LHC and Dark Matter 07/23/10. Bhaskar Dutta Texas A&M University

Transcription

1 LHC and Dark atter 7/3/ Bhaskar Dutta Texas A& University

2 Discovery Time We are about to enter into an era of major discovery Dark atter: we need new particles to explain the content of the universe Standard odel: we need new physics Supersymmetry solves both problems! The super-partners are distributed around GeV to a few TeV LHC: directly probes TeV scale Future results from PLANCK, direct and indirect detection, rare decays etc. experiments in tandem with the LHC will confirm a model If you cannot wait, ask the octopus

3 SUSY at the LHC D (or l + l -, τ+τ High P T jet.drees s talk [mass difference is large] Colored particles are produced and they decay finally into the weakly interacting stable particle High P T jet D The p T of jets and leptons depend on the sparticle masses which are given by models (or l + l -, τ+τ R-parity conserving The signal : jets + leptons + missing E T 3

4 SUSY at the LHC Final states odel Parameters Reconstruct sparticle masses, e.g., ~ Q ~ L l,3,4 q + l ~ + χ ~ + χ ~,, ~ χ h ll + χ We may not be able to solve for masses of all the sparticles from a model Solving for the SS : Very difficult etc. Identifying one side is very tricky! 4

5 SUSY at the LHC We can use simpler models to understand the cascades and solve for the model parameters The best strategy: Calculate the Dark atter content Solve for the minimal model: msugra 4 parameters: m, m /, A, tanβ and Sign(μ The cascades can be understood in a simpler way [hopefully!] Next step: Next to minimal model (Higgs nonuniversality Then 5

6 msugra Parameter space Focus point Coannihilation Region Allahverdi, Dutta, Santoso PLB 687:5, The bounds from CDS/Xenon have started becoming competitive with b s γ and Higgs mass constraints. 6

7 . 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 even with nonuniversal soft breaking. 7

8 CA Region at tanβ 4 Δ ~ τ ~ 5 ~ Can we measure Δ at colliders? Can we measure Δ at colliders? χ 5 GeV Arnowitt, Dutta, Gurrola, Kamon, Krislock and Toback PRL, 8 8

9 Smoking Gun of CA Region SUSY asses g~ χ~ χ~ (CD Typical decay chain and final states at the LHC u ~ L 97% % quarks+ τ s +missing energy u u τ ~ τ τ Unique kinematics Jets + τ s+ missing energy Low energy taus characterize the CA region However, one needs to measure the model parameters to predict the dark matter content in this scenario 9

10 CA Region: Final States SUSY asses g~ χ~ u ~ u L 97% ET jet > GeV p Tτ > 4 GeV u jττ & jτ χ~ (CD τ ~ τ τ Excesses in 3 Final States: ae T miss + 4j be T miss + j+τ ce T miss + b +3j Kinematical variables Example of Analysis Chart for b: % p Tτ > GeV ττ & p T(τ ε τ 5%, f fake % for p T vis > GeV

11 Extracting One side: jττ OS-LS selection of ditaus selects, but if we need to reconstruct the entire side χ~ We use the following subtraction scheme: t

12 miss +4j a E miss T +4j eff E T j +E T j +E T j3 +E T j4 + E T miss [No b jets; ε b ~ 5%] e.g., pp g~ g ~ eff E T j >, E T j,3,4 > 5 No e s, μ s with p T > GeV eff > 4 GeV; E T miss > max [,. eff ] m / 335 GeV eff peak GeV m / 35 GeV eff peak 74 GeV m / 365 GeV eff peak 33 GeV

13 Kinematical Variables using a, b & c 66 equations for 5 SUSY masses peak ( ~ ~ ττ f Δ, χ, χ Slope f( Δ, ~ χ (peak ( j 3 q ~ ~ ~ ττ f L, χ, χ (peak j 4( q ~ ~ ~ τ f L, Δ, χ, χ (peak ( ~ ~ j f5 q ~ τ L, Δ, χ, χ peak f ( g~,q ~ eff 6 L Invert the equations to determine the masses [] taus with 4 and GeV; ττ & p Tτ in OS LS technique [] ττ < ττ endpoint ; Jets with E T > GeV; jττ masses for each jet; Choose the nd large value Peak value ~ True Value q ~ L 66 GeV 84 GeV 3

14 D Relic Density in msugra [] Established the CA region by detecting low energy τ s (p T vis > GeV [] easured 5 SUSY masses (Δ,,, q ~, g ~ ~χ ~χ Ω χ ~ h A ( m, m/ tan β, [3] Determine the dark matter relic density q ~, by determining m, m /, tanβ, and A So far using: a E T miss + 4j b E T miss + j+τ peak j ττ peak ττ peak eff? X X X X 3 4 ( m ( m ( m ( m / / / /, m, m, m, m,tan β, A,tan β, A 4 4

