1. Martin zur Nedden, HU Berlin 1 WS 2007/08: Physik am LHC 6. SUper SYmmetry Beyond the Standard Model Introduction into SUper SYmmetry Minimal Super Symmetric extension of the Standard Model (MSSM) Extended Higgs-Model in MSSM Super Symmetric Interactions SUSY breaking Particle spectra of SUSY (phenomenology) SUSY searches at TEVATRON and strategies for LHC

2. Martin zur Nedden, HU Berlin 2 WS 2007/08: Physik am LHC Global Fit of Standard Model Parameter

3. Martin zur Nedden, HU Berlin 3 WS 2007/08: Physik am LHC Weinberg Angle and Higgs-Masse

4. Martin zur Nedden, HU Berlin 4 WS 2007/08: Physik am LHC Standard Model Symmetry SM describes strong and electroweak interactions, L/R asymmetry Based on symmetries and gauge invariance All forces propagated by exchange of gauge fields (local gauge fields) Gauge-Bosons (Spin = 1): gluons G a μ SU(3) (8,1,0) vector bosons W i μ SU(2) (1,3,0) abelian boson B μ U(1) (1,1,0) Fermions Spin = ½: quarks [U i α,D i α ] L (3,2,1/3) quarks [U i α ] R (3,1,4/3) quarks [D i α ] R (3,1,-2/3) leptons [L α ] L (1,2,-1) leptons [e] R (1,1,-2) Higgs (Spin = 0): H-Doublet [H 0,H - ] (1,2,-1) Masses of quarks, leptons and vector bosons by spontanous symmetry breaking

5. Martin zur Nedden, HU Berlin 5 WS 2007/08: Physik am LHC Motivation for Super Symmetry Fermion Boson Symmetry basic idea: unification of all forces, no difference between fermions (matter) and bosons (forces) generator of the SUSY algebra: Q|boson> = |fermion> Q|fermion> = |boson> Difference in spin = ½, doubling of the number of particles SUSY transformation: δ|b> = ε|f> (anti-) kommutator relations {f,f} =0, [b,b] = 0, {ε,ε} = 0 : SUSY generators are fermionic Q has spin = ½, may change the helicity 2-component spinor super symmetric algebra: connection of particles with different spins

6. Martin zur Nedden, HU Berlin 6 WS 2007/08: Physik am LHC electron selectron quark squark photon photino Unification of bosons with fermions forces with matter fermios bosons fermions Supersymmetric Partners

7. Martin zur Nedden, HU Berlin 7 WS 2007/08: Physik am LHC Minimal Super Symmetric Model (MSSM) Most simple case: N=1 generators 2 super multiplets: NDoF (bosons) = NDoF(fermions) 1. chiral super multiplet [Φ, Ψ] (spin 0, ½), fermions: 2 scalars, Weyl-spinor with helicity, L/R 2. vector multiplet [λ, A] (spin ½, 1), bosons: gauge boson, massless spin ½ fermion each fundamental particle has to occur in a super multiplet each SM particle has a SUSY-partner, Δs = ½ (minimal number of new particles) fermions in the vector multiplet transforms like gauge bosons (same for L/R) chiral multiplet contains all fermions, also with different transformation behaviour unbroken super symmetry: all masses were the same obviously not the case…… SUSY must be (weakly) broken, big masses of super symmetric partners More than 100 new parameters for the theory !?

8. Martin zur Nedden, HU Berlin 8 WS 2007/08: Physik am LHC Extended Higgs Model in MSSM 2 Higgs Dublets needed, to give all particles mass Complex fields 8 degrees of freedom 3 absorbed in the longitudinal components of W- and Z-bosons 5 higgs bosons remains, 3 are neutral h 0 : light Higgs, scalar H 0 : heavy Higgs, scalar A 0 : neutral Higgs, pseudo-scalar, PC-odd H + /H - : charged Higgs, scalar h 0 /H 0 mixing states of Re(H u 0 ) and Re(H d 0 ), Mixing angle α A 0 mixing state of Re(H u 0 ) and Re(H d 0 ), Mixing angle tanβ H + /H - mixing state of H u + and H d -, Mixing angle tanβ new parameter For the masses follows:

9. Martin zur Nedden, HU Berlin 9 WS 2007/08: Physik am LHC Higgs Masses in MSSM Higgs masses depends on 2 parameters: tan β and m A : tan β 1 : m h = 0, m H 2 = M Z 2 + m A 2 tan β : m h = min(M Z, m A ), m H = max(M Z,m A ) Mass terms for A 0, H 0 and H + /H - could be very big! If m A big: m A ~ m H ~ m H +/- Mass of h 0 is limited: 0 < m h < |cos2β|M Z m h < m A < m H m H > M Z, m H +/- > M W Radiative corrections important for m h (enlarges the mass) m h 0 < 150 GeV upper limit for MSSM m h 0 < 190 GeV limit for SUSY

10. Martin zur Nedden, HU Berlin 10 WS 2007/08: Physik am LHC MSSM Higgs Masses All Higgs masses are fixed relative to 2 parameters:

11. Martin zur Nedden, HU Berlin 11 WS 2007/08: Physik am LHC Cancelation of Quantum corrections in SUSY Models

12. Martin zur Nedden, HU Berlin 12 WS 2007/08: Physik am LHC Supersymmetric Particles Chargino: (partner of W) Neutralino: (partner of Z, g) Smuon: (partner of muon)

