1. Precision Cosmology at the LHC Bhaskar Dutta Texas A&M University Precision Cosmology at the LHC125 th August ’ 08 Cosmo 2008, Madison, Wisconsin

2. We are about to enter into an era of major discovery Dark Matter: we need new particles to explain the content of the universe Standard Model: we need new physics Supersymmetry solves both problems! Our best chance to observe SUSY is at the LHC Future results from Planck, direct and indirect detection in tandem with the LHC will confirm a model LHC: The experiment which directly probes TeV scale Discovery Time… The super-partners are distributed around the weak scale Precision Cosmology at the LHC 2

3. The signal : jets + leptons + missing E T SUSY at the LHC (or l + l -,  ) DM Colored particles get produced and decay into weakly interacting stable particles High P T jet [mass difference is large] The p T of jets and leptons depend on the sparticle masses which are given by models R-parity conserving 3 Precision Cosmology at the LHC

4.  Excess in E T miss + Jets  R-parity conserving SUSY  M eff  Measurement of the SUSY scale at 10-20%. Excess in E T miss + Jets Hinchliffe and Paige, Phys. Rev. D 55 (1997) 5520 q The heavy SUSY particle mass is measured by combining the final state particles q q q  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 ] Precision Cosmology at the LHC4

5. SUSY scale can be 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 less than 4% at WMAP  Question: To what accuracy can we calculate the relic density based on the measurements at the LHC? Relic Density and M eff Precision Cosmology at the LHC 5

6. Measurement of Masses We need to measure the masses of the particles. Model parameters need to be determined to check the cosmological status. [Allanach, Belanger, Boudjema and Pukhov’04] If we observe missing energy, then we have a possible dark matter candidate. We want to make sure that we have the correct model to explain the dark matter content Using the model parameters we calculate relic density and compare with WMAP, PLANCK data 6 Precision Cosmology at the LHC Goal:

7. 7 + …. A near degeneracy occurs naturally for light stau in mSUGRA. + + …. Co-annihilation (CA) Process Griest, Seckel ’91 Anatomy of  ann Precision Cosmology at the LHC

8. 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 Arnowitt, Dutta, Santoso’ 01 Precision Cosmology at the LHC 8

9. DM Allowed Regions in mSUGRA Below is the case of mSUGRA model. However, the results can be generalized. [Stau-Neutralino CA 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 [Bulk region] is almost ruled out 9 Precision Cosmology at the LHC

10. CA Region at tan  = 40 Can we measure  M at colliders? 10 Precision Cosmology at the LHC

11. Goal for CA-analysis E stablish the “dark matter allowed region” signal M easure SUSY masses D etermine mSUGRA parameters P redict   h 2 and compare with  CDM h 2 11 Precision Cosmology at the LHC

12. Smoking Gun of CA Region 100% 97% SUSY Masses (CDM) 2 quarks+2  ’s +missing energy Unique kinematics 12 Low energy taus exist in the CA region However, one needs to measure the model Parameters to predict the Dark matter content in this scenario Precision Cosmology at the LHC

13. Number of Counts / 2 GeV p T soft Slope and M  Slope of p T distribution of “soft  ” contains ΔM information Low energy  ’s are an enormous challenge for the detectors p T and M  distributions in true di-  pairs from neutralino decay Precision cosmology at the LHC13 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 Arnowitt, Dutta, Kamon, Kolev, Toback PLB 639 (2006) 46

14. 14 We use ISAJET + PGS4 PLB 639 (2006) 46 Precision Cosmology at the LHC Arnowitt, Dutta, Kamon, Kolev, Toback

15. M  Distribution Clean peak even for low  M We choose the peak position as an observable. 15 Precision Cosmology at the LHC

16. M  peak vs. X Uncertainty Bands with 10 fb -1 16 Precision Cosmology at the LHC

17. Slope(p T soft ) vs. X Uncertainty Bands with 10 fb -1 17 Precision Cosmology at the LHC

18. SUSY Anatomy M j  M  p T(  ) 100% 97% SUSY Masses (CDM) 18 M eff Precision Cosmology at the LHC

19. M j  Distribution M  < M  endpoint Jets with E T > 100 GeV M j  masses for each jet Choose the 2 nd large value  M j   gluino  squark + j “other” jet We choose the peak position as an observable. 19 Precision Cosmology at the LHC

20. M j  peak vs. X 20 Precision Cosmology at the LHC

21. 4 j+E T miss : M eff Distribution  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 ] 21 Precision Cosmology at the LHC At Reference Point M eff peak = 1274 GeV M eff peak = 1220 GeV (m 1/2 = 335 GeV) M eff peak = 1331 GeV (m 1/2 = 365 GeV) Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, PRL, 100, (2008) 231802