15 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 5

16 c E miss T +b+3j eff (b E T jb +E T j +E T j3 +E T j4 + E T miss [j b jet] E T j > GeV, E T j,3,4 > 5 GeV [No e s, μ s with p T > GeV] eff (b > 4 GeV ; E T miss > max [,. eff ] tanβ 48 eff (bpeak 933 GeV tanβ 4 eff (bpeak 6 GeV tanβ 3 eff (bpeak GeV Arbitrary Scale units eff (bpeak (GeV (b eff can be used to probe A and tanβ measuring stop and sbottom masses without 6

17 Determining msugra Parameters Solved by inverting the following functions: peak jττ peak ττ peak eff ( b peak eff X X X X 3 4 ( m ( m ( m ( m / / / /, m, m, m, m,tan β, A,tan β, A fb - Ω χ m m / A tan β ± 35 ± 5 4 ± 6 4 ± ~ h A ( m, m/ tan β, L 5 fb fb δω h / Ω ~ ~ χ χ h 6.% (3 fb 4.% (7 fb 7

18 Case : Summary [] The CA region is established by detecting low energy τ s (p T > GeV [] ττ, Slope, jττ, jτ, and eff measure 5 SUSY masses and test gaugino universality at ~5% ( fb - [3] The dark matter relic density is calculated by determining m, m /, tanβ, and A using jττ, eff, ττ, and eff (b δω h / Ω ~ ~ χ χ h 6% (3 fb δσ χ / σ ~ ~ p χ p 7% (3 fb 8 8

19 Comparison ILC analysis: 5 GeV LHC m Δ (5 fb - We need 5fb - m / A tan β 35 4 Arnowitt, Dutta, Kamon; PLB 5 This result was used in Baltz, Battaglia, Peskin, Wizansky 5 to extract relic density by using ILC and LHC (LCC3 point 5 We can determine Δ at the LHC, Arnowitt, Dutta, Kamon et al, PRL 8 9

20 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 Log[Q] GUT The masses ~ χ, ~ χ, g ~ unify at the grand unified scale in the msugra model Gaugino universality test at ~5% ( fb- Another evidence of a symmetry at the grand unifying scale!

21 . Over-dense D Region A, tanβ 4 m Dilaton effect creates new parameter space m / Lahanas, avromatos, Nanopoulos, PLB649:83-9,7. Smoking gun signals in the region?

22 Reference Points m / 44 GeV; m 47 GeV 86.8% m / 6 GeV; m 44 GeV 77.%

23 Case (a : Higgs m / 44, m 47, tanβ4, m top 75 g~ 4 u u ~ L 44 E miss T > 8 GeV; N(jet > with E T > GeV; E miss T + E j T + E j T > 6 GeV χ~ χ~ % 87% h 4 e ~ R 5 τ ~ ± χ~ 46 N(b > with P T > GeV;.4< ΔR bb < 3

24 4 Kinematical Variables Side-band BG subtraction 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 bb (GeV where: m / 4 5 fb ( m 47 w/ side-band BG subtraction m / 48 eff E j T +E j T +E j3 T +E j4 T + E miss T [No b jets; ε b ~ 5%] (b eff E jb T +E j T +E j3 T +E j4 T + E miss T (bb eff E jb T +E jb T +E j3 T +E j4 T + E miss T ( bbj (GeV 4

25 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 5

26 Determining Ωh 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 - m m / A tanβ 47 ± 5 44 ± 5 ± ± 8 L fb Ω χ ~ h A ( m, m/ tan β, δω ~ h / Ω ~ h ~ 5% χ χ Dutta, Gurrola, Kamon, Krislock, Nanopoulos, Lahanas, avromatos, PRD 9 6

27 Case : Summary Over-dense Dark atter Region: σ OD-CD ~ σ CD / Implication at the LHC: Region where χ decays to Higgs δω CD /Ω CD ~ 5% ( fb - Region where χ decays to stau and Higgs δω CD /Ω CD ~ % (5 fb - 7

28 Case 3 : Focus Point/Hyperbolic Branch m, A, μ, tanβ q ~ l ~ g~ Prospects at the LHC: A few mass measurements are available: nd and 3 rd neutralinos, and gluino ~χ i m /, μ, tanβ Goals: technique on Ωh SUSY mass measurements Can we determine the dark matter content? 8

29 9 μ μ β β β β β β β β χ s c s s c c c s s c c c s s c s W W W W W W W W Μ ~ μ μ β β β β β β β β χ s c s s c c c s s c c c s s c s W W W W W W W W Μ ~ A 4x4 (m /, μ, tanβ g ~ χ χ ~ ~ D 3 3 χ χ ~ ~ D Ωh tan ( β μ Ω χ,, m h / ~ 9 9

