1. Int. Summer School on HEP: SM and BEYOND 25-30 Sept. 2007, Akyaka, Turkey LECTURE I WHY TO GO BEYOND THE SM: THE SUSY ROAD Antonio Masiero Univ. of Padova and INFN, Padova

2. FIGURE OF MERIT OF THE SM POSITIVE ASPECTS: Renormalizable Spont. Broken Gauge Th. Excellent agreement with ALL exps. Automatic conservation of Baryon (B) and Lepton (L) quantum numbers NEGATIVE ASPECTS: Complete lack of prediction of Fermion masses and mixings, even of the number of fermion generations (FLAVOR PROBLEM) The SM does not “truly” unify fundamental interactions: still three gauge coupling constants to describe the 3 strong, weak and elm. Interactions, not to speak of gravity which is just ignored by the SM ( UNIFICATION PROBLEM) GAUGE HIERARCHY PROBLEM; i) how come that the elw, energy scale is 17 orders of magnitude smaller than the Planck scale? No dynamical reason for that within the SM ( “fundamental” aspect of the gauge hierarchy problem); Ii) even if we fix the tree level values of the higgs sector to ensure that the Higgs mass corresponds to the correct elw. scale ( i.e., it is of O(100-1000 GeV), radiative corrections are going to push the mass of the Higgs to the highest available scale present in the theory ( indeed, there exists no symmetry protection for scalar masses differently to what happens for fermion and gauge boson masses) ( “technical aspect of the gauge hierarchy problem)

3. WHY TO GO BEYOND THE SM “OBSERVATIONAL” REASONS HIGH ENERGY PHYSICS (but A FB ……) FCNC, CP  NO (but b sqq penguin …) HIGH PRECISION LOW-EN. NO (but (g-2)  …) NEUTRINO PHYSICS YE m  0,   0 COSMO - PARTICLE PHYSICS YE (DM, ∆ B cos m, INFLAT., DE) Z bb NO YES THEORETICAL REASONS INTRINSIC INCONSISTENCY OF SM AS QFT (spont. broken gauge theory without anomalies) NO ANSWER TO QUESTIONS THAT “WE” CONSIDER “FUNDAMENTAL” QUESTIONS TO BE ANSWERED BY “FUNDAMENTAL” THEORY (hierarchy, unification, flavor) NO YES

4. THE FERMION MASS PUZZLE

5. UNIFICATION of FUNDAMENTAL INTERACTIONS Courtesy of H. Murayama

6. Fundamental COUPLING CONSTANTS are NOT CONSTANT

7. Fundamental interactions unify  S SM (M Z ) < 0.080  S exp (M Z )=0.117  0.002  S SUSY (M Z) Hall, Nomura

8. “MASS PROTECTION” For FERMIONS, VECTOR (GAUGE) and SCALAR BOSONS -FERMIONS chiral symmetry f L f R not invariant under SU(2)x U(1) -VECTOR BOSONS gauge symmetry SIMMETRY PROTECTION FERMIONS and W,Z VECTOR BOSONS can get a mass only when the elw. symmetry is broken m f, m w ≤ NO SYMMETRY PROTECTION FOR SCALAR MASSES “INDUCED MASS PROTECTION” Create a symmetry (SUPERSIMMETRY) Such that FERMIONS BOSONS So that the fermion mass “protection” acts also on bosons as long as SUSY is exact SUSY BREAKING ~ SCALE OF 0 (10 2 -10 3 Gev) LOW ENERGY SUSY

9. ON THE RADIATIVE CORRECTIONS TO THE SCALAR MASSES Prove that for fermion masses the rad. corrections are only logarith. divergent.

10. DESTABILIZATION OF THE ELW. SYMMETRY BREAKING SCALE SCALAR MASSES ARE “UNPROTECTED” AGAINST LARGE CORRECTIONS WHICH TEND TO PUSH THEM UP TO THE LARGEST ENERGY SCALE PRESENT IN THE FULL THEORY EX:

11. NO NEW SYMMETRY IN THE LIMIT SYMMETRY MASS = 0 LIMIT On the contrary, in the limit of massless electron one recovers the chiral symmetry, i.e. the invariance under a separate rotation of the LH and RH components of the electron FERMION AND GAUGE BOSON MASSES WHEN SENT TO ZERO THE THEORY ACQUIRES A NEW SYMMETRY OR, EQUIVALENTLY, THEY ARISE ONLY WHEN A CERTAIN SYMMETRY IS BROKEN, i.e. THEIR VALUE CAN NEVER EXCEED THE SCALE AT WHICH SUCH SYMMETRY IS BROKEN

12. THE FINE-TUNING PROBLEM OR NATURALNESS PROBLEM When SM is embedded in a larger theory where a new scale M>> the electroweak scale the SM higgs mass receives corrections of O(M), i.e. M higgs= M higgs tree-level+ aM +bM +… Need a and b to cancel each other with a precision of O(elw. scale / M)

13. IS THE FINE-TUNING A REAL PROBLEM? WARNING: THERE EXISTS AN EVEN “LARGER” HIERARCHY OR FINE -TUNING OR NATURALNESS PROBLEM: THE COSMOLOGICAL CONSTANT PROBLEM (“ THE NOTHER” OF ALL NATURALNESS PROBLEMS QUANTUM CORRECTIONS PUSH THE VALUE OF THE COSMOLOGICAL CONSTANT UP TO THE LARGEST SYMMETRY SCALE PRESENT IN THE THEORY, I.E. THE “NATURAL” VALUE OF THE COSM. CONST. SHOULD BE OF O(MPLANCK) OR O(MGUT) WE DON’T HAVE ANY SOLUTION FOR THE COSMOLOGICAL CONSTANT PROBLEM SO FAR, I.E. WE “ACCEPT” THE FINE TUNING IN THIS CASE YET I THINK THAT WE NEED TO “SOLVE” THESE FINE TUNINGS PROBLEMS AND NOT SIMPLY ACCEPTING THEM AS GIVEN VALUES FOR DIFFERENT MASS PARAMETRS OF THE FINAL THEORY

