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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.

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Presentation on theme: "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."— Presentation transcript:

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


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