Testing msugra and Extensions at the LHC

Transcription

1 Testing msugra and Extensions at the LHC Bhaskar Dutta and Teruki Kamon Texas A& University BS 9, Northeastern University, Boston nd June 9

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 experiments (e.g.,feri, PAELA, LU, ENON, CDS etc in tandem with the LHC will confirm a model Testing msugra and Extensions

3 SUSY at the LHC D (or l + l -, τ+τ High P T jet [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 Testing msugra and Extensions 3

4 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 ~ Testing msugra and Extensions 4

5 Relic Density and eff SUSY scale can be measured ~-% accuracy Reconstruction of masses of SUSY particles is nontrivial! All of them may not show up with sufficient branching ratios All of the model parameters may not measured! The measurement of scale does not tell us whether this model has right amount of dark matter The dark matter calculation requires other model parameters Question: Can we calculate the relic density based on the measurements at the LHC? To what accuracy? (The dark matter content is measured to be 3% with an accuracy less than 4% at WAP Testing msugra and Extensions 5

6 easurement of asses 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 We need to measure the masses of SUSY particles/model parameters asses/odel parameters need to be determined to check the cosmological status, i.e., we calculate relic density and compare with WAP, PLANCK data Testing msugra and Extensions 6

7 This Talk Goal: Develop techniques to test minimal and non-minimal scenarios and extract Ωh (standard and non-standard cosmology cases at the LHC where a limited number of SUSY mass measurements are available. We start with the minimal model and then go to non-minimal cases 4 cases : Case : Coannihilation region Case : Over-dense D region (σ OdCD ~ σ CD /, σ : D annihilation cross-section Case 3: Focus point region Case 4: Non-universality in Higgs masses We use ISAJET+PGS4 for our calculation Testing msugra and Extensions 7

8 References dn dt ( 3Hn σ v n ( 3Hn σ v n n S( & φ n eq dn dt eq + [Case ] Coannihilation (CA Region Arnowitt,, Dutta, Gurrola, * Kamon, Krislock, * Toback, PRL (8 38 For earlier studies, see Arnowitt et al., PLB 649 (7 73; Arnowitt et al., PLB 639 (6 46 [Case 3] Focus Point Region Arnowitt,, Dutta, Flanagan, # Gurrola, * Kamon, Kolev, Krislock * D density can be diluted by a factor of [Case ] Over-dense Dark atter Region Dutta, Gurrola, * Kamon, Krislock, * Lahanas, avromatos, Nanopoulos PRD 79 (9 55 [Case 4] Non-universality Arnowitt,, Dutta, Kamon, Kolev, Krislock * [Case 5] String odel Dutta, Kamon, Leggett * Testing msugra and Extensions * Graduate student, # REU student 8

9 easurement Strategies We construct kinematic variables using leptons, jets, Higgs, Z, W etc to measure different SUSY masses ττ, τj, ττj : staus are lighter than χ Zj, hj, l+l- : sleptons are heavier than χ Wj, Wττ : smaller μ region Universal Non-Universal The end-points/peak positions of the distributions of these kinematic variables determine SUSY masses/model parameters Testing msugra and Extensions 9

10 msugra: : inimal Scenario 4 parameters + sign tanβ m m A / sign( μ : H u / H :Sign of μ inw d at :Common gaugino mass at :Common scalar mass at :Trilinear couping at ( Z μ H u GUT H GUT d GUT Key experimental constraints Jegerlehner, Nyffeler, ariv:9.336 Higgs. ( g.94 > 4 GeV; 4 μ < Ω < B( b sγ < > 4 GeV 4.5 : ~ 3.σ deviation from S ~ χ h ~ χ ± <.9 (WAP 4 Testing msugra and Extensions

11 Dark atter Allowed Regions tanβ 4 A, μ > 3 Focus Point Region m (GeV c Over-dense D Region a b m / (GeV Excluded by Rare a B decay b sγ No b CD candidate 3uon c magnetic moment Coannihilation Region Testing msugra and Extensions