14. THREE PATHS TO “SOLVE” THE GAUGE HIERARCHY PROBLEM 1. FIND A “ULTRAVIOLET COMPLETION” OF THE SM STABILIZING THE ELW. SCALE AT ITS PHENOMENOGICALLY NEEDED VALUE: NEW PHYSICS AT THE ELW. SCALE PROVIDING A NATURAL CUTOFF FOR THE HIGGS SCALAR MASS AT THAT SCALE THE NEW PARTICLES AND INTERACTIONS SHOULD CANCEL THE QUADRATIC DIVERGENCES WHICH WERE THE SOURCE OF THE ELW. SCALE DE-STABILIZATION

15. DYNAMICAL ELECTROWEAK SYMMETRY BREAKING 2. THE SM HIGGS BOSON IS NOT AN ELEMENTARY PARTICLE BUT RATHER A COMPOSITE PARTICLE ( FOR INSTANCE ARISING FROM A FERMION CONDENSATE) ANALOGOUSLY TO THE PION NO NEED FOR A HIGGS MASS STABILIZATION, THERE IS A NATURAL CUTOFF TO SUCH MASS WHICH IS THE SCALE AT WHICH THE HIGGS CONDENSATE FORMS

16. EXTRA - DIMENSIONS 3. THERE IS NO HIERARCHY PROBLEM BECAUSE THE LARGEST SCALE IS ACTUALLY THE ELECTROWEAK SCALE: THE WEAKNESS OF GRAVITATIONAL INTERACTIONS IS NOT LINKED TO A SUPERLARGE VALUE OF THE PLANCK SCALE, BUT RATHER TO THE FACT THAT GRAVITY “FEELS” NEW DIMENSIONS BEYOND THE 3 + 1 SPACE-TIME ORDINARY DIMENSIONS AND HENCE GOOD PART OF IUTS FLUX LINES GEY “LOST” IN THE BULK OF SUCH EXTRA DIMENSIONS

17. HOW TO COPE WITH THE HIERARCHY PROBLEM LOW-ENERGY SUSY LARGE EXTRA DIMENSIONS DYNAMICAL SYMMETRY BREAKING OF THE ELW. SYMMETRY LANDSCAPE APPROACH (ANTHROPIC PRINCIPLE)

18. THE LARGE EXTRA-DIMENSIONS WAYOUT The idea: Gravity is a very weak force not because of the extremely large scale appearing in the Newton coupling ( i.e., the Planck Mass), but because a ( major) part of the gravity flux lines are “lost” in the bulk, while “we” live on a slice (brane) which receives only a small portion of such lines Virtues: i) we don’t have to explain why Mplanck is much larger than the elw. Scale simply because the Tev scale is the ONLY scale present ; ii) there exist experimental signatures of such idea which could possibly be tested at LHC Problem: i) How to stabilize the very large extra dimensions; ii) no “predictive” unification of interactions

19. THE DYNAMICAL ELW. SYMMETRY BREAKING WAYOUT The idea: a new strong interaction ( “technicolor”) becomes strong at a scale roughly 2000 times larger than the scale where QCD gets strong. The “techniquarks” condensates break the ELW. Symmetry and give rise to the elw. Gauge boson and fermion masses. Virtues: i) there is a dynamics accounting for the large hierarchy between the Planck and elw. Scale; ii) the only examples in Nature of spontaneous symmetry breaking are through fermion condensates; iii) the problem to stabilize the Higgs mass does not exist since the Higgs mass cannot exceed the scale at which the composite higgs exists (cfr. The pion situation Problems: no phenomenologically viable model has been so far constructed; in particular the very precise elw. tests from LEP place very severe contraints on any attempt to put new paticles such the “techniquarks” at the elw. Scale.

20. WHY TO GO BEYOND THE SM “OBSERVATIONAL” REASONS HIGH ENERGY PHYSICS (but A FB ……) FCNC, CP  NO (but b sqq penguin …) HIGH PRECISION LOW-EN. NO (but (g-2)  …) NEUTRINO PHYSICS YE m  0,   0 COSMO - PARTICLE PHYSICS YE (DM, ∆ B cos m, INFLAT., DE) Z bb NO YES THEORETICAL REASONS INTRINSIC INCONSISTENCY OF SM AS QFT (spont. broken gauge theory without anomalies) NO ANSWER TO QUESTIONS THAT “WE” CONSIDER “FUNDAMENTAL” QUESTIONS TO BE ANSWERED BY “FUNDAMENTAL” THEORY (hierarchy, unification, flavor) NO YES

21. Neutrinos are MASSIVE: New Physics IS there!

22. THE FATE OF LEPTON NUMBER L VIOLATED L CONSERVED  Majorana ferm.  Dirac ferm. (dull option) SMALLNESS of m  h  L H  R m  =h  H  M   5 eV h  10 -11 EXTRA-DIM. R in the bulk: small overlap? PRESENCE OF A NEW PHYSICAL MASS SCALE NEW HIGH SCALE SEE - SAW MECHAN. Minkowski; Gell-Mann, Ramond, SlansKy, Vanagida ENLARGEMENT OF THE FERMIONIC SPECTRUM M  R  R + h  L   R  L ~O h     R h    M RR LL NEW LOW SCALE MAJORON MODELS Gelmini, Roncadelli ENLARGEMENT OF THE HIGGS SCALAR SECTOR h  L  L  m  = h    N.B.: EXCLUDED BY LEP! R  LR Models?

