1. Probing Supersymmetric Cosmology at the LHC Alfredo Gurrola On behalf of TAMU (full list of collaborators in the slides to follow) Karlsruhe, Germany - August 19, 2009 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 1

2. Outline Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 2  Motivation  Goals  General approach to extracting Dark Matter relic density  Case studies:  Co-Annihilation  Focus point  Over-dense Dark Matter region  Work in progress

3. Motivation: Content of the Universe “Normal” Matter Still Unknown Does not interact with light (“invisible”) Relic Density Relic Density: A measure of the density of dark matter left in the universe Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 3

4.  Our main goal is to develop techniques/methods to extract the relic density from measurements at the Large Hadron Collider.  Relic density calculation depends on the particular case of interest:Goal Standard Cosmology Non-Standard Cosmology [Case 1] “Coannihilation (CA)” Region Arnowitt, Dutta, Gurrola, Kamon, PRL100 (2008) 231802 Krislock, Toback, PRL100 (2008) 231802 For earlier studies, see Arnowitt et al., PLB 649 (2007) 73; Arnowitt et al., PLB 639 (2006) 46 [Case 2] “Over-dense” Region Dutta, Gurrola, Kamon, Krislock, Lahanas, Mavromatos, Nanopoulos PRD 79 (2009) 055002 [Case 3] “HB/Focus Point” Region Arnowitt, Dutta, Flanagan, Gurrola, Kamon, Kolev, Krislock Supercritical String Cosmology e.g., Rolling dilation in Q-cosmology Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 4

5. General Approach  We want to take a general approach that is “independent” (to the largest possible extent) of the particular model or scenario we are targeting: Measure the global SUSY scale - Allows us to filter out models/scenarios that are not consistent with the global scale1 Identify smoking-gun variables - e.g. Different points in SUSY parameter space can allow for similar global scales. We need to find the “smoking-gun” variables to discriminate between them2 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 5

6. General Approach  We want to take a general approach that is “independent” (to the largest possible extent) of the particular model or scenario we are targeting: Parameterize variables in terms of “physical” values (SUSY masses) & model parameters - The parameterization is done by varying one SUSY mass or model parameter at a time, while keeping other masses/parameter constant3 Determine SUSY masses 4 Determine model parameters - We can also use the determination of the SUSY masses to test e.g. gaugino universality.5  ≟ ? ≟ ?6 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 6

7. mSUGRA (Benchmark Scenario) At the Grand Unified Scale: 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 ) Determines the particle masses at the electroweak scale by solving the Renormalization Group Equations Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 7

8. mSUGRA (Benchmark Scenario) At the Grand Unified Scale: 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 ) Key experimental constraints Jegerlehner and Nyffeler, arXiv:0902.3360 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 8

9. Case 1: Co-Annihilation Region Within this framework, let’s look at the 1 st dark matter allowed region: Co-Annhilation region tan  = 40 A 0 = 0,  > 0 a b c m 0 (GeV) m 1/2 (GeV) Coannihilation Region 1 Excluded by 1)Rare B decay b  s  2)No CDM candidate 3)Muon magnetic moment a b c Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 9

10. Case 1: Co-Annihilation Region At the Grand Unified Scale: 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 ) Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 10 Case 1 benchmark point: m 0 = 210 m 1/2 = 350 tan  = 40 A 0 = 0 sign(  )>0

11. 1., Production is dominant SUSY process at LHC ( ) 2. Interested in events with or pairs 3. & Branching Ratios are ~ 97% Case 1: Signature at LHC Excess in 3 final states:,, Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 11

12. Case 1: Event Selection  In order to target events with, we require ≥ 2 hadronic  ’s    = 50%, f fake = 1% for p T vis > 20 GeV (CDF based)  Require large Missing Transverse Energy to target events with  High P T jets are required to target events with squarks/gluinos [1] References hep-ph/0608193, Phys. Lett. B649 (2007) 73. R. Arnowitt et al a. b. c. d. Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 12

13. Case 1: Smoking Gun Observables Sort τ’s by E T (E T1 > E T2 > …) & use OS-LS method to extract  pairs from the decays on a statistical basis Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 13

14. Case 1: Smoking Gun Observables What is the dependence on the other SUSY masses? Slope of the soft  P T distribution has a  M dependence hep-ph/0603128 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 14 Slope of P T distribution contains ΔM Information.

