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
















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!?



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!?
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

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.

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


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.

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



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 !

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


W-boson coupling

Cabibbo-Kobayashi-Maskawa matrix

3 physical angles

1 physical CP phase

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


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
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.
  • 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?

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)

  • 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
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.
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.