Int. Summer School on HEP: SM and BEYOND 25-30 Sept. 2007, Akyaka, Turkey LECTURE I WHY TO GO BEYOND THE SM: THE SUSY R

1. Int. Summer School on HEP:SM and BEYOND25-30 Sept. 2007, Akyaka, TurkeyLECTURE IWHY 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 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) • HIGH ENERGY PHYSICS • (but AFB……) • 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 cosm, INFLAT., DE) Z bb NO NO NO NO YES YES YES

4. THE FERMION MASS PUZZLE

5. UNIFICATION ofFUNDAMENTAL INTERACTIONS Courtesy of H. Murayama

6. Fundamental COUPLING CONSTANTS are NOT CONSTANT

7. Fundamental interactions unify SSUSY (MZ) Sexp (MZ)=0.1170.002 SSM (MZ) < 0.080 Hall, Nomura

8. ForFERMIONS, VECTOR (GAUGE) and SCALAR BOSONS “MASS PROTECTION” • FERMIONS chiral symmetry • fL fR not invariant • under SU(2)x U(1) SIMMETRY PROTECTION -VECTOR BOSONS gauge symmetry FERMIONS and W,Z VECTOR BOSONS can get a mass only when the elw. symmetry is broken mf, mw ≤ <H> 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 (102-103 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. SYMMETRY MASS = 0 LIMIT NO NEW SYMMETRY IN THE 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 PROBLEMORNATURALNESS 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 SCALETHE 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 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) • HIGH ENERGY PHYSICS • (but AFB……) • 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 cosm, INFLAT., DE) Z bb NO NO NO NO YES YES YES

21. Neutrinos are MASSIVE: New Physics IS there!

22. LVIOLATED LCONSERVED THE FATE OF LEPTON NUMBER  Dirac ferm. (dull option)  Majorana ferm. SMALLNESS of m h LH 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 NEW LOW SCALE SEE - SAW MECHAN. MAJORON MODELS Minkowski; Gell-Mann, Ramond, SlansKy, Vanagida Gelmini, Roncadelli ENLARGEMENT OF THE HIGGS SCALAR SECTOR  R ENLARGEMENT OF THE FERMIONIC SPECTRUM h L L  MR R + h L R m= h    L R LR Models? L ~O h  N.B.: EXCLUDED BY LEP! R h  M

23. MICRO MACRO PARTICLE PHYSICS COSMOLOGY HOT BIG BANG STANDARD MODEL GWS STANDARD MODEL HAPPY MARRIAGE Ex: NUCLEOSYNTHESIS POINTS OF FRICTION BUT ALSO • 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 Nbaryons/Nphoton ~ 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 Nba . = Nantibar AND NO SEPARATION WELL BEFORE THEY DECOUPLE . WE WOULD BE LEFT WITH Nbar./Nphoton << 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 MHIGGS > 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 • CAUSALITY (isotropy of CMBR) • FLATNESS ( close to 1 today) • AGE OF THE UNIV. • PRIMORDIAL MONOPOLES SEVERE COSMOGICAL PROBLEMS COMMON SOLUTION FOR THESE PROBLEMS VERY FAST (EXPONENTIAL) EXPANSION IN THE UNIV.  V() VACUUM ENERGY  dominated by vacuum en. TRUE VACUUM NO WAY TO GET AN “INFLATIONARY SCALAR POTENTIAL” IN THE STANDARD MODEL

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 OBTAINELECTROWEAK 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 BEVIDENCE 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. m = 0 eV m = 1 eV (E..g., Ma 1996) m = 7 eV m = 4 eV LSS PATTERN AND NEUTRINO MASSES

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) # exp(-m/T) # does not change any more #~# m  Tdecoupl. typically ~ m /20    depends on particle physics (annih.) and “cosmological” quantities (H, T0, … 10-3  h2_ ~ <(annih.) V  > TeV2 From T0 Mplaeli ~ 2 / M2 h2 in the range 10-2 -10-1 to be cosmologically interesting (for DM) m ~ 102 -103 GeV (weak interaction) h2 ~ 10-2 -10-1 !!!

36. STABLE ELW. SCALE WIMPs from PARTICLE PHYSICS SUSY EXTRA DIM. LITTLE HIGGS. 1) ENLARGEMENT OF THE SM (x, ) (x, ji) 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 mLSP ~100 - 200 GeV * mLKP ~600 - 800 GeV 3) FIND REGION (S) PARAM. SPACE WHERE THE “L” NEW PART. IS NEUTRAL + ΩL h2 OK mLTP ~400 - 800 GeV * But abandoning gaugino-masss unif. Possible to have mLSP down to 7 GeV Bottino, Donato, Fornengo, Scopel

37. The Energy Scale from the“Observational” New Physics NO NEED FOR THE NP SCALE TO BE CLOSE TO THE ELW. SCALE neutrino masses dark matter baryogenesis inflation The Energy Scale from the “Theoretical” New Physics Stabilization of the electroweak symmetry breaking at MW 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 BEYOND25-30 Sept. 2007, Akyaka, TurkeyLectures 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 B f f B F   Sm2  ~( B - 2f )2 16 2 [m2 B - m2F ]1/2 ~ 1/√GF B In SUSY multiplet F 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)