Measuring Relic Density at the LHC

Transcription

1 easuring Relic Density at the LHC Bhaskar Dutta Collaborators R. Arnowitt, A. Gurrola, T. Kamon, A. Krislock, D. Toback Texas A& University 7 th July 8 easuring Relic Density at the LHC

2 OUTLINE Dark atter (D in Universe D Relic Density (Ωh( in SUSY msugra Co-annihilation (CA Region at the LHC Prediction of D Relic Density (Ωh( Summary Arnowitt,, Dutta, Kamon, Kolev, Toback,, PLB 639 (6 46 Arnowitt, Arusano,, Dutta, Kamon, Kolev,, Simeon, Toback,, Wagner, PLB 649 (7 73 Arnowitt,, Dutta, Gurrola, Kamon, Krislock, Toback,, Phys. Rev. Lett.., (8 38 easuring Relic Density at the LHC

3 Dark atter (D in Universe splitting normal matter and dark matter apart Another Clear Evidence of Dark atter Ordinary atter (8//6 (NASA s Chandra X Observatory time 3 4 Dark atter (Gravitational Lensing Approximately the same size as the ilky Way easuring Relic Density at the LHC 3

4 D Particle in SUSY Astrophysics χ ~ CD Neutralino ( SUSY SUSY is an interesting class of models to provide a weakly interacting massive neutral particle ( ~ GeV. easuring Relic Density at the LHC 4

5 Anatomy of σann CD Co-annihilation (CA (CA Process ~ χ Griest, Seckel ~ τ ( Ω Δ / e +. Δ A near degeneracy occurs naturally for light stau in msugra. A near degeneracy occurs naturally for light stau in msugra. ~ ~ τ χ easuring Relic Density at the LHC 5

6 Coannihilation, GUT Scale In msugra model the lightest stau seems to be naturally close to the lightest neutralino mass especially for large tanβ For example, the lightest selectron mass is related to the lightest neutralino mass in terms of GUT scale parameters: m m +. 5m ~ + (37 GeV / m. 6m E c ~ / Thus for m, E ~ c becomes degenerate with at m / 37 GeV, i.e. the coannihilation region begins at m / (37-4 GeV For larger m / the degeneracy is maintained by increasing m and we get a corridor in the m -m / plane. χ ~χ Arnowitt, Dutta, Santoso The coannihilation channel occurs in most SUGRA models with non-universal soft breaking,

7 D Allowed Regions - Illustration ass of Squarks and Sleptons Excluded (Higgs mass Excluded (Rare B Decay b sγ Excluded (agnetic oment of uon Co-annihilation Region Co-annihilation Region No CD Candidate ass of Gauginos Higgs ass ( h Branching Ratio b sγ agnetic oment of uon CD allowed region easuring Relic Density at the LHC 7

8 inimal Supergravity (msugra tanβ m / m <H> 46 GeV <H d > SUSY model in the framework of unification: β <H u > 4 parameters + sign <H u >/<H d > at Z Common gaugino mass at GUT Common scalar mass at GUT A Trilinear couping at GUT sign(μ Sign of μ in W ( μ H u H d + Arnowitt, Chamesdinne, Nath, PRL 49 (98 97; NPB 7 (983. Barbieri, Ferrara, Savoy, PLB 9 ( Lykken, Hall, Weinberg, PRD 7 ( Higgs > 4 GeV chargino > 4 GeV Key Experimental Constraints.x 4 <B(b s γ <4.5x 4 (g μ : 3 σ deviation from S. 94 Ω ~ h < < χ. 9 easuring Relic Density at the LHC 8

9 D Allowed Regions in msugra Below is the case of msugra model. However, the results can be generalized. [Focus point region] the lightest neutralino has a larger Higgsino component [A-annihilation funnel region] This appears for large values of m / [Stau-Neutralino CA region] [Bulk region] almost ruled out easuring Relic Density at the LHC 9

10 CA Region at tanβ 4 Δ ~ τ ~ 5 ~ Can we measure Δ at colliders? Can we measure Δ at colliders? χ 5 GeV easuring Relic Density at the LHC