15. Case 1: More Observables pp We can combine the  ’s to the jet from the squark decay to provide another mass peak  M  < M  endpoint  Jets with E T > 100 GeV  M j  masses for each jet  Choose the 2 nd largest value  Peak value ~ “True” Value Squark = 660 GeV Squark = 840 GeV Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 15

16.  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 ] Case 1: More Observables - Meff m 1/2 = 335 GeV M eff peak = 1220 GeV m 1/2 = 351 GeV M eff peak = 1274 GeV m 1/2 = 365 GeV M eff peak = 1331 GeV Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 16

17. We have 6 observables defined as functions of 5 SUSY masses Case 1: SUSY Mass Determination  Inverting Eqs. 10 fb -1 141  19 GeV Testing gaugino universality at 15% level. Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 17

18. Case 1: mSUGRA Parameters Established the Co-Annihilation region detected low energy taus (p T vis > 20 GeV) observed the “smoking-gun” ditau mass Determined SUSY Masses e.g. LSP mass was measured to ~14% tested gaugino universality to ~15% (10 fb -1 ) Determining mSUGRA parameters mSUGRA parameters cannot be determined directly from the SUSY masses → we need an observable that can provide us with another independent function of A 0 and tan  In general, it is NOT true that the determination of the SUSY masses from the mSUGRA parameters will give correct results (e.g. gaugino universality does not hold true) Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 18

19.  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 ] Case 1: More Observables - Meff (b) M eff ( b ) can be used to probe A 0 and tan  without measuring stop and sbottom masses tan  = 48 M eff (b)peak = 933 GeV tan  = 40 M eff (b)peak = 1026 GeV tan  = 32 M eff (b)peak = 1122 GeV M eff (b)peak (GeV) Arbitrary Scale units Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 19

20. Solved by inverting the following functions: 10 fb -1 Case 1: mSUGRA Parameters Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 20

21. Conclusion Case No.2 Suspect Over- dense DM Report PRD 79 (2009) 055002 Minimal SUGRA m 1/2 m0m0 Lahanas, Mavromatos, Nanopoulos, PLB 649 (2007) 63 A 0 = 0, tan  = 40 Smoking gun signals in the region? Dilaton effect creates new parameter space. Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 21

22. m 1/2 = 440 GeV; m 0 = 471 GeV m 1/2 = 600 GeV; m 0 = 440 GeV 86.8% 77.0% 2 Reference Points Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 22

23. Case 2(a) : Higgs m 1/2 =440, m 0 =471, tan  =40, m top =175 87% 1041 1044 500 393 181 341 114 462 13% 91 N(b) > 2 with P T > 100 GeV; 0.4<  R bb < 1 E T miss > 180 GeV; N(jet) > 2 with E T > 200 GeV; E T miss + E T j1 + E T j2 > 600 GeV Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 23

24. w/ side-band BG subtraction where: M eff  E T j1 +E T j2 +E T j3 +E T j4 + E T miss [No b jets;  b ~ 50%] M eff (b)  E T j1=b +E T j2 +E T j3 +E T j4 + E T miss M eff (bb)  E T j1=b +E T j2=b +E T j3 +E T j4 + E T miss 4 Kinematical Variables Side-band BG subtraction Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 24

25. Band = Uncertainties with 1000 fb -1 Kinematical Templates Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 25

26. Determining mSUGRA Parameters Solved by inverting the following functions: Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 26

