1. Determining Wh2 at the LHC
- mSUGRA Co-annihilation Case -
Teruki Kamon
Collaborators R. Arnowitt, B. Dutta, A. Gurrola, A. Krislock, D. Toback
Department of Physics, Texas A&M University
NUNPAC Seminar, New Mexico University March 11, 2008
3/11/08
Determining Dark Matter Relic Density at the LHC

2. Determining Dark Matter Relic Density at the LHC
OUTLINE
Dark Matter (DM) in Universe
DM Particle in SUSY & DM Density (Wh2 )
Cosmological Connection in the mSUGRA Co-annihilation (CA) Region
DM Density (Wh2 ) at the LHC
Summary
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Determining Dark Matter Relic Density at the LHC

3. Probing the susy Dark Matter
The LHC - Accelerator
WSUSY DM ≟ WCDM
Production
& Decay
DM !
Detector
Talk
DM Hunters
- Analyzer
Today’s
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Determining Dark Matter Relic Density at the LHC

4. Dark Matter Relic Density at the LHC
arXiv: (hep-ph)
Also see the previous publications:
Arnowitt, Arusano, Dutta, Kamon, Kolev, Simeon, Toback, Wagner, PLB 649 (2007) 73
Arnowitt, Dutta, Kamon, Kolev, Toback, PLB 639 (2006) 46
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Dark Matter Relic Density at the LHC

5. Dark Matter (DM) in Universe
splitting normal matter and dark matter apart
– Another Clear Evidence of Dark Matter –
(8/21/06) 1
Ordinary Matter
(NASA’s Chandra X
Observatory)
time 2 3 4
Approximately
the same size as
the Milky Way
Dark Matter
(Gravitational Lensing)
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Dark Matter Relic Density at the LHC

6. Dark Matter Relic Density at the LHC
DM Particle in SUSY
Astrophysics
SUSY
CDM = Neutralino ( )
SUSY is an interesting class of models to provide a weakly interacting massive neutral particle (M ~ 100 GeV).
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Dark Matter Relic Density at the LHC

7. DM Particle in the SM? I’m hungry.
Can you make the DM sandwich with any Standard Model particles?
No, sir.
But with c10?
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Dark Matter Relic Density at the LHC

8. Determining Dark Matter Relic Density at the LHC
DM SANDWICH
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Determining Dark Matter Relic Density at the LHC

9. Co-annihilation (CA) Process
Anatomy of sann
+ …. +
+ ….
Co-annihilation (CA) Process
Griest, Seckel ’91
An accidental near degeneracy occurs naturally for light stau in many models.
Our benchmark study = mSUGRA
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Dark Matter Relic Density at the LHC

10. + Minimal Supergravity (mSUGRA) b 4 parameters + 1 sign
SUSY model in the framework of unification:
<Hd>
<Hu>
<H> = 246 GeV b +
4 parameters + 1 sign
tanb <Hu>/<Hd> at MZ
m1/ Common gaugino mass at MGUT
m Common scalar mass at MGUT
A Trilinear couping at MGUT
sign(m) Sign of m in W(2) = m Hu Hd
Key Experimental Constraints
MHiggs > 114 GeV
Mchargino > 104 GeV
2.2x10-4 <B(b  s g) <4.5x10-4
(g-2)m : 3 s deviation from SM
Chamseddine, Arnowitt, Nath, PRL 49 (1982) 970;
NPB 227 (1983) 121.
Hall, Lykken, Weinberg, PRD 27 (1983) 2359.
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Dark Matter Relic Density at the LHC

11. DM Allowed Regions (Illustration)
Mass of Squarks and Sleptons
Mass of Gauginos
No CDM Candidate
Excluded
(Magnetic
Moment of
Muon)
(Rare B Decay b  sg )
(Higgs mass)
CDM allowed region
Magnetic Moment of Muon
Higgs Mass (Mh)
Branching Ratio b  sg
Co-annihilation Region
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Dark Matter Relic Density at the LHC

12. DM Allowed Regions in mSUGRA Dark Matter Relic Density at the LHC
[Focus point region]
The lightest neutralino has a larger Higgsino component
[A-annihilation funnel region]
This appears for large values of m1/2
[Stau-Neutralino CA region]
[Bulk region]
Almost ruled out …
Above is the case of mSUGRA model. However, the results can be generalized.
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Dark Matter Relic Density at the LHC

13. Can we measure DM at colliders? Dark Matter Relic Density at the LHC
CA Region at tanb = 40
Can we measure DM at colliders?
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Dark Matter Relic Density at the LHC