23. MICROMACRO PARTICLE PHYSICSCOSMOLOGY GWS STANDARD MODEL HOT BIG BANG STANDARD MODEL HAPPY MARRIAGE Ex: NUCLEOSYNTHESIS BUT ALSO POINTS OF FRICTION -COSMIC MATTER-ANTIMATTER ASYMMETRY -INFLATION - DARK MATTER + DARK ENERGY “OBSERVATIONAL” EVIDENCE FOR NEW PHYSICS BEYOND THE (PARTICLE PHYSICS) STANDARD MODEL

24. THE COSMIC MATTER-ANTIMATTER ASYMMETRY PUZZLE: -why only baryons -why N baryons /N photon ~ 10 -10 NO EVIDENCE OF ANTIMATTER WITHIN THE SOLAR SYSTEM ANTIPROTONS IN COSMIC RAYS: IN AGREEMENT WITH PRODUCTION AS SECONDARIES IN COLLISIONS IF IN CLUSTER OF GALAXIES WE HAD AN ADMIXTURE OF GALAXIES MADE OF MATTER AND ANTIMATTER THE PHOTON FLUX PRODUCED BY MATTER-ANTIMATTER ANNIHILATION IN THE CLUSTER WOULD EXCEED THE OBSERVED GAMMA FLUX IF N ba. = N antibar AND NO SEPARATION WELL BEFORE THEY DECOUPLE. WE WOULD BE LEFT WITH N bar. /N photon << 10 -10 IF BARYONS-ANTIBARYONS ARE SEPARATED EARLIER DOMAINS OF BARYONS AND ANTIBARYONS ARE TOO SMALL SMALL TODAY TO EXPLAIN SEPARATIONS LARGER THAN THE SUPERCLUSTER SIZE ONLY MATTER IS PRESENT HOW TO DYNAMICALLY PRODUCE A BARYON-ANTIBARYON ASYMMETRY STARTING FROM A SYMMETRIC SITUATION

25. COSMIC MATTER-ANTIMATTER ASYMMETRY Murayama

26. SM FAILS TO GIVE RISE TO A SUITABLE COSMIC MATTER-ANTIMATTER ASYMMETRY SM DOES NOT SATISFY AT LEAST TWO OF THE THREE SACHAROV’S NECESSARY CONDITIONS FOR A DYNAMICAL BARYOGENESIS: NOT ENOUGH CP VIOLATION IN THE SM NEED FOR NEW SOURCES OF CPV IN ADDITION TO THE PHASE PRESENT IN THE CKM MIXING MATRIX FOR M HIGGS > 80 GeV THE ELW. PHASE TRANSITION OF THE SM IS A SMOOTH CROSSOVER NEED NEW PHYSICS BEYOND SM. IN PARTICULAR, FASCINATING POSSIBILITY: THE ENTIRE MATTER IN THE UNIVERSE ORIGINATES FROM THE SAME MECHANISM RESPONSIBLE FOR THE EXTREME SMALLNESS OF NEUTRINO MASSES

27. MATTER-ANTIMATTER ASYMMETRY NEUTRINO MASSES CONNECTION: BARYOGENESIS THROUGH LEPTOGENESIS Key-ingredient of the SEE-SAW mechanism for neutrino masses: large Majorana mass for RIGHT-HANDED neutrino In the early Universe the heavy RH neutrino decays with Lepton Number violatiion; if these decays are accompanied by a new source of CP violation in the leptonic sector, then it is possible to create a lepton-antilepton asymmetry at the moment RH neutrinos decay. Since SM interactions preserve Baryon and Lepton numbers at all orders in perturbation theory, but violate them at the quantum level, such LEPTON ASYMMETRY can be converted by these purely quantum effects into a BARYON-ANTIBARYON ASYMMETRY ( Fukugita-Yanagida mechanism for leptogenesis )

28. INFLATION SEVERE COSMOGICAL PROBLEMS COMMON SOLUTION FOR THESE PROBLEMS VERY FAST (EXPONENTIAL) EXPANSION IN THE UNIV. V(  )  TRUE VACUUM VACUUM ENERGY  dominated by vacuum en. NO WAY TO GET AN “INFLATIONARY SCALAR POTENTIAL” IN THE STANDARD MODEL  CAUSALITY (isotropy of CMBR)  FLATNESS (  close to 1 today)  AGE OF THE UNIV.  PRIMORDIAL MONOPOLES

29. NO ROOM IN THE PARTICLE PHYSICS STANDARD MODEL FOR INFLATION V=  2  2 +  4 no inflation Need to extend the SM scalar potential Ex: GUT’s, SUSY GUT’s,… ENERGY SCALE OF “INFLATIONARY PHYSICS”: LIKELY TO BE » Mw DIFFICULT BUT NOT IMPOSSIBLE TO OBTAIN ELECTROWEAK INFLATION IN SM EXTENSIONS

30. THE UNIVERSE ENERGY BUDGET

31. DM: the most impressive evidence at the “quantitative” and “qualitative” levels of New Physics beyond SM QUANTITATIVE: Taking into account the latest WMAP data which in combination with LSS data provide stringent bounds on  DM and  B EVIDENCE FOR NON-BARYONIC DM AT MORE THAN 10 STANDARD DEVIATIONS!! THE SM DOES NOT PROVIDE ANY CANDIDATE FOR SUCH NON- BARYONIC DM QUALITATIVE: it is NOT enough to provide a mass to neutrinos to obtain a valid DM candidate; LSS formation requires DM to be COLD NEW PARTICLES NOT INCLUDED IN THE SPECTRUM OF THE FUNDAMENTAL BUILDING BLOCKS OF THE SM !