11 OST 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. D p easuring Relic Density at the LHC

12 st analysis: Excess in E miss T + Jets Excess in E miss T + Jets R-parity conserving SUSY eff easurement of the SUSY scale at -%. Hinchliffe and Paige, Phys. Rev. D 55 ( E T j > GeV, E T j,3,4 > 5 GeV eff > 4 GeV ( eff E T j +E T j +E T j3 +E T j4 + E T miss E T miss > max [,. eff ] The heavy SUSY particle mass is measured by combining the final state particles q q g~ g~ q q ~ χ χ ~ CS m / 5, m 6; σ 45 fb (gluino 886; (squark 7 easuring Relic Density at the LHC

13 SUSY scale is measured with an accuracy of -% 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 3% with an accuracy of around 4% at WAP Question: Relic Density and eff To what accuracy can we calculate the relic density based on the measurements at the LHC?

14 Goal Establish the CA region signal easure SUSY masses Determine msugra parameters Predict Ω χ h and compare with Ω CD h easuring Relic Density at the LHC 4

15 Analysis Strategy co-annihilation Δ5- GeV easuring Relic Density at the LHC 5

16 Dilepton Endpoint D content easurements of the SUSY masses [e.g.,.. Nojiri, G. Polesselo, D.R. Tovey, JHEP 63 (6 63] Key: Dilepton edge in the χ decay in dilepton (ee, μμ, ττ channels for reconstruction of decay chain. L: (Low ass Case m / 8, m 85; σ 55 pb [post-wap benchmark point B ] (gluino 6 (squark 559 gluino squark+quark B(χ slep_r lep.% B(χ stau_ tau 46% B(χ + sneu_l lep 36% easuring Relic Density at the LHC 6

17 Dilepton Endpoint in CA Region In the CA region (after the experimental constraints, the ee and μμ channels are almost absent Br(χ eeχ, μμχ ~ % Br(χ ττχ ~ % Δ 5-5 GeV Questions: ( How can we establish the D allowed regions? ( To what accuracy can we calculate the relic density based on the measurements at the LHC? easuring Relic Density at the LHC 7

18 Our Reference Point m / 35, m, tanβ 4, μ >, A [ISAJET version 7.64] PLB 639 (6 46 easuring Relic Density at the LHC 8

19 Smoking Gun of CA Region SUSY asses g~ χ~ χ~ (CD u ~ L 97% % u u τ ~ τ τ quarks+ τ s +CD particle Unique kinematics 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 easuring Relic Density at the LHC 9

20 SUSY Anatomy I g~ u ~ L u SUSY asses χ~ χ~ (CD 97% % u ~ τ τ τ (jττ (ττ p T (τ eff E T miss + jets + >τ easuring Relic Density at the LHC

21 Number of Counts / GeV p soft T Slope and ττ p T and ττ distributions in true di-τ pairs from neutralino decay Slope of p T distribution of soft τ contains Δ information Number of Counts / GeV ~ χ ττ~ ( Δ 5.7 GeV ττχ~ E vis T (true >, GeV E vis T (true > 4, GeV E vis T (true > 4, 4 GeV Low energy τ s are an enormous challenge for the detectors easuring Relic Density at the LHC

22 Warming-up Quizzes I. Hadronic or leptonic? Hadronic II. How low in p T? CDF : p T vis >5- GeV [Assumption] ε τ 5%, fake rate % for p T vis > GeV easuring Relic Density at the LHC

23 We use ISAJET + PGS4 PLB 639 (6 46 easuring Relic Density at the LHC 3

24 Distribution ττ Clean peak even for low Δ vis ττ (GeV vis ττ (GeV We choose the peak position as an observable. We choose the peak position as an observable. easuring Relic Density at the LHC 4

25 E miss T + j + τ Background [] Sample of E T miss, jets, and at least taus with p T vis > 4, GeV and ε τ 5%, fake (f j τ %. Optimized cuts : E T jet > GeV; E T jet > GeV; E T miss > 8 GeV; E T jet + E T jet + E T miss > 6 GeV [] Number of SUSY and S events ( fb : E T miss + j + τ Analysis Top : 5 events W+jets : 44 events SUSY : 59 events

26 Slope(p T soft vs. X ~χ (GeV Uncertainty Bands with fb - g ~ (GeV easuring Relic Density at the LHC 6

27 peak ττ vs. X Uncertainty Bands with fb - easuring Relic Density at the LHC 7

28 SUSY Anatomy II g~ u ~ L u SUSY asses χ~ χ~ (CD 97% % u ~ τ τ τ jττ ττ eff p T(τ 3//8 Dark atter Relic Density at the LHC 8