12 ( Ω CD Anatomy of σann Co-annihilation (CA ~ (CA Process χ Griest, Seckel ~ τ α < σ annv > ~ ~ pb Δ +. Δ A near degeneracy occurs naturally for light stau in msugra. e / k T f ~ ~ τ χ Testing msugra and Extensions

13 . 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. Testing msugra and Extensions 3

14 CA Region at tanβ 4 Δ ~ τ ~ 5 ~ Can we measure Δ at colliders? Can we measure Δ at colliders? χ 5 GeV Testing msugra and Extensions 4

15 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 Testing msugra and Extensions 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 5

16 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 Testing msugra and Extensions 6

17 Kinematical Variables using a & b 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 [Next page] Invert the equations to determine the masses 66 GeV [] taus with 4 and GeV; ττ & p Tτ in OS LS technique [] ττ < endpoint ττ ; Jets with E T > GeV; jττ masses for each jet; Choose the nd large value Peak value ~ True Value q ~ L 84 GeV Testing msugra and Extensions 7

18 pp g~ g ~ eff 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., 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 f ( g~,q ~ 6 L Testing msugra and Extensions 8

19 Ω χ D Relic Density in msugra ~ h A Z, m/ tan β, [] Established the CA region by detecting low energy τ s (p T vis > GeV [] easured 5 SUSY masses (Δ, ~χ, ~χ, q ~, g ~ gaugino Universality at ~5% ( fb - [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? 3 4 / / / /, m, m, m, m,tan β, A,tan β, A Testing msugra and Extensions 9

20 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 Testing msugra and Extensions

21 Determining msugra Parameters Solved by inverting the following functions: peak jττ peak ττ peak eff ( b peak eff 3 4 / / / /, 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 Z, m/ tan β, L 5 fb fb δω h / Ω ~ ~ χ χ h 6.% (3 fb 4.% (7 fb Testing msugra and Extensions

22 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 Testing msugra and Extensions

23 . 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? Testing msugra and Extensions 3

24 Reference Points m / 44 GeV; m 47 GeV 86.8% m / 6 GeV; m 44 GeV 77.% Testing msugra and Extensions 4

25 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 ~ 393 Z 9 ± χ~ 46 N(b > with P T > GeV;.4< ΔR bb < Testing msugra and Extensions 5

26 4 Kinematical Variables Side-band BG subtraction end point jbb peak eff ( b peak eff ( bb peak eff 3 4 / / / /, tanβ, A, tanβ, A bb (GeV where: m / 4 5 fb 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 Testing msugra and Extensions 6

27 Kinematical Templates Band Uncertainties with fb - Testing msugra and Extensions 7

28 Determining msugra Parameters Solved by inverting the following functions: end point jbb peak eff ( b peak eff ( bb peak eff 3 4 / / / /, tanβ, A, tanβ, A Testing msugra and Extensions 8

29 Determining Ωh Solved by inverting the following functions: end point jbb peak eff ( b peak eff ( bb peak eff 3 4 / / / /, tanβ, A, tanβ, A fb - m m / A tanβ 47 ± 5 44 ± 5 ± ± 8 L fb Ω χ ~ h A Z, m/ tan β, δω ~ h / Ω ~ h ~ 5% χ χ Testing msugra and Extensions 9

30 Case (b : Stau and Higgs m / 6, m 44, tanβ4, m top 75 g~ 366 u u ~ L 5 Follow Case (a and Case end point jbb peak eff ( b peak eff ( bb peak eff 3 4 / / / /, tanβ, A, tanβ, A χ~ χ~ % 77% h 4 e ~ R 494 τ ~ 376 ± χ~ 46 (peak jττ peak eff ( b peak eff peak ττ 3 4 / / / /, tanβ, A, tanβ, A Testing msugra and Extensions 3