32. THE RISE AND FALL OF NEUTRINOS AS DARK MATTER Massive neutrinos: only candidates in the SM to account for DM. From here the “prejudice” of neutrinos of a few eV to correctly account for DM Neutrinos decouple at ~1 MeV ; being their mass<<decoupling temperature, neutrinos remain relativistic for a long time. Being very fast, they smooth out any possible growth of density fluctuation forbidding the formation of proto-structures. The “weight” of neutrinos in the DM budget is severely limited by the observations disfavoring scenarios where first superlarge structures arise and then galaxies originate from their fragmentation

33. LSS PATTERN AND NEUTRINO MASSES (E..g., Ma 1996) m = 0 eVm = 1 eV m = 7 eVm = 4 eV

34. Cosmological Bounds on the sum of the masses of the 3 neutrinos from increasingly rich samples of data sets

35. WIMPS (Weakly Interacting Massive Particles) #  ~#  m  #  exp(-m  /T) #  does not change any more T decoupl. typically ~ m  /20    depends on particle physics (  annih. ) and “cosmological” quantities (H, T 0, …    h 2 _ ~ 10 -3 TeV 2 ~  2 / M 2  From T 0 M plaeli   h 2 in the range 10 -2 -10 -1 to be cosmologically interesting (for DM) m  ~ 10 2 - 10 3 GeV (weak interaction)  h 2 ~ 10 -2 -10 -1 !!!

36. STABLE ELW. SCALE WIMPs from PARTICLE PHYSICS 1) ENLARGEMENT OF THE SM SUSY EXTRA DIM. LITTLE HIGGS. (x ,  ) (x , j i) SM part + new part Anticomm. New bosonic to cancel  2 Coord. Coord. at 1-Loop 2) SELECTION RULE DISCRETE SYMM. STABLE NEW PART. R-PARITY LSP KK-PARITY LKP T-PARITY LTP Neutralino spin 1/2 spin1 spin0 3) FIND REGION (S) PARAM. SPACE WHERE THE “L” NEW PART. IS NEUTRAL + Ω L h 2 OK * But abandoning gaugino-masss unif. Possible to have m LSP down to 7 GeV m LSP ~100 - 200 GeV * m LKP ~600 - 800 GeV m LTP ~400 - 800 GeV Bottino, Donato, Fornengo, Scopel

37. The Energy Scale from the “Observational” New Physics neutrino masses dark matter baryogenesis inflation NO NEED FOR THE NP SCALE TO BE CLOSE TO THE ELW. SCALE The Energy Scale from the “Theoretical” New Physics Stabilization of the electroweak symmetry breaking at M W calls for an ULTRAVIOLET COMPLETION of the SM already at the TeV scale + CORRECT GRAND UNIFICATION “CALLS” FOR NEW PARTICLES AT THE ELW. SCALE

38. Int. Summer School on HEP: SM and BEYOND 25-30 Sept. 2007, Akyaka, Turkey Lectures II and III BEYOND THE SM: THE SUSY ROAD Antonio Masiero Univ. of Padova and INFN, Padova

39. THE SUSY PATH

41. HIERARCHY PROBLEM: THE SUSY WAY SUSY HAS TO BE BROKEN AT A SCALE CLOSE TO 1TeV LOW ENERGY SUSY m  2   2 Scale of susy breaking F F f f B  B Sm 2  ~( B - 2 f )  2 16  2 [m 2 B - m 2 F ] 1/2 ~ 1/√G F B F In SUSY multiplet SPLITTING IN MASS BETWEEN B and F of O ( ELW. SCALE)

42. NO – GO AND NO NO-GO ON THE ROAD TO GET A SUSY SM

45. ON THE WAY TO SUPERSYMMETRIZE THE SM

46. D. KAZAKOV

48. IN SUSY WE NEED TO INTRODUCE AT LEAST TWO HIGGS DOUBLETS IN ORDER TO PROVIDE A MASS FOR BOTH THE UP- AND DOWN- QUARKS

49. BREAKING SUSY The world is clearly not supersymmetric: for instance, we have not seen a scalar of Q=1 and a mass of ½ MeV, i.e. the selectron has to be heavier than the electron and, hence, SUSU has to be broken SUSY HAS TO BE BROKEN AT A SCALE > 100 GeV SINCE NO SUSY PARTNERS HAVE BEEN SEEN UP TO THOSE ENERGIES, roughly COLORED S-PARTICLE MASSES > 200 GeV UNCOLORED S- PARTICLE MASSES > 100 GeV

50. Little digression: how to break a symmetry EXPLICIT BREAKING: add to a Lagrangian invariant under a certain symmetry S some terms which do not respect such symmetry S. Advantage: freedom in choosingsuch terms and possibility to dapt them to the phenomenological requests one has Disadvantage: losing the virtues related to the presence of a symmetry in the theory ( ex: if S is the elw. symmetry, adding an explicit mass tem to the W boson would spoil the renormalizability of the theory)