14. Smoking Gun of CA Region Dark Matter Relic Density at the LHC
Reference Point
m1/2 = 350, m0 = 210
tanb = 40, A0 = 0, m >0
[ISAJET version 7.64]
SUSY Masses
Unique kinematics
97%
100%
(CDM)
2 quarks+2 t’s
+CDM particle
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Dark Matter Relic Density at the LHC

15. Dark Matter Relic Density at the LHC
Most Wanted!
This is one of the key reactions to discover the neutralinos at the LHC.
We will have to extract this reaction out of many trillion pp collisions and measure SUSY masses.
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Dark Matter Relic Density at the LHC

16. Wc ≟ 0.23 Dark particle hunting
[SUSY DM particles at the LHC] ≟ [DM in the Universe]
Well, I (a theorist) can calculate the amount of the SUSY dark matter (W)
in the Universe
(using a model of the Universe).
Wc ≟ 0.23
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Dark Matter Relic Density at the LHC

17. Dark Matter Relic Density at the LHC
Goals
Establish the “CA region” signal
Determine SUSY masses and mSUGRA parameters
Measure Wch2 and compare with WCDMh2
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Dark Matter Relic Density at the LHC

18. Dark Matter Relic Density at the LHC
Analysis Strategy
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Dark Matter Relic Density at the LHC

19. Dark Matter Relic Density at the LHC
Excess in ETmiss + Jets
Excess in ETmiss + Jets  R-parity conserving SUSY
Meff  Measurement of the SUSY scale at 10-20%.
Hinchliffe and Paige, Phys. Rev. D 55 (1997) 5520
ETj1 > 100 GeV, ETj2,3,4 > 50 GeV
Meff > 400 GeV (Meff  ETj1+ETj2+ETj3+ETj4+ ETmiss)
ETmiss > max [100, 0.2 Meff]
HM1: High Mass Scenario 1
m1/2= 250, m0= 60; s = 45 fb
M(gluino) = 1886; M(squark) = 1721 q
The heavy SUSY particle mass is measured by
combining the final state particles
CMS
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Dark Matter Relic Density at the LHC

20. Dark Matter Relic Density at the LHC
Dilepton Endpoint
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 c20 decay in dilepton (ee, mm, tt) channels for reconstruction of decay chain.
LM1:
(Low Mass Case 1)
m1/2= 180, m0= 850;
s = 55 pb
[post-WMAP benchmark
point B’]
M(gluino) = 611
M(squark) = 559
gluino  squark+quark
B(c20 slepR lep) = 11.2%
B(c20  stau1 tau) = 46%
B(c1+  sneuL lep) = 36%
Spiropoulou
(SUSY2007)
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Dark Matter Relic Density at the LHC

21. Dilepton Endpoint in CA Region Dark Matter Relic Density at the LHC
In the CA region, the ee and mm channels are almost absent. We are in a different game:
Br(c20  eec20, mmc10) ~ 0%
Br(c20  ttc10) ~ 100%
DM = 5-15 GeV
Questions:
How can we establish the DM allowed regions?
To what accuracy can we calculate the relic density based on the measurements at the LHC?
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Dark Matter Relic Density at the LHC

22. Dark Matter Relic Density at the LHC
SUSY Anatomy I
100%
97%
SUSY Masses
(CDM)
M(jtt)
M(tt)
Meff
pT(t)
ETmiss + jets + >2t
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Dark Matter Relic Density at the LHC

23. Dark Matter Relic Density at the LHC
pTsoft Slope and Mtt
pT and Mtt distributions in true di-t pairs from neutralino decay with |h| < 2.5
Number of Counts / 2 GeV
Slope of pT distribution of “soft t” contains ΔM information
Low energy t’s are an enormous challenge for the detectors
ETvis(true) > 20, 20 GeV
Number of Counts / 1 GeV
ETvis(true) > 40, 20 GeV
ETvis(true) > 40, 40 GeV
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Dark Matter Relic Density at the LHC

24. Warming-up Quizzes Hadronic or leptonic? How low in pT?
Hadronic, because e or m does not tell us the evidence of tau leptons
How low in pT?
CDF : pTvis >15-20 GeV
Worries about triggers at the LHC?
ETmiss + jet trigger for SUSY
Lepton+tau trigger for Z’s (calibration)
[Assumption]
et = 50% , fake rate 1% for pTvis > 20 GeV
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Dark Matter Relic Density at the LHC

25. Dark Matter Relic Density at the LHC
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Dark Matter Relic Density at the LHC

26. Mtt Distribution Clean peak even for low DM
We choose the peak position as an observable.
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Dark Matter Relic Density at the LHC

27. Dark Matter Relic Density at the LHC
180
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Dark Matter Relic Density at the LHC

28. Dark Matter Relic Density at the LHC
OS-LS Slope(pTsoft ) OS
OS-LS
Mtt < Mttend point LS
pTvis (GeV)
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Dark Matter Relic Density at the LHC