31 Determining Ωh Solved by inverting the following functions: (peak jττ peak eff ( b peak eff peak ττ 3 4 / / / /, tanβ, A, tanβ, A 5 fb - m m / A tanβ 44 ± 3 6 ± 6 ± 45 4 ± 3 L 5 fb Ω χ ~ h A Z, m/ tan β, δω ~ h / Ω ~ h ~ 9% χ χ stau helps to determine tanβ accurately. Testing msugra and Extensions 3

32 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 - Future Works: o ore over-dense and under-dense cases? Testing msugra and Extensions 3

33 Case 3 : Focus Point Region m, A, μ, tanβ q ~ l ~ Z Z Z Z 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? Testing msugra and Extensions 33

34 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 Z W Z W Z W Z W Z W Z W Z W Z 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 Z W Z W Z W Z W Z W Z W Z W Z Μ ~ A 4x4 (m /, μ, tanβ g ~ χ χ ~ ~ D 3 3 χ χ ~ ~ D Ωh tan ( β μ Ω χ,, m Z h / ~ SUGRA odels at the LHC 34 34

35 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 ~ Testing msugra and Extensions 35

36 Ωh Determination δμ.7% μ δ tanβ ~ 3% tanβ δ m m / / 5. 6% δωh Ωh ~ 8% LHC Goal: D and D 3 at -% and gluino mass at 5% Testing msugra and Extensions 36

37 Case 4 : Non-U U SUGRA Nature may not be so kind Our studies have been done based on a minimal scenario SUGRA. Let s consider a non-universal scenario: Higgs nonuniversality: m Hu, m Hd m 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 Testing msugra and Extensions 37

38 Reference Point Ωh. Testing msugra and Extensions 38

39 Decays at Reference Point Testing msugra and Extensions 39

40 Extraction of odel Parameters Testing msugra and Extensions 4

41 (jj E miss T > 8 GeV; N(J > with E T > GeV; E miss T + E J T + E J T > 6 GeV N(j i > with p T > GeV (j i j k A clear peak at the W mass, but can we see the BG shape? Testing msugra and Extensions 4

42 Data-driven (jj Extraction Event Jets (jj (jj a, b, c (a,b (a,c(b,c a. b (a, a, (a, b, (a, c (b, a, (b, b, (b, c 3 3a, 3b, 3c, 3d (3a, a, (3a, b, (3b, a, (3b, b, (3c, a, (3c, b, (3d, a, (3d, b For each j i in Event, (j i j k is calculated with j k (a, b (3a, 3b, (3a, 3c, (3a, 3d, (3b, 3c, (3b, 3d, (3c, 3d in Event (jj > nnn GeV for normalization Testing msugra and Extensions 4

43 Testing msugra and Extensions (j (jj i j k (j i j k (j i j k (j i j k c (j i j k (jj > GeV for normalization For each j i in Event, (j i j k is calculated with j k in Event (j i j k

44 Future Testing msugra and Extensions

45 Testing msugra and Extensions 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 cosmological motivated regions of the minimal SUGRA model have distinct signatures Based on these measurement, the dark matter content of the universe will be calculated to compare with WAP/PLANCK data.

46 Conclusion The CA region can be established by detecting low energy τ s (p T vis > GeV Determine SUSY masses using: ττ, Slope, jττ, jτ, eff e.g., Peak( ττ f ( gluino, stau,, Gaugino universality test at ~5% ( fb - easure the dark matter relic density by determining m, m /, tanβ, and A using jττ, eff, ττ, and eff (b We obtain: ~ χ ~ χ δω h / Ω ~ ~ χ χ h 6% (3 fb Focus point region also determines the parameters with high accuracy Testing msugra and Extensions 46

47 Conclusion For large m, when staus are not present, the msugra parameters can still be extracted, but with less accuracy This analysis can be applied to any SUSY model Work is in progress to determine non-universal model Parameters, m H m +, m + etc. ( δ m H ( δ