27. Determining  h 2 Solved by inverting the following functions: 1000 fb -1 Note: These regions have large  h 2 if one just calculate based on standard cosmology. We put a factor of 0.1 for this non-standard cosmology. Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 27

28. Case 2(b) : Stau and Higgs m 1/2 =600, m 0 =440, tan  =40, m top =175 20.5% 1366 1252 494 376 249 462 114 462 77% Follow Case 2(a) and Case 1 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 28

29. Determining  h 2 Solved by inverting the following functions: 500 fb -1 b/c stau helps to determine tan  accurately. Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 29

30. Case 2 Summary Over-dense Dark Matter Region:  OD-CDM ~  CDM /10 Implication at the LHC: Higgs Region where  2 0 decays to Higgs  CDM /  CDM ~ 150% (1000 fb -1 ) stauHiggs Region where  2 0 decays to stau and Higgs  CDM /  CDM ~ 20% (500 fb -1 ) Future Work: o More over-dense and under-dense cases? Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 30

31. Case No.3 SuspectHB/FP Report In progress Minimal SUGRA Prospects at the LHC A few mass measurements are available: 2 nd and 3 rd neutralinos, and gluinoQuestion Can we make a cosmological measurement? Z Z Z Z Abram Krislock’s image of HB/FP, October 18, 2008 m 0, A 0, , tan  m 1/2,  tan  Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 31

32. A 4x4 (m 1/2, , tan  ) Part 1 : New to Probe  h 2 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 32

33.  D 21 and  D 32  and  tan   D 21 and  D 32   and  tan   D 21 / D 21  D 31 / D 31  tan  / tan   /  assuming Example (  = 195, tan  = 10): (1)D. Tovey, “Dark Matter Searches of ATLAS,” PPC 2007 (2)H. Baer et al., “Precision Gluino Mass at the LHC in SUSY Models with Decoupled Scalars,” Phys. Rev. D75, 095010 (2007), reporting 8% with 100 fb -1 (1) (2) 300 fb -1 Let’s test this idea: arbitrary scale Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 33

34.  h 2 Determination LHC Goal: D 21 and D 32 at 1-2% and gluino mass at 5% Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 34

35. Reconstructing two top quarks! e.g., "Perspectives for the detection and measurement of Supersymmetry in the focus point region of mSUGRA models with the ATLAS detector at LHC," U. De Sanctis, T. Lari, S. Montesano, C. Troncon, arXiv:0704.2515v1 [hep-ex] (Eur.Phys.J.C52:743-758,2007)  No gluino mass measurement. Question (& HW) Can we improve the gluino mass measurement by using a simultaneous detection of neutralinos and tops? Part 2 : Mass Measurements Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 35

36. CSI Summary Reports: mSUGRA tan  = 40 A 0 = 0,  > 0 a b c Excluded by 1)Rare B decay b  s  2)No CDM candidate 3)Muon magnetic moment a b c m 0 (GeV) m 1/2 (GeV) Over-dense DM Region Coannihilation Region HB/Focus Point Region Note: g  2 data may still be controversial. 1 2 3 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 36

37. “Smoking Gun Signal” Snapshots tan  = 40 A 0 = 0,  > 0 a b c Excluded by 1)Rare B decay b  s  2)No CDM candidate 3)Muon magnetic moment a b c m 0 (GeV) m 1/2 (GeV) LS OS OS  LS PRL100 (2008) 231802 PRD 79 (2009) 055002 T. Kamon, Talk at “The LHC and Dark Matter” Univ. of Michigan, Jan. 7, 2009 1 2 3 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 37

38. Goals Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 38  Our main goal is to develop techniques/methods to extract the relic density from measurements at the Large Hadron Collider.  Standard Cosmology vs. Non-Standard Cosmology  Standard:  mSUGRA Co-Annihilation Region  mSUGRA Focus Point Region  Non-Standard:  Over-dense Dark Matter Region  Minimal vs. Non-Minimal scenarios  Minimal: mSUGRA  Non-Minimal: Work in Progress (see backup slides)