22. Determination of tan  Measuring Relic Density at the LHC22 Determination of tan  is a real problem Instead, we use observables involving third generation sparticles: M eff (b) [ the leading jet is a b-jet ] We can determine tan  and A 0 with good accuracy This procedure can be applied to different SUGRA models One way is to determine stop and sbottom masses and then solve for A 0 and tan  Problem: Stop creates a background for sbottom and … E.g., stop mass matrix:

23. 3 j+1b+E T miss :M eff (b) Distribution  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 ] 23 Precision Cosmology at the LHC M eff (b)peak = 1122 GeV (m 1/2 = 365 GeV) At Reference Point M eff (b)peak = 1026 GeV M eff (b)peak = 933 GeV (m 1/2 = 335 GeV) M eff (b) M eff (b) can be used to determine A 0 and tan  even without measuring stop and sbottom masses Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, Phys. Rev. Lett. 100, (2008) 231802

24. Observables SM+SUSY Background gets reduced Ditau invariant mass: M  Jet-  -  invariant mass: M j  Jet-  invariant mass: M j  P T of the low energy  M eff : 4 jets +missing energy M eff (b) : 4 jets +missing energy Since we are using 7 variables, we can measure the model parameters and the grand unified scale symmetry (a major ingredient of this model) 1.Sort  ’s by E T (E T 1 > E T 2 > …) Use OS  LS method to extract  pairs from the decays All these variables depend on masses => model parameters 24 Precision Cosmology at the LHC

25. 7 Eqs (as functions of SUSY parameters) Invert the equations to determine the masses Determining SUSY Masses (10 fb  1 ) 1  ellipse 10 fb -1 25 Phys. Rev. Lett. 100, (2008) 231802 M eff (b) = f 7 (g, q L, t, b) ~~~~ Measurement of Dark Matter Content at the LHC

26. GUT Scale Symmetry We can probe the physics at the Grand unified theory (GUT) scale The masses,, unify at the grand unified scale in SUGRA models 0 1  ~ m 1/2 mass MZMZ M GUT Log[Q] g ~ 0 1  ~ 0 2  ~ 0 2  ~ g ~ Gaugino universality test at ~15% (10 fb-1) Another evidence of a symmetry at the grand unifying scale! Use the masses measured at the LHC and evolve them to the GUT scale using mSUGRA

27. [1] Established the CA region by detecting low energy  ’s (p T vis > 20 GeV) [2] Determined SUSY masses using: M , Slope, M j , M j , M eff e.g., Peak(M  ) = f (M gluino, M stau, M, M ) [3] Measure the dark matter relic density by determining m 0, m 1/2, tan , and A 0 DM Relic Density in mSUGRA 0 1  ~ 0 2  ~ 27 Precision Cosmology at the LHC

28. Determining mSUGRA Parameters 28 Precision Cosmology at the LHC

29. Mass Measurements  mSUGRA M  peak, M eff (b)peak …. Sensitive to A 0, tan  m   and  m 1/2 M j  peak, M eff peak …. Sensitive to m 0, m 1/2 29 Precision Cosmology at the LHC

30. Determining mSUGRA Parameters Solved by inverting the following functions: 10 fb -1 30 Phys. Rev. Lett. 100, (2008) 231802 Precision Cosmology at the LHC

31. Focus Point (FP) m 0 is large, m 1/2 can be small, e.g., m 0 = 3550 GeV, m 1/2 =314 GeV, tan  =10, A0=0 31 M(gluino) = 889 GeV, ΔM(χ 3 0 - χ 1 0 ) = 81 GeV, ΔM(χ 2 0 - χ 1 0 ) = 59 GeV, ΔM(χ 3 0 - χ 2 0 ) = 22 GeV Br(g → χ 2 0 tt) = 10.2% Br(g → χ 2 0 uu) = 0.8% Br(g → χ 3 0 tt) = 11.1% Br(g → χ 3 0 uu) = 0.009% ~ ~ ~ ~ - - - - Precision Cosmology at the LHC

32. M(ll) (GeV) Events/GeV 32 Dilepton Mass at FP Tovey, PPC 2007; Baer, Barger, Salughnessy, Summy, Wang, PRD, 75, 095010 (2007), Crockett, Dutta, Flanagan, Gurrola, Kamon, Kolev, VanDyke, 08; Precision Cosmology at the LHC