30 Focus Point: Leptons Large m sfermions are heavy m 355 GeV; m / 3 GeV; A ; tanß ; μ> Direct three-body decays χ~ n χ ~ + leptons Edges give m(χ~ n -m(χ ~ Tovey, PPC 7 ~ χ ~ χ ll χ~ 3 ~ χ ll Events ATLAS 3 fb - ll χ / ndf 34.7 / 35 Prob.48 p 7.5 ±.37 p 6.5 ± 8.66 p ± 9.4 p ±.96 p ±.95 Parameter Without cuts Exp. value 68± ± ± Preliminary (GeV inv Similar analysis: Error (-~.5 GeV G. oortgat-pick 7 3

31 δd and δd 3 δμ and δ tanβ Example (μ 95, tanβ : assuming δ g ~ / g ~ δd /D δd 3 /D 3 δ tanβ / tanβ δ tanβ / tanβ arbitrary scale arbitrary scale arbitrary scale δd D δμ/μ Let s test this idea: 3 3 fb fb -. 7% δd D 3 3. % δμ/μ δ g ~ 4. 5% ( ( ( ( D. Tovey, Dark atter Searches of ATLAS, PPC 7 ( H. Baer et al., Precision Gluino ass at the LHC in SUSY odels with Decoupled Scalars, Phys. Rev. D75, 95 (7, reporting 8% with fb - g ~ 3

32 Ωh Determination δμ.7% μ δ tanβ ~ 3% tanβ δ m m / / 5. 6% δωh Ωh ~ 8% Dutta, Flanagan, Kamon, Krislock, to appear LHC Goal: D and D 3 at -% and gluino gluino mass at 5% 3

33 Bulk Region The most part of this region in msugra is experimentally (Higgs mass limit, b s γ ruled out Relic density is satisfied by t channel selectron, stau and sneutrino exchange Perform the end point analysis to determine the masses msugra point: m 7; A -3 m / 5; μ>; tanβ; Nojiri, Polsello, Tovey 5 sparticle ~ χ ~ χ ~ l ~ g ~ u L mass End pts value error m ll 8..9 lq( (max 365. lq (min l lq (max 45.5 llq (min 7.9 ττ (max The error of relic density:.8 ±.(stat + sys Includes: (+.,. (A; (+.,. tan β; (+.,.5 m(τ~ [With a luminosity 3 fb -, ττ edge controlled to GeV] 33

34 Case 4 : Non-U U SUGRA Nature may not be so kind Our studies have been done based on a minimal scenario( msugra Let s consider a non-universal scenario: Higgs nonuniversality: m Hu, m Hd m (most plausible extension easy to explain the D content: Reduce μ or heavy Higgs/pseudoscalar (A resonance Case steps: Reduce Higgs coupling parameter, μ, by increasing m Hu, ore annihilation (less abundance correct values of Ωh Find smoking gun signals Technique to calculate Ωh μ m Hu m ( + δ, m m (+ δ, u Hd δ d ( + D [ δ ] m u tan β For low and intermediate tanβ... + d... Where D <.3 34

35 Reference Point Ωh. Testing msugra and Extensions 35

36 Decays at Reference Point + leptons + leptons So far we have used observables with: leptons + jets, taus + jets, + jets, Higgs + jets In the non-universal scenario: We use W + jets etc 36

37 Extraction of odel Parameters 37 37

38 Extraction of Observables To select one side correctly : We collect W+j pairs: related pairs plus random pairs Use jets from the previous events to generate random pairs Normalize and perform: Same jet-previous jet Random pairs will be cancelled Left with only related pairs Successful identification of one side of the production process! N jet > 4, p T > 3 E T j, >, E T miss > 8 E T miss + E T j + E T j > 6 No e s, μ s with p T > 5 38

39 Jet+ t t invariant mass J+ t invariant mass J+ t invariant mass 39 39

40 Extraction of odel Parameters Utilizing the characteristic decays, we can create some observables to determine our model parameters eff (m, m /, jττ (m, m /, jt (m, m /, μ, tanβ jw (m, m /, μ, tt (m, m /, μ, tanb P T (low energy tau (m, m /, m, tanb m m 366 ± 6GeV, m H u / 76.7 ± 9.9GeV, tanβ 39.5 ± 3.8,A Ωh ± 3.GeV, Dutta, Kamon, Kolev, Krislock, Oh, to appear 3± 34GeV For fb - m m H u 367 ± 57GeV, m / Ωh ± 9.3GeV, 77 ± 3GeV, tanβ 39.5 ± 4.6,A ± 73GeV For fb - 4

41 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 measure the sparticle masses (highly non trivial!, establish the model and make connection between particle physics and cosmology Different cosmologically motivated regions of the minimal SUGRA model have distinct signatures. Use the signatures to construct a decision tree It is possible to determine model parameters and the relic density based on the LHC measurements non-universal model parameters (Higgs nonuniversality----can be determined 4