39. Goals [Case 1] “Coannihilation (CA)” Region Arnowitt, Dutta, Gurrola, *) Kamon, PRL100 (2008) 231802 Krislock, *) Toback, PRL100 (2008) 231802 For earlier studies, see Arnowitt et al., PLB 649 (2007) 73; Arnowitt et al., PLB 639 (2006) 46 [Case 2] “Over-dense Dark Matter” Region Dutta, Gurrola, *) Kamon, Krislock, *) Lahanas, Mavromatos, Nanopoulos PRD 79 (2009) 055002 [Case 3] “HB/Focus Point” Region Arnowitt, Dutta, Flanagan, #) Gurrola, *) Kamon, Kolev, Krislock *) [Case 4] “Non-universality” Arnowitt, Dutta, Kamon, Kolev, Krislock *) [Case 5] New project 1 Dutta, Kamon, Krislock, *) Gupta *) Graduate student, #) REU student W   Constant in time? e.g., Quintessence – Scalar field dark energy [Case 6] New project 2 Allahverdi, Bornhauser, Dutta, Kamon, Richardson- McDaniel *) Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 39

40. SummaryGoal: Develop technique(s) to test minimal and non-minimal scenarios and extract  h 2 (standard and non-standard cosmology cases) at the LHC where a limited number of SUSY mass measurements are available. So far 4 cases were studied or are being studied: Case 1: Coannihilation region Case 2: Over-dense DM region (  OdCDM ~  CDM /10) Case 3: HB/Focus Point region Case 4: Non-universal Higgs Future:  Further improvements  New cases … in progress CSI: Cosmology at the LHC Collider Scene Investigation Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 40

41. Backup Slides

42. Case No.4 Suspect Non- universal Higgs Report In progress Non-minimal SUGRA [Non-universality Case] Is a cosmological measurement possible? 1)Start with over-abundance region in SSC-like mSUGRA (e.g., m 1/2 = 500, m 0 = 360, m Hu = 360) 2)Reduce Higgs coupling parameter, , by increasing m Hu (m 1/2 = 500, m 0 = 360, m Hu =732)  Extra contributions to  h 2  More annihilation (less abundance)  Normal values of  h 2 3)Find smoking gun signals 4)Technique to calculate  h 2

43. W’s

44. Start with “JW” N(j) > 2 with p T > 30 GeV N(b) > 0 with p T > 30 GeV N(  ) = 0 with p T > 20 GeV E T miss > 180 GeV; N(J) > 2 with E T > 200 GeV; E T miss + E T J1 + E T J2 > 600 GeV Note there might be b-jets and/or  -jets in event, but not counted as “J” nor “j”. 500-360-732 Endpoint = 774 GeV 739 GeV Ture = 739 GeV (  4 0 ) M JW 739 GeV Ture = 739 GeV (  4 0 ) & Jet Mix to extract W’s & 714 GeV Ture = 714 GeV (  1 +/  ) [Vetoing events with any  ’ s with p T > 20 GeV]

45. m Hu m 1/2 -m 0 -m Hu 732 500-360-732 694 500-360-694500-360-582 h2h2h2h2 0.1100.2110.462 M JW (q~  C1  W+N1) 714 (0.20*0.42) 813 (0.31*0.48) 867 (0.57*0.31) M JW (q~  C2  W+N2   h) 727 (0.46*0.92) 650 (0.35*0.54) 652 (0.087*0.30) M JW (q~  C2  W+N3  Z) 652 (0.46*0.18*0.46) NAN (0.35*0.00)NAN (0.087*0.00) M JW (q~  N4  W+C1) 739 (0.24*0.74) 654 (0.19*0.85) 650 (0.053*0.56) M bW (t1  C1  W+N1) 485550594 gluino1161 u L, u R 1113, 10781111, 10771111, 1076 b 1, b 2 ; t 1, t 2 946, 989; 781, 992948, 993; 787, 996954, 1005; 787, 996 C 1, C 2 291, 427329, 442376, 511 N 1 ~N 4 199, 293, 316, 432202, 328, 368, 445205, 375, 482, 511 500-360-694 M JW, shifting with m Hu 500-360-582500-360-732 867 813 739 Endpoint = 774 GeV 739 GeV Ture = 739 GeV (  4 0 ) Endpoint = 856 GeV 813 GeV Ture = 813 GeV (  1 +/- ) Endpoint = 900 GeV 867 GeV Ture = 867 GeV (  1 +/- )