51. SPONTANEOUS BREAKING:: THE THEORY IS INVARIANT UNDER A CERTAIN SYMMETRY S ( i.e., the FULL Lagrangian respects S), however THE VACUUM OF THE THEORY IS NOT INVARIANT UNDER S TRANSFORMATIONS. ADVANTAGE: POSSIBILITY OF PRESERVING THE NICE PROPERTIES RELATED TO THE PRESENCE OF A SYMMETRY ( EX: SPONTANEOUSLY BROKEN GAUGE THEORIES ARE RENORMALIZABLE ) DISADVANTAGE: SCHEME IS MORE CONSTRAINED; ONE CANNOT CHOOSE THE BREAKING TERMS “ARBITRARILY”

52. SPONTANEOUS BREAKING OF SUSY FIRST ATTEMPT: SPONTANEOUS BREAKING OF SUSY ( letting history teach: since spontaneous breaking of the electroweak symmetry was so successful, try to repeat it in the SUSY case) PROBLEM: NO phenomenologically viable model results from spontaneously broken SUSY ( ex: one of the two selectrons remains lighter than the electron…)

53. 2 nd ATTEMPT TO BREAK SUSY: THE EXPLICIT BREAKING WISH: add to the SUSY version of the SM Lagrangian some terms which are NOT SUSY invariant, i.e. add an explicit breaking of SUSY, but try to PRESERVE the nice properties of having SUSY in the game ( for instance, still quadratic divergences should be absent even when SUSY is explicitly broken) special class of explicitly breaking terms called SOFT BREAKING TERMS OF SUSY

54. THE BASKET WHERE TO PICK UP THE WANTED ( OR NEEDED) SUSY SOFT BREAKING TERMS

55. THE SOFT BREAKING TERMS OF THE MINIMAL SUSY SM (MSSM)

56. WHICH SUSY HIDDEN SECTOR SUSY BREAKING AT SCALE  F OBSERVABLE SECTOR SM + superpartners MSSM : minimal content of superfields MESSENGERS F = M W M Pl GRAVITY M gravitino ~ F/M Pl ~ (10 2 -10 3 ) GeV GAUGE INTERACTIONS F = (10 5 - 10 6 ) GeV M gravitino ~ F/M Pl ~ (10 2 - 10 3 )eV

57. D. kAZAKOV

58. THE FATE OF B AND L IN THE SM AND MSSM IN THE SM B AND L ARE “AUTOMATIC” SYMMETRIES: NO B or L VIOLATING OPERATOR OF DIM.≤4 INVARIANT UNDER THE GAUGE SIMMETRY SU(3) X SU(2) X U(1) IS ALLOWED ( B AND L ARE CONSERVED AT ANY ORDER IN PERTURBATION THEORY, BUT ARE VIOLATED AT THE QUANTUM LEVEL (ONLY B – L IS EXACTLY PRESERVED ) IN THE MSSM, THANKS TO THE EXTENDED PARTICLE SPECTRUM WITH NEW SUSY PARTNERS CARRYING B AND L, IT IS POSSIBLE TO WRITE ( RENORMALIZABLE) OPERATORS WHICH VIOLATE EITHER B OR L IF BOTH B AND L VIOLATING OPERATORS ARE PRESENT, GIVEN THAT SUSY PARTNER MASSES ARE OF O(TEV), THERE IS NO WAY TO PREVENT A TOO FAST PROTON DECAY UNLESS THE YUKAWA COUPLINGS ARE INCREDIBLY SMALL!

59. ADDITIONAL DISCRETE SYMMETRY IN THE MSSM TO SLOW DOWN P - DECAY SIMPLEST (and nicest) SOLUTION: ADD A SYMMETRY WHICH FORBIDS ALL B AND L VIOLATING OPERATORS R PARITY SINCE B AND L 4-DIM. OPERATORS INVOLVE 2 ORDINARY FERMIONS AND A SUSY SCALAR PARTICLE, THE SIMPLEST WAY TO ELIMINATE ALL OF THEM: R = +1 FOR ORDINARY PARTICLES R = - 1 FOR SUSY PARTNERS IMPLICATIONS OF IMPOSING R PARITY: i) The superpartners are created or destroyed in pairs ; ii) THE LIGHTEST SUPERPARTNER IS ABSOLUTELY STABLE

60. BROKEN R PARITY PROTON DECAY REQUIRES THE VIOLATION OF BOTH B AND L NOT NECESSARY TO HAVE R PARITY TO KILL B AND L VIOLATING OPERATORS ENOUGH TO IMPOSE AN ADDITIONAL DISCRETE SYMMETRY TO FORBID EITHER B OR L VIOLATING OPERATORS; RESTRICTIONS ON THE YUKAWA COUPLINGS OF THE SURVIVING B OR L VIOLATING OPERATORS

61. D. KAZAKOV

62. FROM THE MSSM TO THE CMSSM ( constrained MSSM) PROLIFERATION OF PARAMETRS IN THE SOFT BREAKING SECTOR OF THE MSSM: OVERALL NUMBER OF PARAM. IN THE MSSM IS 124 (large number, but are we sure that a fundamental theory should have a “small” number of parameters?) MOST OF THIS ENORMOUS PARAM. SPACE IS IN ANY CASE ALREADY RULED OUT BY THE VARIOUS PHENOMENOLOGICAL CONSTRAINTS ON SUSY) POSSIBLE TO DRASTICALLY REDUCE THE NUMBER OF PARAM. IMPOSING ( REASONABLE?) THEORETICAL ASSUMPTIONS ON THE SOFT BREAKING SECTOR: FLAVOR UNIVERSALITY IN THE SCALAR SOFT TERMS AND GAUGINO MASS UNIVERSALITY AT THE GRAND UNIFICATION SCALE