29 jττ vs. X easuring Relic Density at the LHC 9

30 j Distribution ττ end jττ q ~ ~ χ q ~ ~ χ ~ χ other jet gluino squark + j ττ < ττ endpoint Jets with E T > GeV jττ masses for each jet Choose the nd large value jττ ( We choose the peak position as an observable. We choose the peak position as an observable. easuring Relic Density at the LHC 3

31 peak j ττ vs. X easuring Relic Density at the LHC 3

32 SUSY Anatomy III g~ u ~ L u SUSY asses χ~ χ~ (CD 97% % u ~ τ τ τ jττ ττ eff p T(τ easuring Relic Density at the LHC 3

33 Distribution eff E T j > GeV, E T j,3,4 > 5 GeV [No e s, μ s with p T > GeV] eff > 4 GeV ( eff E T j +E T j +E T j3 +E T j4 + E T miss [No b jets; ε b ~ 5%] E T miss > max [,. eff ] At Reference Point eff peak 74 GeV eff peak GeV (m / 335 GeV eff peak 33 GeV (m / 365 GeV easuring Relic Density at the LHC 33

34 Five Observables. Sort τ s by E T (E T > E T > Use OS LS method to extract τ pairs from the decays N τ N ± ± τ ± τ m τ S+SUSY Background gets reduced Ditau invariant mass: ττ Jet-τ-τ invariant mass: jττ Jet-τ invariant mass: jτ P T of the low energy τ eff : 4 jets +missing energy All these variables depend on masses > model parameters Since we are using 5 variables, we can measure the model parameters and the grand unified scale symmetry (a major ingredient of this model

35 6 Eqs (as functions of 5 SUSY masses Determining SUSY asses ( fb peak ττ Slope (peak jττ (peak jτ (peak jτ peak eff f f f 6 ~ ~ ( Δ, χ, χ ~ ( Δ, χ ~, ~ (, ~ f3 ql χ χ ( ~,, ~, ~ f4 ql Δ χ χ ( ~,, ~, ~ f5 ql Δ χ χ ( g ~, q ~ Invert the equations to determine the masses L fb - ~ ~ χ g ~ g ~ σ ellipse Δ q L.6 ±. / / 748 ± 5; 6 ± 5; ~ χ ~ χ g ~ ~ χ 83± ; 4± 9; 3. ±. ( theory ±.8 ( theory 5.9 Phys. Rev. Lett.., (8 38 easuring Relic Density at the LHC 35

36 GUT Scale Symmetry We can probe the physics at the Grand unified theory (GUT scale mass g ~ ~ χ ~ χ m / Use the masses measured at the LHC and evolve them to the GUT scale using msugra Z Log[Q] GUT The masses ~ χ, ~ χ, g ~ unify at the grand unified scale in SUGRA models Gaugino universality test at ~5% ( fb- Another evidence of a symmetry at the grand unifying scale!

37 D Relic Density in msugra [] Established the CA region by detecting low energy τ s (p T vis > GeV [] Determined SUSY masses using: ττ, Slope, jττ, jτ, eff e.g., Peak( ττ f ( gluino, stau,, ~ χ ~ χ [3] easure the dark matter relic density by determining m, m /, tanβ, and A easuring Relic Density at the LHC 37

38 Determining msugra Parameters j ττ? ττ eff X X X X 3 4 ( m ( m ( m ( m / / / /, m, m, m, m,tan β,,tan β, A A m m / A tan β???? Ω χ ~ h A Z( m, m/ tan β, δω h / Ω ~ ~ χ χ h??? (??? fb easuring Relic Density at the LHC 38

39 Determination of tanβ Determination of tanβ is a real problem One way is to determine stop and sbottom masses and then solve for A and tanβ E.g., stop mass matrix: mq L +... mt ( At + μcotβ mt ( At + μcotβ +... Problem: Stop creates a background for sbottom and Instead, we use observables involving third generation sparticles: eff (b [the leading jet is a b-jet] We can determine tanβ and A with good accuracy This procedure can be applied to different SUGRA models mt R easuring Relic Density at the LHC 39