33. 33 Determination of masses: FP Relic density calculation depends on , tan  and m 1/2 All other masses are heavy! m 1/2  and tan  can be solved from M(gluino), ΔM (χ 3 0 - χ 1 0 ) and ΔM (χ 2 0 - χ 1 0 ) Errors of : M(gluino), ΔM (χ 3 0 - χ 1 0 ) ΔM (χ 2 0 - χ 1 0 ) 300 fb -1 4.5 % 1.2% 1.7% Higher jet, b-jet, lepton multiplicity requirement increase the signal over background rate Chargino masses can be measured!Work in Progress… Precision Cosmology at the LHC tan   22% 0.1%

34. Bulk Region The most part of this region in mSUGRA is experimentally (Higgs mass limit, b  s  ) ruled out mSUGRA point: The error of relic density: 0.108 ± 0.01(stat + sys) sparticlemass 97.2 398 189 607 533 End ptsvalueerror m ll 81.20.09 M lq( (max)3652.1 M lq (min)266.91.6 Ml lq (max)4252.5 M llq (min)2071.9 M  (max)62.25.0 Relic density is mostly satisfied by t channel selectron, stau and sneutrino exchange Perform the end point analysis to determine the masses 0101 ~ 0202 ~ l ~ g ~ uLuL ~ m 0 =70; A 0 =-300 m 1/2 =250;  >0; tan  =10; [With a luminosity 300 fb -1,  edge controlled to 1 GeV] Nojiri, Polsello, Tovey’05 ~ Includes: (+0.00,−0.002 )M(A); (+0.001, −0.011) tan β; (+0.002,−0.005) m(  2 ) Precision Cosmology at the LHC

35. Accuracy of tan  35 The accuracy of determining tan  is not so good if we do not have staus in the final states. E.g., raise m 0 The final states contain Z, Higgs, staus Lahanas, Mavromatos, Nanopoulos, Phys.Lett.B649:83-90,2007. Dilaton effect creates new parameter space Precision Cosmology at the LHC

36.  2 0 DecayBranching Ratios  2 0 Decay Branching Ratios Identify and classify  2 0 decays Dutta, Gurrola, Kamon, Krislock, Lahanas, Mavromatos, Nanopoulos, arXiv:0808.1372

37. Observables involving Z and Higgs We can solve for masses by using the end-points Precision Cosmology at the LHC

38. Observables Higgs + plus jet + missing energy dominated region: Effective mass: M eff (peak): f 1 (m 0,m 1/2 ) Effective mass with 1 b jet: M eff (b) (peak): f 2 (m 0,m 1/2, A 0, tan  ) Effective mass with 2 b jets: M eff (2b) (peak): f 3 (m 0,m 1/2, A 0, tan  ) Higgs plus jet invariant mass: M bbj (end-point): f 4 (m 0,m 1/2 ) 4 observables=> 4 mSUGRA parameters However there is no stau in the final states: accuracy for determining tan  will be less Precision Cosmology at the LHC

39. 39 Error with 1000 fb-1 Observables… Precision Cosmology at the LHC

40. Determining mSUGRA Parameters Solved by inverting the following functions: 1000 fb -1 40 Precision Cosmology at the LHC

41. 2 tau + missing energy dominated regions: Solved by inverting the following Observables: 500 fb -1 For 500 fb -1 of data Dutta, Gurrola, Kamon, Krislock, Lahanas, Mavromatos, Nanopoulos, arXiv:0808.1372 Precision Cosmology at the LHC

42. Conclusion Signature contains missing energy (R parity conserving) many jets and leptons : Discovering SUSY should not be a problem ! Once SUSY is discovered, attempts will be made to connect particle physics to cosmology Based on these measurement, the dark matter content of the universe will be calculated to compare with WMAP/PLANCK data. Four different cosmological motivated regions of the minimal SUGRA model have distinct signatures

43. The CA region can be established by detecting low energy  ’s (p T vis > 20 GeV) Determine SUSY masses using: M , Slope, M j , M j , M eff e.g., Peak(M  ) = f (M gluino, M stau, M, M ) Gaugino universality test at ~15% (10 fb -1 ) Measure the dark matter relic density by determining m 0, m 1/2, tan , and A 0 using M j , M eff, M , and M eff (b) We obtain:Conclusion… 0 1  ~ 0 2  ~ 43 Precision Cosmology at the LHC Focus point region also determines the parameters with high accuracy

44. Concusion… For large m 0, when staus are not present, the mSUGRA parameters can still be extracted, but with less accuracy It is also possible to determine nonuniversal model Parameters,, This analysis can be applied to any SUSY model We can use new observables, M eff (2b), M eff (t) etc