13. Martin zur Nedden, HU Berlin 13 WS 2007/08: Physik am LHC Super Partners q L, q R, l L, l R squarks, sleptons (spin = 0) Gauge bosons g, W, B (gluino, Wino, Bino) = gauginos SM: coupling of W 0 /B 0 to Z 0 /γ Zino, Photino Higgs (scalar) 2 Higgsinos (chiral super multiplet) chiral super multiplet: left handed particles only gauge interaction the same for squarks/sleptons and quarks/leptons unification with gravity: Graviton Gravitino neutral fermionic partners Wino/Bino have the same quantum numbers as the super symmetric Higgs partners: mixing to 4 neutralinos χ 0 i (i=1..4) : the lightest neutralino is the LSP (if R-parity is conserved) charged Higgsinos: mixing to charginos χ +/- j, (j=1,2)

14. Martin zur Nedden, HU Berlin 14 WS 2007/08: Physik am LHC SUSY Interactions (R-Parity conserved) R-parity: +1 for normal particles, -1 for super symmetric partners Feynman graphs: replace at any SM-vertex (3 or 4 particle interaction) two legs by the corresponding super symmetric partners The coupling constants remains the same as in SM (strong or electroweak)

15. Martin zur Nedden, HU Berlin 15 WS 2007/08: Physik am LHC MSUGRA - Parameters m 0 : universal scalar mass at GUT scale m ½ : universal gaugino mass at GUT scale tan β : ratio of Higgs vacuum expectation value sgn μ: sing of Higgsino mass parameter A 0 : universal s-fermion mass mixing parameter M(SUSY) < 1 TeV for LSP important limits from LEP and TEVATRON

16. Martin zur Nedden, HU Berlin 16 WS 2007/08: Physik am LHC MSUGRA Masses

17. Martin zur Nedden, HU Berlin 17 WS 2007/08: Physik am LHC MSUGA Szenarios 1

18. Martin zur Nedden, HU Berlin 18 WS 2007/08: Physik am LHC MSUGRA Szenarios 2

19. Martin zur Nedden, HU Berlin 19 WS 2007/08: Physik am LHC SUSY at Hadron-Colliders search strategy: Big contribution from standard model QCD-background (Jets) look for high p T leptons and MET - squarks and gluinos : MET (strong interaction) - neutralinos and charginos : MET and high pT leptons (electro weak interaction)

20. Martin zur Nedden, HU Berlin 20 WS 2007/08: Physik am LHC Squark und Gluino Searches at TEVATRON production: decay: Search for Jets und E T miss

21. Martin zur Nedden, HU Berlin 21 WS 2007/08: Physik am LHC Result: Upper Limits (exclusions limits)

22. Martin zur Nedden, HU Berlin 22 WS 2007/08: Physik am LHC Search for Neutralinos and Charginos No improved SUSY limit found by TEVATRON up to now

23. Martin zur Nedden, HU Berlin 23 WS 2007/08: Physik am LHC Recostruction of SUSY Particles Neutralino 2 SbottomGluino CMS MC analysis M = 595 GeV M = 510 GeV M = 174 GeV M = 150 GeV M = 96 GeV edge = 78.9 +/- 2.1 GeVM = 499.4 +/- 6.6 GeV M = 585.1 +/- 11.1 GeV

24. Martin zur Nedden, HU Berlin 24 WS 2007/08: Physik am LHC SUSY in R-Parity violating Processes neutralino (LSP) unstable, no longer a dark matter candidate lepton / and baryon number conservation violated much more possible decay channels …. L - violation B - violation L - violation

25. Martin zur Nedden, HU Berlin 25 WS 2007/08: Physik am LHC Neutralino in R-Parity violating Decays production: decay: Evidence: 3 charged leptons in FS

26. Martin zur Nedden, HU Berlin 26 WS 2007/08: Physik am LHC Search at Tevatron (Neutralino decay) production: decay: Evidence: 3 charged leptons in FS Result from D0, TEVATRON: upper limit

27. Martin zur Nedden, HU Berlin 27 WS 2007/08: Physik am LHC Masse of the lightest MSSM-Higgs Mass of the lightest Higgs as a function of M A und tan(ß) from 1.6 to 15

28. Martin zur Nedden, HU Berlin 28 WS 2007/08: Physik am LHC Supersymmetric Higgs

29. Martin zur Nedden, HU Berlin 29 WS 2007/08: Physik am LHC Search for the neutral MSSM Higgs Searches at TEVATON: using multi – jet events

30. Martin zur Nedden, HU Berlin 30 WS 2007/08: Physik am LHC Di-Jet Mass (D0 / Tevatron) MSSM Higgs Search for overshoot in the invariant mass distribution of the two jets with the highest p T At least 3 b-flavoured jet are requested per event BG: multi jet production

31. Martin zur Nedden, HU Berlin 31 WS 2007/08: Physik am LHC Upper Limit for the MSSM-Higgs Mass based on di-Jet events

32. Martin zur Nedden, HU Berlin 32 WS 2007/08: Physik am LHC Search for the MSSM charged Higgs Search for MET + J + X: Direct production in weak IA, compeditiv to t Wb

33. Martin zur Nedden, HU Berlin 33 WS 2007/08: Physik am LHC MSSM – Higgs Search at LHC All region is covered…

34. Martin zur Nedden, HU Berlin 34 WS 2007/08: Physik am LHC SUSY Mass Spectra

35. Martin zur Nedden, HU Berlin 35 WS 2007/08: Physik am LHC LHC discovery potential Time Mass sensitivity 1 month ~ 1.3 TeV 1 year ~ 1.8 TeV 3 years ~ 2.5 TeV Maximum limit ~ 3 TeV Supersymmetric Particles and dark Matter The neutralino is a good candidat for dark matter in the univers, if R-parity is conserved.

36. Martin zur Nedden, HU Berlin 36 WS 2007/08: Physik am LHC LEP: Higgsmasse versus tanß