1. March 25, 2009Probing SUGRA Models at the LHC1 Teruki Kamon and Bhaskar Dutta (full list of collaborators in the next page) on (1) Coannihilation, (2) Over-dense Dark Matter, (3) Focus Point, (4) Non-universarity, (5) String Model String Phenomenology and Related Topics, Mitchell Workshop on String Phenomenology and Related Topics, with Focus on LHC Opportunities and Dark Matter Cook’s Branch, TX, March 23 ~27, 2009 1

2. CSI: LHC THE SECOND SEASON C ollider S cene I nvestigationGoal: 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: Focus point region Case 4: Non-universality 2Teruki KamonProbing SUGRA Models at the LHC

3. Programs at Glance [Case 1] “Coannihilation (CA)” Region Arnowitt, Dutta, Gurrola, *) Kamon, Krislock, *) Toback, PRL100 (2008) 231802 & arXiv:0802.2968 (hep-ph) 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 & arXiv:0808.1372 (hep-ph) [Case 3] “Focus Point” Region Arnowitt, Dutta, Flanagan, #) Gurrola, *) Kamon, Kolev, Krislock *) [Case 4] “Non-universality” Arnowitt, Dutta, Kamon, Kolev, Krislock *) [Case 5] “String Model” Dutta, Kamon, Leggett *) *) Graduate student, #) REU student W   Constant in time? e.g., Quintessence – Scalar field dark energy Teruki KamonProbing SUGRA Models at the LHC33

4. “Probe” Metric Minimal SUGRA Non-minimal SUGRA Teruki KamonProbing SUGRA Models at the LHC44

5. Identify smoking-gun signal(s) and kinematical variables in a minimal benchmark model. Prepare kinematical templates by changing one mass at a time. (a)Measure SUSY masses (b)Determine the benchmark model parameters non-minimalcase(s)  ≟ 0.23 (DarkSUSY) (ISAJET/PYTHIA+PGS4) Teruki KamonProbing SUGRA Models at the LHC55   0.23  = 0.23 Approach non-minimalcase(s)

6. 4 parameters + 1 sign mSUGRA as Minimal Scenario Key experimental constraints Teruki KamonProbing SUGRA Models at the LHC66

7. Dark Matter Allowed Regions 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 Region2 Coannihilation Region1 Focus Point Region3 Note: g  2 data may still be controversial. Teruki KamonProbing SUGRA Models at the LHC77

8. SUSY Phenomenology Snapshots PRL100 (2008) 231802 PRD 79 (2009) 055002 In progress 10 fb  1 LS OS OS  LS m 0 (GeV) m 1/2 (GeV) 1 2 3 Teruki KamonProbing SUGRA Models at the LHC88

9. We assume the following luminosity scenario … Teruki KamonProbing SUGRA Models at the LHC

10. Case 1: CA Region   = 50%, f fake = 1% for p T vis > 20 G eV M j  &M j  97% SUSY Masses (CDM) p T  > 40 GeV p T  > 20 GeV E T jet > 100 GeV M  & p T(  ) 100% Excesses in 3 Final States: a)E T miss + 4j b)E T miss + 2j+2  c)E T miss + b +3j Example of Analysis Chart: Kinematical variables Teruki KamonProbing SUGRA Models at the LHC10

11.  Invert the equations to determine the masses  6 equations for 5 SUSY masses [1] 2 taus with 40 and 20 GeV; M  & p T   in OS  LS technique [2] M  100 GeV; M j  masses for each jet; Choose the 2 nd large value  Peak value ~ True Value 1 1 2 Constructing Kinematical Variables (see page 14) Teruki KamonProbing SUGRA Models at the LHC11

12. Example: Templates in E T miss +2j+2  Clean peak even for low  M  Varying only one mass Teruki KamonProbing SUGRA Models at the LHC The peak position is less sensitive to a tau polarization. "Measuring tau-polarisation in Neutralino2 decays at the LHC," T. Nattermann, K. Desch, P. Wienemann, C. Zendler, arXiv:0903.0714v1 [hep-ph]

13. Independent of the gluino masses! Example: Templates in E T miss +2j+2  Clean peak even for low  M Uncertainty bands with 10 fb -1  Varying only one mass Teruki KamonProbing SUGRA Models at the LHC13