63. D. KAZAKOV

64. RADIATIVE ELECTROWEAK SYMMETRY BREAKING IN MSSM CMSSM both higgses have positive masses squared at the GUT scale (like having µ 2 positive in the SM scalar potential), hence the tree level potential of the CMSSM does not lead to the spontaneous breaking of the elw. symmetry The masses squared of the higgses decrease during the running from the GUT scale down to lower energies; in particular, the decrease is enhanced for the mass of the higgs coupled to the top quark given the large value of the top Yukawa coupling

66. CMSSM + RADIATIVE ELW. BREAKING: A 4 – PARAMETER WORLD FREE PARAM. IN THE CMSSM : IMPOSING THE RAD. BREAKING OF THE ELW. SYMMETRY ONE ESTABLISHES A RELATION BETWEEN THE ELW. BREAKING SCALE AND THE SOFT SUSY PARAMETERS FURTHER REDUCING THE NUMBER OF THE FREE PARAM. IN THE CMSSM TO FOUR, FOR INSTANCE THE FIRST FOUR PARAM. ABOVE + THE SIGN OF µ ( THE ELW. SYMM. BREAKING FIXES ONLY THE SQUARE OF µ

67. D. KAZAKOV

70. LOW-ENERGY SUSY AND UNIFICATION

71. Int. Summer School on HEP: SM and BEYOND 25-30 Sept. 2007, Akyaka, Turkey LECTURE IV (DESPERATELY) SEEKING SUSY: ACCELERATOR PHYSICS, FLAVOR AND DARK MATTER SYNERGY Antonio Masiero Univ. of Padova and INFN, Padova

72. VIRTUAL EFFECTS for REAL NEW PHYSICS THE HEISENBERG’S UNCERTAINTY PRINCIPLE ENSURES THAT MEASUREMENTS OF PROCESSES INVOLVING LOOPS ( I.E., WITH THE PRESENCE OF VIRTUAL PARTICLES) CAN GIVE ACCESS TO HIGH MASS SCALE PHYSICS BEFORE ACCELERATORS ARE ABLE TO DIRECTLY PROBE THOSE SCALES EX. : the suppression of K L  +  - hint for the existence of the CHARM quark. Calculation of its mass from the observed rate of K - K oscillations. Heaviness of the TOP quark from observed largeness of B - B oscillations.

73. Flavor Physics: the Triumph of the CKM flavor structure of the SM By now we have achieved a “redundant” determination of the CKM mixing elements entering the quark mixing in the SM, i.e. we are probing the validity of the CKM ansatz predicted by the SM The CKM flavor structure of the SM is the DOMINANT SOURCE of the hadronic flavor mixing ( with new physics sources of flavor confined to be not larger than 20% of the CKM source)

74. ELW. SYMM. BREAKING STABILIZATION VS. FLAVOR PROTECTION: THE SCALE TENSION UV SM COMPLETION TO STABILIZE THE ELW. SYMM. BREAKING:  UV ~ O(1 TeV) Isidori

75. FLAVOR BLINDNESS OF THE NP AT THE ELW. SCALE? THREE DECADES OF FLAVOR TESTS ( Redundant determination of the UT triangle verification of the SM, theoretically and experimentally “high precision” FCNC tests, ex. b s + γ, CP violating flavor conserving and flavor changing tests, lepton flavor violating (LFV) processes, …) clearly state that: A) in the HADRONIC SECTOR the CKM flavor pattern of the SM represents the main bulk of the flavor structure and of CP violation; B) in the LEPTONIC SECTOR: although neutrino flavors exhibit large admixtures, LFV, i.e. non – conservation of individual lepton flavor numbers in FCNC transitions among charged leptons, is extremely small: once again the SM is right ( to first approximation) predicting negligibly small LFV

76. FROM DETERMINATION TO VERIFICATION OF THE CKM PATTERN FOR HADRONIC FLAVOR DESCRIPTION TREE LEVEL ONE - LOOP A. BURAS et al.

77. Single channels understood? Allowed to take the avg.?

78. Is CP violation entirely due to the KM mechanism? Y.Nir For CPV in FLAVOR CHANGING * PROCESSES it is VERY LIKELY ** that the KM mechanism represents the MAIN SOURCE *** *FC CPV : as for flavor conserving CPV there could be new phases different from the CKM phase ( importance of testing EDMs!) **VERY LIKELY: the alternative is to invoke some rather puzzling coincidence (e.g., it could be that sin2  is not that predicted by the SM, but H SM + H NP in the B d -B d mixing has the same phase as that predicted by the SM alone or it could be that the phase of the NP contribution is just the same as the SM phase) *** MAIN SOURCE : Since S  K is measured with an accuracy ~ 0.04, while the SM accuracy in predicting sin2  is ~0.2 still possible to have H NP ≤ 20% H SM in B d -B d mixing

79. What to make of this triumph of the CKM pattern in flavor tests? New Physics at the Elw. Scale is Flavor Blind CKM exhausts the flavor changing pattern at the elw. Scale MINIMAL FLAVOR VIOLATION New Physics introduces NEW FLAVOR SOURCES in addition to the CKM pattern. They give rise to contributions which are <20% in the “flavor observables” which have already been observed! MFV : Flavor originates only from the SM Yukawa coupl.

