SUSY and Superstrings

1. SUSY and Superstrings Masahiro Yamaguchi Tohoku University Asian School Particles, Strings and Cosmology (NasuLec) September 25-28, 2006@Nasu, Japan

2. Phenomenology ofSUSYand Superstrings Masahiro Yamaguchi Tohoku University Asian School Particles, Strings and Cosmology (NasuLec) September 25-28, 2006@Nasu, Japan

3. 1. Introduction • Success of Standard Model • All particles (except Higgs) found • Experimental Data in Good fit with standard model predictions • no apparent deviation from SM (except neutrino oscillations) • Expect LHC to find Higgs and/or something else Han, Tanaka

4. Motivations for Beyond Standard Model • Some phenomena require Beyond SM • baryon number asymmetry in universe • dark matter • dark energy???? • neutrino oscillations • Standard Model is incomplete. • Origin of electroweak scale • Why 3-2-1 gauge groups? Why particular matter representations?  grand unification? • Why three generations? • Too many parameters • Quantum gravity  superstrings?

5. Approaches to Beyond SM H.Murayama

6. Approaches to Beyond SM (cont.) H.Murayama

7. Models of Beyond Standard Model to solve the naturalness problem • Supersymmetry • Technicolor • Top color • Little Higgs • Higgsless model • large extra dimensions • warped extra dimensions (Randall-Sundrum) • ………..

8. Supersymmetry • Promising solution to explain the naturalness problem in electroweak sector • Gauge coupling Unification achieved in supersymmetric extension

9. strength 0.12 0.1 0.08 0.06 0.04 0.02 energy scale 2.5 5 7.5 10 12.5 15 Gauge Coupling Unification Gauge coupling constants change as energy scale changes Minimal Supersymmetric Standard Model Three couplings (SU(3), SU(2), U(1)) meet at one point ~1016 GeV accidental? or suggests unification of forces in SUSY!? MSSM SM

10. I will discuss SUSY breaking masses SUSY breaking/Mediation mechanisms • directly measured by experiments • Hints to Ultra High Energy Physics • constrained by FCNC problem new physics evidence in flavor physics?

11. Superstrings (top-down approach) • Ultimate unified theory including quantum gravity • What implications to real world? • Obstacle: superstring is physics near Planck scale • many possibilities to come down to EW scale • supersymmetry at string scale • extra dimensions 104 dim • many massless modes • everything seems possible!?

12. Here I will describe (a small piece of) recent development of string phenomenology • moduli stabilization • flux compactification Important Step • Still need further developments of string theory • need experimental hints  LHC, ….

13. Talk Plan • Introduction • Standard Model and Beyond Overview of Standard Model Motivations for Beyond SM • Supersymmetry Basic Ideas Mediation Mechanisms of SUSY breaking Phenomenology and Cosmology • Alternatives Warped Extra Dimensions • Moduli Stabilization and Beyond SM KKLT set-up: low energy SUSY & Warped extra dim.

14. 2. Standard Model and Beyond 2.1 Great Success of Standard Model Gauge Symmetry Flavor Structure

15. Gauge Symmetry Nature of forces • strong, weak, electromagnetic forces = gauge force SU(3) x SU(2) x U(1) • gauge symmetry  force is mediated by gauge boson (vector boson) e.g.) U(1) case

16. Coupling between matter and gauge boson: - solely controlled by the gauge invariance (in renormalizable theory) - characterized by charge (or representation) of matter  coupling universality This has been intensively tested in electroweak sector at LEP/SLD experiments. ~90’s Z/W bosons The idea of gauge symmetry is established experimentally.

17. Gauge boson mass: Gauge boson mass term breaks gauge invariance. How can we obtain gauge boson mass in a gauge invariant way? Higgs Mechanism based on spontaneous symmetry breaking A vacuum is chosen at one point  Spontaneous Symmetry Breaking (SSB)

18. Spontaneous symmetry breaking of global symmetry Nambu-Goldstone boson SSB of gauge symmetry Would-be NG boson is absorbed into gauge boson  Gauge boson gets massive. Gauge tr. By chooing  appropriately, one can eliminate 2.

19. gauge boson mass  (coupling) x (charge) x (order parameter) physical degrees of freedom  Higgs boson

20. Higgs Mechanism in SM Gauge symmetry beraking Minimal Standard Model: SU(2) doublet Higgs with Y=+1

22. Gauge-Higgs sector

23. Masses Higgs-gauge coupling Cf. Higgs production at e^+ e^- collider

24. Elementary Higgs or Dynamical SB? 3 would-be Nambu-Goldstone bosons • elementary Higgs is not necessary • possibility of dynamical symmetry breaking e.g. technicolor “techni-pions” Two problems on dynamical symmetry breaking • how to generate lepton/quark masses • Radiative corrections: often conflict with EW precision data Elementary Higgs in SM is the most economical way.

