigger on the jets and missing ET

12. 1. Sort τ’s by E T (E T 1 > E T 2 > …) and use OS-LS method to extract  pairs from the decays 2. Use counting method (N OS-LS ) & ditau invariant mass (M  ) to measure mass difference  M (between the lightest stau and the neutralino) and gluino mass 3. Measure the P T of the low energy  to estimate the mass difference  M Three Observables

13. Since we are using 3 variables, we can measure  M, M gluino and the universality relation of the gaugino masses i.e. M gluino measured from the M eff method may not be accurate for this parameter space since the tau jets may pass as jets in the M eff observable. The accuracy of measuring these parameters are important for calculating relic density. SUSY Parameters

14. high energy  High Energy Proton-Proton collisions produce lots of Squarks and Gluinos which eventually decay Identify a special decay chain that can reveal  M information low energy  A Smoking Gun at the LHC?

15. Version 7.69 (m 1/2 = 347.88, m 0 = 201.1)  M gluino = 831 Chose di-  pairs from neutralino decays with (a) |  | < 2.5 (b)  = hadronically-decaying tau 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 E T  > 20 GeV is essential! M  vis in ISAJET

16. EVENTS WITH CORRECT FINAL STATE : 2  + 2j + E T miss APPLY CUTS TO REDUCE SM BACKGROUND (W+jets, …) E T miss > 180 GeV, E T j1 > 100 GeV, E T j2 > 100 GeV, E T miss + E T j1 + E T j2 > 600 GeV ORDER TAUS BY P T & APPLY CUTS ON TAUS: WE EXPECT A SOFT  AND A HARD  P T all > 20 GeV, P T  1 > 40 GeV LOOK AT  PAIRS AND CATEGORIZE THEM AS OPPOSITE SIGN (OS) OR LIKE SIGN (LS) OS: FILL LOW OS P T HISTOGRAM WITH P T OF SOFTER  FILL HIGH OS P T HISTOGRAM WITH P T OF HARDER  LS: FILL LOW LS P T HISTOGRAM WITH P T OF SOFTER  FILL HIGH LS P T HISTOGRAM WITH P T OF HARDER  LOW OS HIGH OS LOW LS HIGH LS LOW OS-LS HIGH OS-LS E T miss + 2j + 2  Analysis Path

17. E T miss + 2j + 2  Analysis [1] ISAJET + ATLFAST sample of E T miss, 2 jets, and at least 2 taus with p T vis > 40, 20 GeV and   = 50%, fake (f j   ) = 1%. Optimized cuts : E T jet1 > 100 GeV; E T jet2 > 100 GeV; E T miss > 180 GeV; E T jet1 + E T jet2 + E T miss > 600 GeV [2] Number of SUSY and SM events (10 fb  1 ): Top: 115 events W+jets: 44 events SUSY : 590 events top SUSY M gluino = 830 GeV  M = 10.6 GeV) E T miss + 2j + 2  Analysis

18. A small  M can be detected in first few years of LHC. 10-20 fb  1 +5%  5% [Assumption] The gluino mass is measured with  M/M gluino =  5% in a separate analysis. 2  : Discovery Luminosity

19. Also, get more events for large  M Slope of P T distribution contains ΔM Information Slope of P T distribution is largely unaffected by Gluino Mass Low energy  ’s are an enormous challenge for the detectors P T Distribution of our softest 

20. Look at the mass of the    - in the events Can use the same sample to subtract off the non-  2 backgrounds  Clean peak! Larger  M:  More events  Larger mass peak Clean peak Even for low  M More Observables

21. The slope of the P T distribution of the t’s only depends on the  M The event rate depends on both the Gluino mass and  M Can make a simultaneous measurement An important measurement without Universality assumptions ! Results for ~300 events (10 fb -1 depending on the Analysis ) Measurement of  M and Gluino Mass

22. Peak of M  As the neutralino masses rise the M tt peak rises Peak of M 

23. } ~15 GeV or ~3% Universal scenario?

24. Results for ~300 events (10 fb -1 depending on the Analysis) } ~15 GeV or ~2% } ~ 0.5 GeV or ~5% Assuming Universality

25.  M and M gluino  m 0 and m 1/2 (for fixed A 0 and tan  We determine  m 0 /m 0 ~ 1.2% and  m 1/2 /m 1/2 ~2 % (for A 0 =0, tan  =40) (at 10 fb -1 ) Determination of m 0 and m 1/2

26.  M and M gluino  (for fixed A 0 and tan  )  h 2 /  h 2 ~ 7% (10 fb -1 ) (for A 0 =0, tan  =40) Determination of Relic Density

27.  h 2 /  h 2 ~ 7% for A 0 =0, tan  =40 (10 fb -1 ) Analysis with visible E T  > 20 GeV establishes stau- neutralino coannihilation region 2  analysis: Discovery with 10 fb  1   M  /  M ~ 5%,  m g  /m g ~ 2% using M peak, N OS-LS and p T The analyses can be done for the other models that don’t suppress  2 0 production.  M eff will establish the existence of SUSY Different observables are needed to establish the dark matter allowed regions in SUSY model at the LHC  Universality of gaugino masses can be checked Conclusion

28. Backups

29. E T miss + 2j + 2  Analysis [1] ISAJET + ATLFAST sample of E T miss, 2 jets, and at least 2 taus with p T vis > 40, 20 GeV and   = 50%, fake (f j   ) = 1%. Optimized cuts : E T jet1 > 100 GeV; E T jet2 > 100 GeV; E T miss > 180 GeV; E T jet1 + E T jet2 + E T miss > 600 GeV [2] Number of SUSY and SM events (10 fb  1 ): Top: 115 events W+jets: 44 events SUSY : 590 events top SUSY M gluino = 830 GeV  M = 10.6 GeV)

30. A small  M can be detected in first few years of LHC. 10-20 fb  1 2  Analysis : Discovery Luminosity +5%  5% [Assumption] The gluino mass is measured with  M/M gluino =  5% in a separate analysis. Negligible f j   dependence