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

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susy and superstrings

SUSY and Superstrings

Masahiro Yamaguchi

Tohoku University

Asian School Particles, Strings and Cosmology (NasuLec)

September 25-28, 2006@Nasu, Japan

phenomenology of susy and superstrings

Phenomenology ofSUSYand Superstrings

Masahiro Yamaguchi

Tohoku University

Asian School Particles, Strings and Cosmology (NasuLec)

September 25-28, 2006@Nasu, Japan

1 introduction
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
slide4
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?
models of beyond standard model to solve the naturalness problem
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)
  • ………..
supersymmetry
Supersymmetry
  • Promising solution to explain the naturalness problem in electroweak sector
  • Gauge coupling Unification achieved in supersymmetric extension
slide9

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

slide10
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?
superstrings top down approach
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!?
slide12
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, ….
talk plan
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.

2 standard model and beyond
2. Standard Model and Beyond

2.1 Great Success of Standard Model

Gauge Symmetry

Flavor Structure

gauge symmetry
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

slide16
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.

slide17
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)

slide18
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.

slide19
gauge boson mass

 (coupling) x (charge)

x (order parameter)

physical degrees of freedom

 Higgs boson

higgs mechanism in sm
Higgs Mechanism in SM

Gauge symmetry beraking

Minimal Standard Model:

SU(2) doublet Higgs with Y=+1

slide23

Masses

Higgs-gauge coupling

Cf. Higgs production at e^+ e^- collider

elementary higgs or dynamical sb
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.

two roles played by sm higgs
Two Roles played by SM Higgs
  • generates W/Z gauge boson masses

spontaneous gauge symmetry breaking

2) generates quark/lepton masses

 Yukawa couplings

quarks and leptons
Quarks and Leptons
  • 3 replicas (3 generations)
  • gauge quantum numbers
yukawa interaction
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 !

slide28
3 generations

y_u and y_d : 3 x 3 matrices

generation mixing

CP violating phase (Kobayashi-Maskawa)

flavor mixing generation mixing
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

slide30

W-boson coupling

Cabibbo-Kobayashi-Maskawa matrix

3 physical angles

1 physical CP phase

slide31
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
slide32

Examples

No lepton flavor violation in SM

One can freely rotate mass eigenbasis of

massless neutrinos.

present status of sm
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
slide34
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~)

2 2 motivations for beyond standard model
2.2. Motivations for Beyond Standard Model

Call for Beyond SM

  • phenomena
  • SM is unsatisfactory. There must be more fundamental theory.
phenomena
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
standard model is unsatisfactory
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?

slide38
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)

proposals
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
common issues in beyond sm around ew scale
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
slide41
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.
slide42
Suppose there is new massive vector boson X with

Exchange of X boson  lepton flavor violation

flavor problem in beyond sm
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.
guide for model building
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.