80. What a SuperB can do in testing CMFV L. Silvestrini at SuperB IV

81. SCKM basis SUPER CKM: basis in the LOW - ENERGY phenomenology where through a rotation of the whole superfield (fermion + sfermion) one obtains DIAGONAL Yukawa COUPL. for the corresponding fermion field fi  fifi ~ ~  ~ ~ x f j ~ o Unless m f and m f are aligned, f is not a mass eigenstate Hall, Kostelecki, Raby ~  ij f  ij f   ij f / m f ave ~

82. BOUNDS ON THE HADRONIC FCNC: 1 - 3 DOWN GENERATION

83. SuperB vs. LHC Sensitivity Reach in testing  SUSY SuperB can probe MFV ( with small-moderate tan  ) for TeV squarks; for a generic non-MFV MSSM sensitivity to squark masses > 100 TeV ! L. Silvestrini

84. LFV and NEW PHYSICS Flavor in the HADRONIC SECTOR: CKM paradigm Flavor in the LEPTONIC SECTOR: - Neutrino masses and (large) mixings - Extreme smallness of LFV in the charged lepton sector of the SM with massive neutrinos: l i l k suppressed by (m 2 - m 2 ) / M W 2 ik

85. Non-diagonality of the slepton mass matrix in the basis of diagonal lepton mass matrix depends on the unitary matrix U which diagonalizes (f + f ) ~ SUSY SEESAW: Flavor universal SUSY breaking and yet large lepton flavor violation Borzumati, A. M. 1986 (after discussions with W. Marciano and A. Sanda)

86. LFV in SUSYGUTs with SEESAW M Pl M GUT M R M W Scale of appearance of the SUSY soft breaking terms resulting from the spontaneous breaking of supergravity Low-energy SUSY has “memory” of all the multi-step RG occurring from such superlarge scale down to M W potentially large LFV Barbieri, Hall; Barbieri, Hall, Strumia; Hisano, Nomura, Yanagida; Hisano, Moroi, Tobe Yamaguchi; Moroi;A.M.,, Vempati, Vives; Carvalho, Ellis, Gomez, Lola; Calibbi, Faccia, A.M, Vempati LFV in MSSMseesaw:  e  Borzumati, A.M.   Blazek, King; General analysis: Casas Ibarra; Lavignac, Masina,Savoy; Hisano, Moroi, Tobe, Yamaguchi; Ellis, Hisano, Raidal, Shimizu; Fukuyama, Kikuchi, Okada; Petcov, Rodejohann, Shindou, Takanishi; Arganda, Herrero; Deppish, Pas, Redelbach, Rueckl; Petcov, Shindou

87. Bright prospects for the experimental sensitivity to LFV Running: BaBar, Belle Upcoming: MEG (2007) Future: SuperKEKB (2011) PRISM/PRIME (next decade) Super Flavour factory (?) Experiments:

88. µ e+  in SUSYGUT: past and future CALIBBI, FACCIA, A.M., VEMPATI

89. LFV from SUSY GUTsLorenzo Calibbi and PRISM/PRIME conversion experiment

90. LFV LHC SENSITIVITIES IN PROBING THE SUSY PARAM. SPACE CALIBBI, FACCIA, A.M., VEMPATI

91. Large mixing large b-s transitions in SUSY GUTs In SU(5) d R l L connection in the 5-plet Large (  l 23 ) LL induced by large f of O(f top ) is accompanied by large (  d 23 ) RR In SU(5) assume large f (Moroi) In SO(10) f large because of an underlying Pati-Salam symmetry (Darwin Chang, A.M., Murayama) See also: Akama, Kiyo, Komine, Moroi; Hisano, Moroi, Tobe, Yamaguchi, Yanagida; Hisano, Nomura; Kitano,Koike, Komine, Okada

92. FCNC HADRON-LEPTON CONNECTION IN SUSYGUT If M Pl M GUT M W soft SUSY breaking terms arise at a scale > M GUT, they have to respect the underlying quark-lepton GU symmetry constraints on  quark from LFV and constraints on  lepton from hadronic FCNC Ciuchini, A.M., Silvestrini, Vempati, Vives PRL general analysis Ciuchini, A.M., Paradisi, Silvestrini, Vempati, Vives hep-ph/0702144

93. DEVIATION from  - e UNIVERSALITY A.M., Paradisi, Petronzio

94. H mediated LFV SUSY contributions to R K Extension to B l deviation from universality Isidori, Paradisi

95. SUSY & DM : a successful marriage Supersymmetrizing the SM does not lead necessarily to a stable SUSY particle to be a DM candidate. However, the mere SUSY version of the SM is known to lead to a too fast p-decay. Hence, necessarily, the SUSY version of the SM has to be supplemented with some additional ( ad hoc?) symmetry to prevent the p- decay catastrophe. Certainly the simplest and maybe also the most attractive solution is to impose the discrete R-parity symmetry MSSM + R PARITY LIGHTEST SUSY PARTICLE (LSP) IS STABLE. The LSP can constitute an interesting DM candidate in several interesting realizations of the MSSM ( i.e., with different SUSY breaking mechanisms including gravity, gaugino, gauge, anomaly mediations, and in various regions of the parameter space).