40 eff (b Distribution E T j > GeV, E T j,3,4 > 5 GeV [No e s, μ s with p T > GeV] eff (b > 4 GeV ( eff (b E T jb +E T j +E T j3 +E T j4 + E T miss [j b jet] E T miss > max [,. eff ] At Reference Point eff (bpeak 6 GeV eff (bpeak 933 GeV (m / 335 GeV eff (bpeak GeV (m / 365 GeV (b eff can be used to determine A and tanβ even without measuring stop and sbottom masses Phys. Rev. Lett.., (8 38 easuring Relic Density at the LHC 4

41 ass easurements msugra eff (bpeak. Sensitive to A and tanβ eff peak. Very insensitive to A and tanβ easuring Relic Density at the LHC 4

42 Determining msugra Parameters Solved by inverting the following functions: j ττ ττ eff ( b eff f f f f 3 4 ( m ( m ( m ( m / / / /, m, m, m, m,tan β, A,tan β, A fb - m m / A tan β ± 35 ± 5 4 ± 6 4 ± Ω χ ~ h A Z( m, m/ tan β, L 5 fb fb Phys. Rev. Lett.., (8 38 δω h / Ω ~ ~ χ χ h 6% (3 fb easuring Relic Density at the LHC 4

43 Accuracy of tanβ The accuracy of determining tanβ is not so good if we do not have staus in the final states. Dutta, Kamon, Gurrola, Krislock, Nanopoulos 8 E.g., raise m The final states can contain Z, Higgs hep-ph/65 Lahanas, avromatos, Nanopoulos easuring Relic Density at the LHC 43

44 χ Decay Branching Ratios Identify and classify χ decays Dutta, Kamon, Gurrola, Krislock, Nanopoulos 8

45 Observables involving Z and Higgs Number of Counts / 5 GeV Z +Jet Effective ass (GeV Number of Counts / 5 GeV nd bbj (GeV We can solve for masses by using the end-points

46 Observables Higgs + plus jet + missing energy dominated region: Effective mass: eff (peak: f (m,m / Effective mass with b jet: eff (b (peak: f (m,m /, A, tanβ Effective mass with b jets: eff (b (peak: f 3 (m,m /, A, tanβ Higgs plus jet invariant mass: bbj (end-point: f 4 (m,m / 4 observables> 4 msugra parameters However there is no stau in the final states: accuracy for determining tanβ will be less Ref: Dutta, Kamon, Gurrola, Krislock, Nanopoulos 8

47 Observables Error with fb- Dutta, Kamon, Gurrola, Krislock, Nanopoulos 8 47

48 Determining msugra Parameters Solved by inverting the following functions: end point jbb peak eff ( b peak eff ( bb peak eff X X X X 3 4 ( m ( m ( m ( m / / / /,m,m,m,m, tanβ, A, tanβ, A fb - Ω χ m m / A tanβ 47 ± 44 ± 5 ± ± 8 ~ h A Z( m, m/ tan β, L fb δω ~ χ h / Ω ~ h ~ 5% χ Teruki Kamon easurement Relic Density at the LHC 48

49 tau + missing energy dominated regions: Solved by inverting the following functions: (peak jττ peak eff ( b peak eff peak ττ X X X X 3 4 ( m ( m ( m ( m / / / /,m,m,m,m δω ~ χ h / Ω ~ h ~ 9% χ, tanβ, A, tanβ, A 5 fb - Ω χ m m / A 44 ± 3 6 ± 6 ± 45 tanβ 4 ± 3 ~ h A Z( m, m/ tan β, For 5 fb - of data Dutta, Kamon, Gurrola, Krislock, Nanopoulos 8

50 Summary [] Established the CA region by detecting low energy τ s (p T vis > GeV [] Determined SUSY masses using: ττ, Slope, jττ, jτ, eff e.g., Peak( ττ f ( gluino, stau,, ~ χ ~ χ Gaugino universality test at ~5% ( fb - [3] easured the dark matter relic density by determining m, m /, tanβ, and A using jττ, eff, ττ, and eff (b δω h / Ω ~ ~ χ χ h 6% (3 fb easuring Relic Density at the LHC 5

51 Summary [4] For large m, when staus are not present, the msugra parameters can still be extracted, but with less accuracy [5] It will be interesting to determine nonuniversal model Parameters, e.g., μ (Higgs sector nonuniversality work is in progress