25. Two Roles played by SM Higgs • generates W/Z gauge boson masses spontaneous gauge symmetry breaking 2) generates quark/lepton masses  Yukawa couplings

26. Quarks and Leptons • 3 replicas (3 generations) • gauge quantum numbers

27. Yukawa Interaction Standard Model…. chiral gauge theory RH quarks and LH quarks are in different representation in SU(2) x U(1) • No gauge invariant mass term for quarks/leptons • Quark/Lepton mass generation: tightly related to SSB. In SM, the interaction with Higgs yields quark/lepton masses --- very natural and economical !

28. 3 generations y_u and y_d : 3 x 3 matrices generation mixing CP violating phase (Kobayashi-Maskawa)

29. Flavor Mixing (Generation Mixing) from weak eigenbasis to mass eigenbasis No flavor-changing-neutral current (FCNC) at tree level Gauge sym (coupling universality) is essential

30. W-boson coupling Cabibbo-Kobayashi-Maskawa matrix 3 physical angles 1 physical CP phase

31. Flavor mixing is suppressed in SM Z-boson: no flavor mixing W-boson: only source of flavor mixing • suppression(GIM mechanism) • loop level • small quark mass

32. Examples No lepton flavor violation in SM One can freely rotate mass eigenbasis of massless neutrinos.

33. Present Status of SM • Gauge Symmetry: successful precision test of electroweak theory @LEP/Tevatron consistent with SM • Flavor Structure • all quarks/leptons discovered • flavor mixing in CKM framework: works well K, B-mesons • Neutrinos: neutrino oscillation requires beyond SM

34. Higgs boson • final piece of SM • not discovered (yet?) Higgs search Direct search: EW data prefers light Higgs < 250 GeV or so. Expects discovery at LHC (2007~)

35. 2.2. Motivations for Beyond Standard Model Call for Beyond SM • phenomena • SM is unsatisfactory. There must be more fundamental theory.

36. Phenomena • Particle Physics • collider experiments: SM looks perfect • Nu oscillation requires beyond SM(beyond minimal SM) • Cosmological Observations • dark energy 73% • dark matter 23% • baryons 4%  origins? • Inflationary scenario requires better understanding of scalar dynamics

37. Standard Model is unsatisfactory Gauge structure • why SU(3)xSU(2)xU(1) ? why g3 >g2>g1? • why charge quantization Qp+Qe=0! Flavor structure • Matter Representation • Why 3 generations Too many parameters -- any rationale to explain them? Gravity is not included consistently  string theory?

38. Energy Scale of Standard Model • electroweak scale 100 GeV • Planck scale 10^18 GeV • Why this big gap? • How EW scale is stabilized against huge radiative corrections? ---quadratic divergence Naturalness problem (gauge hierarchy problem)

39. Proposals • High Scale Cut-off • Quadratic divergence disappears due to symmetry • Low-Energy Supersymmetry • Low Scale (Effective) Cut-off • Quadratic divergence is due to the fact that Higgs is elementary scalar • Technicolor • Extra dimensions • little Higgs (Higgs as pseudo NG boson) • Higgs does not exist. • Higgsless model: Symmetry breaking by boundary condition of extra dimensions

40. Common Issues in Beyond SM (around EWscale) • Many of Beyond-SM introduce • new particles • new interaction • HOPE discovery of new particles/interaction at future experiments • DANGER new particles/interaction conflict with experiments

41. 1) Contribution to gauge boson propagators • S, T parameters • Some models such as technicolor: excluded 2) Flavor Problem in Beyond SM • Standard Model is too good to hide all flavor mixing phenomena (GIM mechanism) • Introduction of new particles/interaction may give too large FCNCs.

42. Suppose there is new massive vector boson X with Exchange of X boson  lepton flavor violation

43. Flavor Problem in Beyond-SM • Exchange of New particles/interaction  four fermi interaction • Kaon m > O(10^6) GeV • B-meson m> O(10^4) GeV • LFV m> O(10^5) GeV • Beyond-SM should be able to hide FCNC processes.

44. Guide for model building We should seek for model • solve naturalness problem • not disturb electroweak precision data • not generate too large FCNC • hopefully offer dark matter candidate • hopefully offer collider signatures Low-energy SUSY is such a framework.