29. Dark Matter Relic Density at the LHC
Slope(pTsoft ) vs. X
Uncertainty Bands with 10 fb-1
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Dark Matter Relic Density at the LHC

30. Dark Matter Relic Density at the LHC
Mtt peak vs. X
Uncertainty Bands
with 10 fb-1
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Dark Matter Relic Density at the LHC

31. Dark Matter Relic Density at the LHC
SUSY Anatomy II
100%
97%
SUSY Masses
(CDM)
Mjtt
Mtt
Meff
pT(t)
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Dark Matter Relic Density at the LHC

32. Mjtt Distribution Mtt < Mttendpoint Jets with ET > 100 GeV
Mjtt masses for each jet
Choose the 2nd large value
 Mjtt(2)
“other” jet
gluinosquark + j
Peak value ~ True Value
We choose the peak position as an observable.
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Dark Matter Relic Density at the LHC

33. Dark Matter Relic Density at the LHC
Mjttpeak vs. X
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Dark Matter Relic Density at the LHC

34. Dark Matter Relic Density at the LHC
SUSY Anatomy III
100%
97%
SUSY Masses
(CDM)
Mjtt
Mtt
Meff
pT(t)
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Dark Matter Relic Density at the LHC

35. Dark Matter Relic Density at the LHC
Meff Distribution
ETj1 > 100 GeV, ETj2,3,4 > 50 GeV [No e’s, m’s with pT > 20 GeV]
Meff > 400 GeV (Meff  ETj1+ETj2+ETj3+ETj4+ ETmiss [No b jets; eb ~ 50%])
ETmiss > max [100, 0.2 Meff]
At Reference Point
Meffpeak = 1220 GeV
(m1/2 = 335 GeV)
Meffpeak = 1331 GeV
(m1/2 = 365 GeV)
Meffpeak = 1274 GeV
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Dark Matter Relic Density at the LHC

36. Determining SUSY Masses (10 fb-1)
6 equations for 5 SUSY masses
26015 GeV
1s ellipse
10 fb-1
Invert the equations to determine the masses
We test a gaugino univesality at 15% level.
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Dark Matter Relic Density at the LHC

37. DM Relic Density in mSUGRA Dark Matter Relic Density at the LHC
[1] Established the CA region by detecting low energy t’s (pTvis > 20 GeV)
[2] Determined SUSY masses using:
Mtt, Slope, Mjtt, Mjt, Meff
e.g., Peak(Mtt) = f (Mgluino, Mstau, M , M )
Gaugino universality test at ~15% (10 fb-1)
[3] Measure the dark matter relic density by determining m0, m1/2, tanb, and A0 1 c ~ 2
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Dark Matter Relic Density at the LHC

38. Determining mSUGRA Parameters Dark Matter Relic Density at the LHC
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Dark Matter Relic Density at the LHC

39. Dark Matter Relic Density at the LHC
Introducing Meff(b)
ETj1 > 100 GeV, ETj2,3,4 > 50 GeV [No e’s, m’s with pT > 20 GeV]
Meff(b) > 400 GeV (Meff(b)  ETj1=b+ETj2+ETj3+ETj4+ ETmiss [j1 = b jet])
ETmiss > max [100, 0.2 Meff]
Meff(b)peak = 933 GeV
(m1/2 = 335 GeV)
Meff(b)peak = 1122 GeV
(m1/2 = 365 GeV)
At Reference Point
Meff(b)peak = 1026 GeV
Meff(b)peak
Meff(b)peak
Meff(b) can be used to determine A0 and tanb even
without measuring stop and sbottom masses
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Dark Matter Relic Density at the LHC

40. Mass Measurements  mSUGRA Dark Matter Relic Density at the LHC
Meff(b)peak & Mttpeak …. Sensitive to A0 and tanb
[Meffpeak …. Insensitive to A0 and tanb]
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Dark Matter Relic Density at the LHC

41. Determining mSUGRA Parameters Dark Matter Relic Density at the LHC
Solved by inverting the following functions:
10 fb-1
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Dark Matter Relic Density at the LHC

42. Dark Matter Relic Density at the LHC
Summary
[1] Established the CA region by detecting low energy t’s (pTvis > 20 GeV)
[2] Determined SUSY masses using:
Mtt, Slope, Mjtt, Mjt, Meff
e.g., Peak(Mtt) = f (Mgluino, Mstau, M , M )
Gaugino universality test at ~15% (10 fb-1)
[3] Measured the dark matter relic density by determining m0, m1/2, tanb, and A0 using Mjtt, Meff, Mtt, and Meff(b) 1 c ~ 2
3/11/08
Dark Matter Relic Density at the LHC