14. Example: Templates in E T miss +4j  E T j1 > 100, E T j2,3,4 > 50  No e’s,  ’s with p T > 20 GeV  M eff > 400 GeV;  E T miss > max [100, 0.2 M eff ] M eff M eff  E T j1 +E T j2 +E T j3 +E T j4 + E T miss [No b jets;  b ~ 50%] 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 e.g., Teruki KamonProbing SUGRA Models at the LHC14

15. Testing gaugino universality at 15% level. 10 fb -1 141  19 GeV SUSY Masses in E T miss +4j and E T miss +2j+2   6 equations for 5 SUSY masses  Inverting Eqs. Teruki KamonProbing SUGRA Models at the LHC15

16. [1] Established the CA region by detecting low energy  ’ s (p T vis > 20 GeV) [2] Measured 5 SUSY masses and tested gaugino Universality at ~15% (10 fb -1 ) DM Relic Density in mSUGRA [3] Determine the dark matter relic density by determining m 0, m 1/2, tan , and A 0 Teruki KamonProbing SUGRA Models at the LHC16

17. Example: Templates in E T miss +b+3j M eff (b)  E T j1=b +E T j2 +E T j3 +E T j4 + E T miss [j1 = b jet] 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 ; E T miss > max [100, 0.2 M eff ] M eff (b) can be used to probe A 0 and tan  without measuring stop and sbottom masses M eff (b)peak (GeV) tan  = 48 M eff (b)peak = 933 GeV tan  = 40 M eff (b)peak = 1026 GeV tan  = 32 M eff (b)peak = 1122 GeV Arbitrary Scale units Teruki KamonProbing SUGRA Models at the LHC17

18. Determining mSUGRA Parameters Solved by inverting the following functions: 10 fb -1 Teruki KamonProbing SUGRA Models at the LHC18

19. [1] The CA region was established by detecting low energy  ’s (p T >20 GeV) quasi model- independent way [2] Kinematical templates for M , Slope, M j , M j , and M eff were prepared in a quasi model- independent way, measuring 5 SUSY masses and testing gaugino universality at ~15% (10 fb -1 ) [3] The dark matter relic density was calculated by determining m 0, m 1/2, tan , and A 0 using M j , M eff, M , and M eff (b) Case 1 Summary Teruki KamonProbing SUGRA Models at the LHC19

20. Case 2: Over-dense DM Region Case 2: Over-dense DM Region Smoking gun signals in the region? A 0 = 0, tan  = 40 PLB 649 (2007) 63 m 1/2 m0m0 Teruki KamonProbing SUGRA Models at the LHC20

21. 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 Teruki KamonProbing SUGRA Models at the LHC21

22. 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 Teruki KamonProbing SUGRA Models at the LHC22

23. 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 Teruki KamonProbing SUGRA Models at the LHC23

24. Band = Uncertainties with 1000 fb -1 Kinematical Templates Teruki KamonProbing SUGRA Models at the LHC24

25. Determining mSUGRA Parameters Solved by inverting the following functions: Teruki KamonProbing SUGRA Models at the LHC25

26. 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. Teruki KamonProbing SUGRA Models at the LHC26

27. 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 Teruki KamonProbing SUGRA Models at the LHC27

28. Determining  h 2 Solved by inverting the following functions: 500 fb -1 b/c stau helps to determine tan  accurately. Teruki KamonProbing SUGRA Models at the LHC28

29. 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? Teruki KamonProbing SUGRA Models at the LHC29

30. Case 3 : Focus Point Region Prospects at the LHC Prospects at the LHC: A few mass measurements are available: 2 nd and 3 rd neutralinos, and gluino Can we make a cosmological measurement? Z Z Z Z An image by Abram Krislock, October 18, 2008 Goals: 1)New technique on  h 2 2)SUSY mass measurements (e.g., ATLAS)  Can we improve? m 0, A 0, , tan  m 1/2,  tan  Teruki KamonProbing SUGRA Models at the LHC30 Ref: "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)

31. A 4 x 4 (m 1/2, , tan  ) Part 1 : New to Probe  h 2 Teruki KamonProbing SUGRA Models at the LHC31

32.  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 Teruki KamonProbing SUGRA Models at the LHC32

33.  h 2 Determination LHC Goal: D 21 and D 32 at 1-2% and gluino mass at 5% Teruki KamonProbing SUGRA Models at the LHC33

34. Part 2 : Can we improve the measurements? E T miss > 150 GeV  total = 3.1 pb OSDF OSSF 19%5.3%11%10% Teruki KamonProbing SUGRA Models at the LHC34

