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

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

3. 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. 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. 5 Approaches to Beyond SM H.Murayama

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

7. 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. 8 Supersymmetry Promising solution to explain the naturalness problem in electroweak sector Gauge coupling Unification achieved in supersymmetric extension

9. 9 2.557.51012.515 energyscale 0.02 0.04 0.06 0.08 0.1 0.12 strength 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 ~10 16 GeV accidental? or suggests unification of forces in SUSY!? MSSMSM

10. 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. 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. 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. 13 Talk Plan 1.Introduction 2.Standard Model and Beyond Overview of Standard Model Motivations for Beyond SM 3.Supersymmetry Basic Ideas Mediation Mechanisms of SUSY breaking Phenomenology and Cosmology 4.Alternatives Warped Extra Dimensions 5.Moduli Stabilization and Beyond SM KKLT set-up: low energy SUSY & Warped extra dim.

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

15. 15 Gauge Symmetry -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 Nature of forces

16. 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. 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. 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   

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

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

21. 21

22. 22 Gauge-Higgs sector

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

24. 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. 25 Two Roles played by SM Higgs 1)generates W/Z gauge boson masses spontaneous gauge symmetry breaking 2) generates quark/lepton masses  Yukawa couplings

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

27. 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. 28 3 generations y_u and y_d : 3 x 3 matrices generation mixing CP violating phase (Kobayashi-Maskawa)

29. 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. 30 W-boson coupling Cabibbo-Kobayashi-Maskawa matrix 3 physical angles 1 physical CP phase

31. 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. 32 Examples No lepton flavor violation in SM One can freely rotate mass eigenbasis of massless neutrinos.

33. 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. 34 Higgs boson –final piece of SM –not discovered (yet?) Higgs search Expects discovery at LHC (2007~) EW data prefers light Higgs < 250 GeV or so. Direct search:

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

36. 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. 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. 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. 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. 40 Common Issues in Beyond SM (around EW scale) 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. 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. 42 Suppose there is new massive vector boson X with Exchange of X boson  lepton flavor violation

43. 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. 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.