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Precision Cosmology at the LHC

Precision Cosmology at the LHC. Bhaskar Dutta Texas A&M University. Cosmo 2008, Madison, Wisconsin. 25 th August ’ 08. Discovery Time…. We are about to enter into an era of major discovery. Dark Matter: we need new particles to explain the content of the universe.

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Precision Cosmology at the LHC

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  1. Precision Cosmology at the LHC Bhaskar Dutta Texas A&M University Cosmo 2008, Madison, Wisconsin 25th August ’ 08 Precision Cosmology at the LHC

  2. Discovery Time… 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! The super-partners are distributed around the weak scale Our best chance to observe SUSY is at the LHC LHC: The experiment which directly probes TeV scale Future results from Planck, direct and indirect detection in tandem with the LHC will confirm a model 2 Precision Cosmology at the LHC

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

  4. Excess in ETmiss + Jets The heavy SUSY particle mass is measured by combining the final state particles q q q q • Excess in ETmiss + Jets  R-parity conserving SUSY • Meff Measurement of the SUSY scale at 10-20%. Hinchliffe and Paige, Phys. Rev. D 55 (1997) 5520 • ETj1>100 GeV, ETj2,3,4> 50 GeV • Meff > 400 GeV (Meff ETj1+ETj2+ETj3+ETj4+ ETmiss) • ETmiss > max [100, 0.2 Meff] Precision Cosmology at the LHC 4

  5. Relic Density and Meff 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? Precision Cosmology at the LHC 5

  6. Measurement of Masses 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 the particles. Model parameters need to be determined to check the cosmological status. [Allanach, Belanger, Boudjema and Pukhov’04] Goal: Using the model parameters we calculate relic density and compare with WMAP, PLANCK data 6 Precision Cosmology at the LHC

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

  8. Coannihilation, GUT Scale In mSUGRA model the lightest stau seems to be naturally close to the lightest neutralino mass especially for large tanb For example, the lightest selectron mass is related to the lightest neutralino mass in terms of GUT scale parameters: Thus for m0 = 0, becomes degenerate with at m1/2 = 370 GeV, i.e. the coannihilation region begins at Arnowitt, Dutta, Santoso’ 01 m1/2 = (370-400) GeV For larger m1/2 the degeneracy is maintained by increasing m0 and we get a corridor in the m0 - m1/2 plane. The coannihilation channel occurs in most SUGRA models even with non-universal soft breaking. 8 Precision Cosmology at the LHC

  9. DM 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 m1/2 [Stau-Neutralino CA region] [Bulk region] is almost ruled out Precision Cosmology at the LHC

  10. CA Region at tanb = 40 Can we measure DM at colliders? Precision Cosmology at the LHC

  11. Goal for CA-analysis • Establish the “dark matter allowed region” signal • Measure SUSY masses • Determine mSUGRA parameters • Predict Wch2 and compare with WCDMh2 Precision Cosmology at the LHC

  12. Smoking Gun of CA Region 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 SUSY Masses Unique kinematics 97% 100% (CDM) 2 quarks+2 t’s +missing energy 12 Precision Cosmology at the LHC

  13. pTsoft Slope and Mtt ETvis(true) > 20, 20 GeV Number of Counts / 1 GeV ETvis(true) > 40, 20 GeV ETvis(true) > 40, 40 GeV Arnowitt, Dutta, Kamon, Kolev, Toback PLB 639 (2006) 46 pT and Mtt distributions in true di-t pairs from neutralino decay Number of Counts / 2 GeV Slope of pT distribution of “soft t” contains ΔM information Low energy t’s are an enormous challenge for the detectors Precision cosmology at the LHC 13

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

  15. Mtt Distribution Clean peak even for low DM We choose the peak position as an observable. Precision Cosmology at the LHC

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

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

  18. SUSY Anatomy SUSY Masses 97% 100% (CDM) Meff Mjtt Mtt pT(t) 18 Precision Cosmology at the LHC

  19. Mjtt Distribution Mtt < Mttendpoint Jets with ET > 100 GeV Mjtt masses for each jet Choose the 2nd large value  Mjtt(2) “other” jet gluinosquark + j We choose the peak position as an observable. 19 Precision Cosmology at the LHC

