1. 1

2. 2

3. 3 H

4. 4 The SM and Beyond Inconsistency at high energies due to Landau pole Inconsistency at high energies due to Landau pole Large number of free parameters Large number of free parameters Formal unification of strong and electroweak interactions Formal unification of strong and electroweak interactions Still unclear mechanism of EW symmetry breaking Still unclear mechanism of EW symmetry breaking CP-violation is not understood CP-violation is not understood Flavour mixing and the number of generations is arbitrary Flavour mixing and the number of generations is arbitrary The origin of the mass spectrum in unclear The origin of the mass spectrum in unclear The problems of the SM: The way beyond the SM: The SAME fields with NEW The SAME fields with NEW interactions interactions GUT, SUSY, String NEW fields with NEW NEW fields with NEW interactions interactions Compositeness, Technicolour, preons preons

5. 5 Grand Unified Theories Unification of strong, weak and electromagnetic interactions within Grand Unified Theories is the new step in unification of all forces of Nature Creation of a unified theory of everything based on string paradigm seems to be possible D=10 GUT

6. 6 PART I : SUPERSYMMETRY

7. 7 What is SUSY Supersymmetry is a boson-fermion symmetry that is aimed to unify all forces in Nature including gravity within a singe framework Modern views on supersymmetry in particle physics are based on string paradigm, though low energy manifestations of SUSY can be found (?) at modern colliders and in non-accelerator experiments

8. 8 Motivation of SUSY in Particle Physics Unification with Gravity Unification of matter (fermions) with forces (bosons) naturally arises from an attempt to unify gravity with the other interactions Unification with Gravity Unification of gauge couplings Solution of the hierarchy problem Dark matter in the Universe Superstrings Local translation = general relativity !

9. 9 Motivation of SUSY in Particle Physics Unification of gauge couplings Running of the strong coupling

10. 10 Motivation of SUSY RG Equations Input Output SUSY yields unification! Unification of the Coupling Constants in the SM and in the MSSM Unification of the Coupling Constants in the SM and in the MSSM

11. 11 Motivation of SUSY Solution of the Hierarchy Problem Solution of the Hierarchy Problem Destruction of the hierarchy by radiative corrections Cancellation of quadratic terms SUSY may also explain the origin of the hierarchy due to radiative mechanism SUSY may also explain the origin of the hierarchy due to radiative mechanism

12. 12 Motivation of SUSY Dark Matter in the Universe Dark Matter in the Universe SUSY provides a candidate for the Dark matter – a stable neutral particle The flat rotation curves of spiral galaxies provide the most direct evidence for the existence of large amount of the dark matter. Spiral galaxies consist of a central bulge and a very thin disc, and surrounded by an approximately spherical halo of dark matter

13. 13 Cosmological Constraints New precise cosmological data Supernova Ia explosion CMBR thermal fluctuations (news from WMAP ) Dark Matter in the Universe: Hot DM (not favoured by galaxy formation) Cold DM (rotation curves of Galaxies) SUSY

14. 14Supersymmetry Grassmannian parameters SUSY Generators This is the only possible graded Lie algebra that mixes integer and half-integer spins and changes statistics

15. 15 Basics of SUSY Quantum states:Vacuum = Energy helicity State Expression# of states vacuum1 1-particle 2-particle ……… N-particle Total # of states

16. 16 SUSY Multiplets Chiral multiplet Vector multiplet helicity # of states -1/2 0 1/2 1 2 1 helicity # of states -1 -1/2 1/2 1 1 1 scalarspinor vector Members of a supermultiplet are called superpartners Extended SUSY multiplets N=4SUSY YMhelicity - 1 –1/2 0 1/2 1 λ = -1 # of states 1 4 6 4 1 N=8SUGRAhelicity -2 –3/2 –1 –1/2 0 1/2 1 3/2 2 λ = -2# of states 1 8 28 56 70 56 28 8 1 spin For renormalizable theories (YM) For (super)gravity

17. 17 Matter Superfields - general superfield –reducible representation chiral superfield: component fields spin=0 spin=1/2auxiliary SUSY transformationSuperpotential F-component is a total derivative is SUSY invariant

18. 18 Gauge superfields real superfield Gauge transformation Wess-Zumino gauge physical fields Field strength tensor Covariant derivatives

19. 19 SUSY Lagrangians Superfields Components no derivatives Constraint

20. 20 Superfield Lagrangians Grassmannian integration in superspace Gauge fields Gauge transformation Gauge invariant interaction Superpotential Matter fields

21. 21 Gauge Invariant SUSY Lagrangian

22. 22 Spontaneous Breaking of SUSY if and only if Energy

23. 23 Mechanism of SUSY Breaking Fayet-Iliopoulos (D-term) mechanism (in Abelian theory) O’Raifertaigh (F-term) mechanism D-termF-term

24. 24 Minimal Supersymmetric Standard Model (MSSM) SM: 28 bosonic d.o.f. & 90 (96) fermionic d.o.f. SUSY: # of fermions = # of bosonsN=1 SUSY: There are no particles in the SM that can be superpartners Even number of the Higgs doublets – min = 2 Cancellation of axial anomalies (in each generation) Higgsinos -1+1=0 SUSY associates known bosons with new fermions and known fermions with new bosons

25. 25 Particle Content of the MSSM sleptons leptons squarksquarks Higgses { higgsinos {

26. 26 SUSY Shadow World One half is observed! One half is NOT observed!