35. 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 Teruki KamonProbing SUGRA Models at the LHC35

36. Case 4 : Non-U SUGRA Nature may not be so kind … Nature may not be so kind … Our studies have been done based on a minimal scenario (= mSUGRA).… Let’s consider a non-minimal case (= non universality) and address “Can we make a cosmological measurement?” An image by Abram Krislock, March18, 2009 Steps: 1)Start with over-abundance region in mSUGRA 2)Reduce Higgs coupling parameter, , by increasing m Hu, …  Extra contributions to  h 2  More annihilation (less abundance)  normal values of  h 2 3)Find smoking gun signals  Technique to calculate  h 2 Teruki KamonProbing SUGRA Models at the LHC36

37. Teruki KamonProbing SUGRA Models at the LHC37 Reference Point  h 2 =0.112

38. Teruki KamonProbing SUGRA Modles at the LHC38 Decays at Reference Point

39. Teruki KamonProbing SUGRA Models at the LHC39 Extraction of Model Parameters Work in Progress …

40. CSI: LHC THE SECOND SEASON 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: Focus point region Case 4: Non-universality Future:  Further improvements  New cases … in progress 40Teruki KamonProbing SUGRA Models at the LHC

41. OS  LS M  Distribution Clean peak even for low  M Independent of the gluino masses! Uncertainty Bands with 10 fb -1 Appendix 1Teruki KamonProbing SUGRA Models at the LHC

42. OS  LS Slope (p T soft ) Uncertainty Bands with 10 fb -1 Independent of the gluino masses! Appendix 2Teruki KamonProbing SUGRA Models at the LHC

43. 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) Appendix 3Teruki KamonProbing SUGRA Models at the LHC

44.  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 Teruki KamonProbing SUGRA Models at the LHC Appendix 4

45. BACKUPs

46. 1)Find smoking gun signal(s) 2)Determine as many SUSY masses as possible 3) Test with a minimal SUSY scenario  see if we can extract the model parameters. 4) Calculate the dark matter relic density 5)Work on non-minimal case Teruki KamonProbing Supersymmetric Cosmology at the LHC Example 3

47. SUSY Phenomenology/Prospects hep-ph/0603128 hep-ph/0808.1372 In progress 10 fb  1 LS OS OS  LS D0 collaboration (Tevatron ) Phys. Lett. B 660 (2008) 449 m 0 (GeV) m 1/2 (GeV) 1 2 3 47Teruki KamonProbing Supersymmetric Cosmology at the LHC 1 2 3

48. 1)N( ℓ ) > 2 p T > 10 GeV |  | < 2.5 2) E T miss > 150 GeV 3)Selection of W  jj p T (j) > 20 GeV 0.9 <  R(j,j) < 3.2   M(jj) < 77  10 GeV 4)Selection of 2 nd t  Wb p T (b) > 30 GeV ???? 1.2 <  R(jj, b) < 3.2 2 nd Top? 48Teruki KamonProbing Supersymmetric Cosmology at the LHC Nikolay – Need an update

49. 49Teruki KamonProbing Supersymmetric Cosmology at the LHC e.g., Quintessence – Scalar field dark energy W   Constant in time?

50. Case 1: CA Region  Program: (1)Establish the “CA region” signal (2)Determine SUSY masses/mSUGRA parameters (3)Measure   h 2 and compare with  CDM h 2 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 p T  > 20 GeV is essential! In the CA region, the ee and  channels are almost absent.

51.  M = 5-15 GeV Smoking Gun of CA Region? R. Arnowitt et al., Phys. Lett. B639 (2006) 46 Case 1: CA Region

52.  SUSY DM ≟  CDM Catching SUSY Dark Matter SUSY Signals at the LHC  DM Density (  h 2 ) 52 Teruki Kamon Probing Supersymmetric Cosmology at the LHC

53. MENU ~SPECIALS~ *Dark Energy Power Drink.. $73 - Chef’s choice *Dark Matter Sandwich …… $23 - Neutral, long-lived *Atomic Soup ………………. $4 - All elements in one No, Sir. But with neutralino? I am hungry. Can you make the DM sandwich with any Standard Model particle? “Dark Matter” Sandwich 53Teruki KamonProbing Supersymmetric Connection with DM

54.  SUSY DM ≟  CDM Catching SUSY Dark Matter SUSY Signals at the LHC  DM Density (  h 2 ) 54 Teruki Kamon Dark Matter Sandwich