  20. Mjttpeak vs. X 20 Precision Cosmology at the LHC

  21. 4 j+ETmiss: Meff Distribution At Reference Point Meffpeak = 1220 GeV (m1/2 = 335 GeV) Meffpeak = 1331 GeV (m1/2 = 365 GeV) Meffpeak = 1274 GeV Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, PRL, 100, (2008) 231802 • ETj1>100 GeV, ETj2,3,4> 50 GeV [No e’s, m’s with pT > 20 GeV] • Meff > 400 GeV (Meff ETj1+ETj2+ETj3+ETj4+ ETmiss[No b jets; eb ~ 50%]) • ETmiss > max [100, 0.2 Meff] Precision Cosmology at the LHC

  22. Determination of tanb • One way is to determine stop and sbottom masses and then solve for A0 and tanb E.g., stop mass matrix: Problem: Stop creates a background for sbottom and … • Instead, we use observables involving third generation sparticles:Meff(b) [the leading jet is a b-jet] • We can determine tanb and A0 with good accuracy This procedure can be applied to different SUGRA models • Determination of tanb is a real problem So far: Only PT and Mtt depends on DM ( ) 22 Precision Cosmology at the LHC

  23. 3 j+1b+ETmiss :Meff(b) Distribution Meff(b)peak = 1122 GeV (m1/2 = 365 GeV) At Reference Point Meff(b)peak = 933 GeV (m1/2 = 335 GeV) Meff(b)peak = 1026 GeV Meff(b) can be used to determine A0 and tanb even without measuring stop and sbottom masses Arnowitt, Dutta, Gurrola, Kamon, Krislock, Toback, Phys. Rev. Lett. 100, (2008) 231802 • ETj1>100 GeV, ETj2,3,4> 50 GeV [No e’s, m’s with pT > 20 GeV] • Meff(b)> 400 GeV (Meff(b)ETj1=b+ETj2+ETj3+ETj4+ ETmiss[j1 = b jet]) • ETmiss > max [100, 0.2 Meff] 23 Precision Cosmology at the LHC

  24. Observables • Sort t’s by ET (ET1 > ET2 > …) • Use OS-LS method to extract t pairs from the decays SM+SUSY Background gets reduced • Ditau invariant mass: Mtt • Jet-t-t invariant mass: Mjtt • Jet-t invariant mass: Mjt • PT of the low energy t • Meff : 4 jets +missing energy • Meff(b) : 4 jets +missing energy All these variables depend on masses => model parameters Since we are using 7 variables, we can measure the model parameters and the grand unified scale symmetry (a major ingredient of this model) 24 Precision Cosmology at the LHC

  25. Determining SUSY Masses (10 fb-1) ~ ~ Meff(b) = f7(g, qL, t, b) 7 Eqs (as functions of SUSY parameters) 1s ellipse 10 fb-1 ~ ~ Invert the equations to determine the masses Phys. Rev. Lett. 100, (2008) 231802 Precision Cosmology at the LHC

  26. GUT Scale Symmetry m1/2 ~ ~ g g mass ~ ~ c c 0 0 1 1 ~ ~ c c 0 0 2 2 MGUT Log[Q] MZ We can probe the physics at the Grand unified theory (GUT) scale Use the masses measured at the LHC and evolve them to the GUT scale using mSUGRA The masses , , unify at the grand unified scale in SUGRA models Gaugino universality test at ~15% (10 fb-1) Another evidence of a symmetry at the grand unifying scale!