27. 27 The MSSM Lagrangian The Yukawa Superpotential Yukawa couplings Higgs mixing term R-parity B - Baryon Number L - Lepton Number S - Spin The Usual Particle : R = + 1 SUSY Particle : R = - 1 superfields These terms are forbidden in the SM

28. 28 R-parity Conservation The consequences: The superpartners are created in pairs The lightest superparticle is stable Physical output: The lightest superparticle (LSP) should be neutral - the best candidate is neutralino (photino or higgsino) It can survive from the Big Bang and form the Dark matter in the Universe

29. 29 Interactions in the MSSM

30. 30 Creation of Superpartners at colliders Experimental signature: missing energy and transverse momentum LEP II

31. 31 SUSY Production at Hadron Colliders Annihilation channel Gluon fusion, qq scattering and qg scattering channels No new data so far due to insufficient luminosity at the Tevatron

32. 32 Decay of Superpartners squarks sleptons chargino neutralino gluino Final sates

33. 33 Soft SUSY Breaking Hidden sector scenario: four scenarios: 1.Gravity mediation 2.Gauge mediation 3.Anomaly mediation 4.Gaugino mediation SUGRAS-dilaton, T-moduli gravitino mass

34. 34 Soft SUSY Breaking Cont’d Gauge mediation Scalar singlet S Messenger Φ gravitino mass Anomaly mediation LSP=slepton Results from conformal anomaly = β function gauginosquark LSP=gravitino

35. 35 Soft SUSY Breaking Cont’d Gaugino mediation SUSY spectra for various mediation mechanisms All scenarios produce soft SUSY breaking terms Soft = operators of dimension scalar filedsgauginos Net result of SUSY breaking

36. 36 We like elegant solutions

37. 37 Parameter Space of the MSSM Parameter Space of the MSSM Five universal soft parameters: and versus andin the SM SUGRA Universality hypothesis: soft terms are universal and repeat the Yukawa potential Three gauge coupligs Three (four) Yukawa matrices The Higgs mixing parameter Soft SUSY breaking terms Three gauge coupligs Three (four) Yukawa matrices The Higgs mixing parameter Soft SUSY breaking terms

38. 38 Mass Spectrum Mass Spectrum

39. 39 Mass Spectrum

40. 40 SUSY Higgs Bosons 4=2+2=3+ 1 8=4+4=3+ 5

41. 41 The Higgs Potential Minimization Solution At the GUT scale No SSB in SUSY theory !

42. 42 Renormalization Group Eqns

43. 43 RG Eqns for the Soft Masses

44. 44 Radiative EW Symmetry Breaking Due to RG controlled running of the mass terms from the Higgs potential they may change sign and trigger the appearance of non-trivial minimum leading to spontaneous breaking of EW symmetry - this is called Radiative EWSB

45. 45 The Higgs Bosons Masses CP-odd neutral Higgs A CP-even charged Higgses H CP-even neutral Higgses h,H Radiative corrections

46. 46 Constrained MSSM Unification of the gauge couplings Radiative EW Symmetry Breaking Heavy quark and lepton masses Rare decays (b -> sγ) Anomalous magnetic moment of muon LSP is neutral Amount of the Dark Matter Experimental limits from direct search Requirements: Allowed region in the parameter space of the MSSM Parameter space:

47. 47 SUSY Fits Exp.input data Fit low tan  Parameters high tan  Minimize

48. 48 Low and High tanβ Solutions Requirements: EWSB bτ unification Low tanβ solution High tanβ solution bτ unification is the consequence of GUT Non working for the light generations

49. 49 Allowed Regions in Parameter Space μ is defined from the EWSB  - is the best fit value All the requirements are fulfilled simultaneously !