46. Extraction of Model Parameters Work in Progress … Observable Model Parameters M eff (m 0, m 1/2 ) m 0, m 1/2 M J  (m 0, m 1/2 ) M JW (m 0, m 1/2,  (m Hu ), tan  ),  (m Hu ), tan  M W  (m 1/2,  (m Hu ), tan  ) M eff (b) (m 0, m 1/2,  (m Hu ), tan , A 0 ) A0A0

47. Case No.5 Suspect Hints from Tevatron Report In progress Minimal-type SO(10) Work in Progress …

48. Case No.6 Suspect ? Report In progress Non-minimal SUGRA Work in Progress …

49. B s  

50. From the Tevatron

51. B (B s  ) : “Prospect in 2002” and Now CDF(3.7 fb  1 ) CDF(1.9 fb  1 ) 51

52. Cases 1 & 2

53. OS  LS Slope (p T soft ) Uncertainty Bands with 10 fb -1 Independent of the gluino masses!

54. M j  Distribution 1) M  100 GeV; M j  masses for each jet 2) Choose the 2 nd large value  Peak value ~ True Value M j    (GeV)

55.  2 0 DecayBranching Ratios  2 0 Decay Branching Ratios m 1/2 = 500 GeV, m 0 = 470 GeV m 1/2 = 600 GeV, m 0 = 440 GeV

56. Case 3 56

57. Gluino Decays E T miss > 150 GeV  total = 3.1 pb OSDF OSSF 19%5.3%11%10% Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 36

58. Simultaneous Detection of Neutralinos and Top(s) Working on the gluino mass estimate … E T miss + Dilepton + Jets [1 ] N( ℓ ) > 2 p T > 10 GeV; |  | < 2.5 [2 ] E T miss > 150 GeV [3 ] Selection of W  jj p T (j) > 30 GeV; 0.4 <  R(j,j) < 1.5 M(jj) < 78  15 GeV [4 ] Selection of t  Wb p T (b) > 30 GeV 0.4 <  R(jj, b) < 2 Aug. 19, 2009 Probing Supersymmetric Cosmology at the LHC 37

59. Case 4 59

60. JetMix: Hunt for W  jj j i N(j i ) > 2 with p T > 30 GeV E T miss > 180 GeV; N(J) > 2 with E T > 200 GeV; E T miss + E T J1 + E T J2 > 600 GeV j i X M(j i j k ) j k X  1 For each j i in Event X, M(j i j k ) is calculated with j k in Event X  1 M(j i j k ) M(j i j k )  M(j i j k )  M(j i j k ) M(j i j k )

61.  e   e  [1] So far, the world of physics has been described by the Standard Model (SM). SM does NOT provide a solution to the Dark Matter problem. [2] Supersymmetry Every SM Fermion (Boson) has a Boson (Fermion) supersymmetry partner (example: ) [3] Supersymmetry (SUSY) extensions of the SM naturally provide a weakly interacting massive particle as a Cold Dark Matter candidate: Lightest SUSY Particle (LSP) [4] We choose to work with a theoretically and experimentally well motivated model: Minimal Supergravity (mSUGRA): LSP = [5] Within the mSUGRA framework, is required to produce the correct DM abundance. Dark Matter and Supersymmetry 03/22/08 Dark Matter at the LHC 5