  27. DM Relic Density in mSUGRA ~ c 0 1 ~ c 0 2 [1] Established the CA region by detecting low energy t’s (pTvis > 20 GeV) [2] Determined SUSY masses using: Mtt, Slope, Mjtt, Mjt, Meff e.g., Peak(Mtt) = f (Mgluino, Mstau, M , M ) [3] Measure the dark matter relic density by determining m0, m1/2, tanb, and A0 Precision Cosmology at the LHC

  28. Determining mSUGRA Parameters Precision Cosmology at the LHC

  29. Mass Measurements mSUGRA Mttpeak, Meff(b)peak …. Sensitive to A0 , tanb, m0andm1/2 Mjttpeak, Meffpeak …. Sensitive to m0, m1/2 Precision Cosmology at the LHC

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

  31. Focus Point (FP) Br(g → χ20 tt) = 10.2% Br(g → χ20 uu) = 0.8% Br(g → χ30 tt) = 11.1% Br(g → χ30 uu) = 0.009% - ~ ~ - - ~ - ~ • m0 is large, m1/2 can be small, e.g., m0= 3550 GeV, m1/2=314 GeV, tanb=10, A0=0 M(gluino) = 889 GeV, ΔM(χ30- χ10) = 81 GeV, ΔM(χ20- χ10) = 59 GeV, ΔM(χ30- χ20) = 22 GeV 31 Precision Cosmology at the LHC

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

  33. Determination of masses: FP Higher jet, b-jet, lepton multiplicity requirement increase the signal over background rate Relic density calculation depends on m, tanb and m1/2 All other masses are heavy! m1/2, m and tanb can be solved from M(gluino), ΔM (χ30- χ10) and ΔM (χ20- χ10) Errors of : M(gluino), ΔM (χ30- χ10) ΔM (χ20- χ10) 300 fb-1 4.5 % 1.2% 1.7% tanbm 22% 0.1% Chargino masses can be measured! Work in Progress… 33 Precision Cosmology at the LHC

  34. Bulk Region ~ ~ ~ 01 g uL ~ ~ l 02 The most part of this region in mSUGRA is experimentally (Higgs mass limit, bs g) ruled out Relic density is mostly satisfied by t channel selectron, stau and sneutrino exchange Perform the end point analysis to determine the masses mSUGRA point: m0=70; A0=-300 m1/2=250; m>0; tanb=10; Nojiri, Polsello, Tovey’05 The error of relic density: 0.108 ± 0.1(stat + sys) ~ Includes: (+0.00,−0.002 )M(A); (+0.001, −0.011) tan β; (+0.002,−0.005) m(t2) [With a luminosity 300 fb-1, tt edge controlled to 1 GeV] Precision Cosmology at the LHC

  35. Accuracy of tanb The accuracy of determining tanb is not so good if we do not have staus in the final states. E.g., raise m0 The final states contain Z, Higgs, staus Dilaton effect creates new parameter space Lahanas, Mavromatos, Nanopoulos, Phys.Lett.B649:83-90,2007. 35 Precision Cosmology at the LHC

  36. c20DecayBranching Ratios Identify and classify c20 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: Meff (peak): f1(m0,m1/2) • Effective mass with 1 b jet: Meff (b) (peak): f2(m0,m1/2, A0, tanb) • Effective mass with 2 b jets: Meff (2b) (peak): f3(m0,m1/2, A0, tanb) • Higgs plus jet invariant mass: Mbbj(end-point): f4(m0,m1/2) 4 observables=> 4 mSUGRA parameters However there is no stau in the final states: accuracy for determining tanb will be less Precision Cosmology at the LHC

  39. Observables… Error with 1000 fb-1 39 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 Four 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 WMAP/PLANCK data. Precision Cosmology at the LHC

  43. Conclusion… ~ c 0 1 ~ c 0 2 The CA region can be established by detecting low energy t’s (pTvis > 20 GeV) Determine SUSY masses using: Mtt, Slope, Mjtt, Mjt, Meff e.g., Peak(Mtt) = f (Mgluino, Mstau, M , M ) Gaugino universality test at ~15% (10 fb-1) Measure the dark matter relic density by determining m0, m1/2, tanb, and A0 using Mjtt, Meff,Mtt, and Meff(b) We obtain: Focus point region also determines the parameters with high accuracy Precision Cosmology at the LHC

  44. Concusion… For large m0, 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 It is also possible to determine nonuniversal model Parameters, , We can use new observables, Meff(2b), Meff(t), measure heavier chargino, neutralino masses etc

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