50. 50 Masses of Superpartners

51. 51 Allowed regions of parameter space Fit to all constraints Fit to Dark Matter constraint From the Higgs searches measurementFrom In allowed region one fulfills all the constraints simultaneously and has the suitable amount of the dark matter

52. 52 Mass Spectrum in CMSSM Symbol Low tan  High tan  214, 413170, 322 1028, 1016481, 498 413, 1026322, 499 1155950 303, 270663, 621 290658 1028, 9361040, 1010 279, 403537, 634 953, 1010835, 915 727, 1017735, 906 h, H95, 1344119, 565 A, H1340, 1344565, 571 SUSY Masses in GeV Fitted SUSY Parameters Symbol Low tan  High tan  tan  1.7135.0 m 0 200600 m 1/2 500400  (0) 1084-558 A(0)00 1/  GUT 24.8 M GUT 16 1.6 10 16 1.6 10

53. 53 The Lightest Superparticle Gravity mediation stable propertysignature jets/leptons Gauge mediation stable photons/jets lepton Anomaly mediation stable lepton R-parity violation LSP is unstable  SM particles Rare decays Neutrinoless double  decay Modern limit

54. 54 The Higgs Mass Limit Indirect limit from radiative corrections Direct limit from Higgs non-observation at LEP II (CERN) 113 < m H < 200 GeV At 95 % C.L.

55. 55 Higgs Searches 114 -115 GeV Event m H  113.4 GeV at 95 % C.L.

56. 56 The Higgs Mass Limit The Higgs Mass Limit ( Theory ) The SM Higgs m H  134 GeV  SUSY Higgs m H  130 GeV

57. 57 SUSY Searches at LEP ~ ~ ~ charginos neutralinos m  +  100 GeV m  0  40 GeV m l  100 GeV sleptons squarks

58. 58 SUSY Searches at Tevatron mq  300 GeV mg  195 GeV ~ ~ The reach of Tevatron inplane Exclusion: World’s Best Limits Dilepton Channel 3 jet channel

59. 59 Tevatron Discovery Reach

60. 60 SUSY Searches at LHC 5 σ reach in jetschannel Reach limits for various channels at 100 fb

61. 61 S uperparticles Discovery of the new world of SUSY Back to 60’s New discoveries every year

62. 62 PART II: EXTRA DIMENSIONS

63. 63 Why don’t we see extra dimensions

64. 64 Kaluza-Klein Approach Pseudo-Euclidean space Minkowski space compact space Metrics Fields K-K modes Eigenfunctions of Laplace operator on internal space K d Radius of the compact space Masses Couplings

65. 65 Multidimensional Gravity Action K-K Expansion Newton constant Plank Mass Reduction formula

66. 66 Low Scale Gravity Modified Newton potential 10

67. 67 Brane World Compact DimensionsNon-compact dimensions Kink soliton Energy density brane SM New D4-brane Bulk Localization on the brane R (Potential well) Space-time of Type I superstring

68. 68 The ADD Model SM graviton metric K-K gravitons Interactions with the fields on the brane The # of KK gravitons with masses Emission rate

69. 69 Particle content of ADD model 4-dimensional picture 1 massless graviton (spin 2) + matter KK tower of massive gravitons (spin 2) (d-1) KK spin 1 decoupling fields KK tower of real scalar decoupling fields KK tower of scalar fields (zero mode – radion) (4+d)-dimensional picture: (4+d)-dimensional massless graviton + matter The SM fields are localized on the brane, while gravitons propagate in the bulk The “gravitational” coupling is

70. 70 HEP Phenomenology New phenomena: graviton emission & virtual graviton exchange KK states production bg LHC

71. 71 HEP Phenomenology II Virtual graviton exchange Spin=2 Angular distribution SM q q -

72. 72 Randall-Sandrum Models Plank TeV D4-brane Bulk Metric warp factor Positive tension Negative tension Matter Perturbed Metric gravitonradion

73. 73 Randall-Sandrum Model cont’d Hierarchy Problem ! Brane 1 Massless graviton massive K-K gravitons massless radion Brane 2 Wrap factor Massless graviton massive K-K gravitons massless radion

74. 74 HEP Phenomenology The first KK graviton mode M ~ 1 TeV Drell-Yan process Excess in dijet process TevatronLHC Exclusion plots for resonance production Excluded D-Y Dj Run I Run II D-Y

75. 75 HEP Phenomenology II The x-section of D-Y production Tevatron (M ~ 700 GeV)LHC (M ~ 1500 GeV) First KK modeFirst and subsequent KK modes

76. 76 HEP Phenomenology III LHC Angular dependence LHC

77. 77 ED Conclusion ADD Model The M EW /M PL hierarchy is replaced by The scheme is viable For M small enough it can be checked at modern and future colliders For d=2 cosmological bounds on M are high (> 100 TeV), but for d>2 are mild RS Model The M EW /M PL hierarchy is solved without new hierarchy A large part of parameter space will be studied in future collider experiments With the mechanism of radion stabilization the model is viable Cosmological scenarios are consistent (except the cosmological constant problem)

78. 78 What comes beyond the Standard Model ?