96. WHO IS THE LSP? SUPERGRAVITY ( transmission of the SUSY breaking from the hidden to the obsevable sector occurring via gravitational interactions): best candidate to play the role of LSP: NEUTRALINO ( i.e., the lightest of the four eigenstates of the 4x4 neutralino mass matrix) In CMSSM: the LSP neutralino is almost entirely a BINO

97. GRAVITINO LSP? GAUGE MEDIATED SUSY BREAKING (GMSB) : LSP likely to be the GRAVITINO ( it can be so light that it is more a warm DM than a cold DM candidate ) Although we cannot directly detect the gravitino, there could be interesting signatures from the next to the LSP ( NLSP) : for instance the s-tau could decay into tau and gravitino, Possibly with a very long life time, even of the order of days or months

98. HUNTING FOR DARK MATTER DIRECT DM SEARCHES INDIRECT DM SEARCHES

99. INDIRECT SEARCHES OF DM WIMPs collected inside celestial bodies ( Earth, Sun): their annihilations produce energetic neutrinos WIMPs in the DM halo: WIMP annihilations can take place ( in particular, their rate can be enhanced with there exists a CLUMPY distribution of DM as computer simulations of the DM distribution in the galaxies seem to suggest. From the WIMP annihilation: -- energetic neutrinos ( under-ice, under-water exps Amanda, Antares, Nemo, Antares, …) --photons in tens of GeV range ( gamma astronomy on ground Magic, Hess, … or in space Glast…) --antimatter: look for an excess of antimatter w.r.t. what is expected in cosmic rays ( space exps. Pamela, AMS, …)

100. SEARCHING FOR WIMPs WIMPS HYPOTHESIS DM made of particles with mass 10Gev - 1Tev ELW scale With WEAK INTERACT. LHC, ILC may PRODUCE WIMPS WIMPS escape the detector MISSING ENERGY SIGNATURE FROM “KNOWN” COSM. ABUNDANCE OF WIMPs PREDICTION FOR WIMP PRODUCTION AT COLLIDERS WITHOUT SPECYFING THE PART. PHYSICS MODEL OF WIMPs BIRKEDAL, MATCHEV, PERELSTEIN, FENG,SU, TAKAYAMA

101. Tightness of the DM constraints in Minimal Supergravity Ellis et al.

102. Tightness of the DM constraint on minimal supergravity Ellis, Olive, Santoso, Spanos

103. Tightness …3

104. LFV - DM CONSTRAINTS IN MINIMAL SUPERGRAVITY A.M., Profumo, Vempati, Yaguna

105. A.M., PROFUMO, ULLIO

109. DM SUSY:HOW FAR ARE WE IN DIRECT SEARCHES? Ellis et al.

111. SPIN - INDEPENDENT NEUTRALINO - PROTON CROSS SECTION FOR ONE OF THE SUSY PARAM. FIXED AT 10 TEV

112. REACH OF FUTURE FACILITIES FOR NEUTRALINO DETECTION THROUGH ANTIMATTER SEARCHES WITH FIXED M 1 = 500 GEV N03 adiabatically contracted profile Burkert profile

115. SEARCHING FOR WIMPs WIMPS HYPOTHESIS DM made of partcles with mass 10Gev - 1Tev ELW scale With WEAK INTERACT LHC, ILC may PRODUCE WIMPS WIMPS escape the detector MISSING ENERGY SIGNATURE FROM “KNOW” COSM. ABUNDANCE OF WIMPs PREDICTION FOR WIMP PRODUCTION AT COLLIDERS WITHOUT SPECYFING THE PART. PHYSICS MODEL OF WIMPs BIRKEDAL, MATCHEV, PERELSTEIN, FENG,SU, TAKAYAMA

117. DMDE DO THEY “KNOW” EACH OTHER? DIRECT INTERACTION  (quintessence) EITH DARK MATTER DANGER:  Very LIGHT m  ~ H 0 -1 ~ 10 -33 eV Threat of violation of the equivalence principle constancy of the fundamental “constants”,… INFLUENCE OF  ON THE NATURE AND THE ABUNDANCE OF CDM Modifications of the standard picture of WIMPs FREEZE - OUT CDM CANDIDATES

118. NEUTRALINO RELIC ABUNDANCE IN GR AND S-T THEORIES OF GRAVITY

119. ON THE COMPLEMENTARITY OF DM and LFV SEARCHES to DIRECT LHC SEARCHES FOR NP Twofold meaning of such complementarity: i)synergy in “reconstructing” the “fundamental theory” staying behind the signatures of NP; ii) coverage of complementary areas of the NP parameter space ( ex.: multi-TeV SUSY physics)

120. FCNC, CP ≠, (g-2), (  ) 0 m  n    … LINKED TO COSMOLOGICAL EVOLUTION Possible interplay with dynamical DE NEW PHYSICS AT THE ELW SCALE DM - FLAVOR for DISCOVERY and/or FUND. TH. RECONSTRUCTION A MAJOR LEAP AHEAD IS NEEDED LFV NEUTRINO PHYSICSLEPTOGENESIS TEVATRON I L C

123. LES JEUX SONT FAITS; RIEN NE VA PLUS FINALLY AFTER SO MUCH SPECULATION THE WORD COMES TO THE EXPERIMENT: LHC WILL TELL US WHETHER THERE IS AND POSSIBLY WHAT IT IS THE NP RELATED TO THE ELW. SYMMETRY BREAKING

124. ON THE SUSY BET Dialogue between a professor and a student at a summer school : -Q: professor, what is the most likely NP? -A: no doubt, SUSY (MSSM) -Q: professor, what is the probability that SUSY is the right NP at the TeV scale? -A: let’s say, 5% or so -Q: But, professor, you said that SUSY is the most likely NP, and now you say that it has 5% chance to be it? -A: yes, but you should consider that all the rest has been proposed as NP has 5 per mille probabibility to be right!