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### SUSY and Superstrings

### Phenomenology ofSUSYand Superstrings

Why this big gap? How EW scale is stabilized against huge radiative corrections? ---quadratic divergence

Masahiro Yamaguchi

Tohoku University

Asian School Particles, Strings and Cosmology (NasuLec)

September 25-28, [email protected], Japan

Masahiro Yamaguchi

Tohoku University

Asian School Particles, Strings and Cosmology (NasuLec)

September 25-28, [email protected], Japan

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?

Approaches to Beyond SM

H.Murayama

Approaches to Beyond SM (cont.)

H.Murayama

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 problem

- Promising solution to explain the naturalness problem in electroweak sector
- Gauge coupling Unification achieved in supersymmetric extension

strength problem

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

I will discuss SUSY breaking masses problemSUSY breaking/Mediation mechanisms

- directly measured by experiments
- Hints to Ultra High Energy Physics
- constrained by FCNC problem new physics evidence in flavor physics?

Superstrings problem(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 104 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 of string phenomenology

- 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 of string phenomenology

2.1 Great Success of Standard Model

Gauge Symmetry

Flavor Structure

Gauge Symmetry of string phenomenology

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: of string phenomenology

- 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: of string phenomenology

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)

Spontaneous symmetry breaking of global symmetry of string phenomenology 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 of string phenomenology

(coupling) x (charge)

x (order parameter)

physical degrees of freedom

Higgs boson

Higgs Mechanism in SM of string phenomenology

Gauge symmetry beraking

Minimal Standard Model:

SU(2) doublet Higgs with Y=+1

Gauge-Higgs sector of string phenomenology

Elementary Higgs or Dynamical SB? of string phenomenology

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 of string phenomenology

- generates W/Z gauge boson masses
spontaneous gauge symmetry breaking

2) generates quark/lepton masses

Yukawa couplings

Quarks and Leptons of string phenomenology

- 3 replicas (3 generations)
- gauge quantum numbers

Yukawa Interaction of string phenomenology

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 of string phenomenology

y_u and y_d : 3 x 3 matrices

generation mixing

CP violating phase (Kobayashi-Maskawa)

Flavor Mixing (Generation Mixing) of string phenomenology

from weak eigenbasis to mass eigenbasis

No flavor-changing-neutral current (FCNC) at tree level

Gauge sym (coupling universality) is essential

W-boson coupling of string phenomenology

Cabibbo-Kobayashi-Maskawa matrix

3 physical angles

1 physical CP phase

Flavor mixing is suppressed in SM of string phenomenology

Z-boson: no flavor mixing

W-boson: only source of flavor mixing

- suppression(GIM mechanism)
- loop level
- small quark mass

Examples of string phenomenology

No lepton flavor violation in SM

One can freely rotate mass eigenbasis of

massless neutrinos.

Present Status of SM of string phenomenology

- 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 of string phenomenology
- 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 of string phenomenology

Call for Beyond SM

- phenomena
- SM is unsatisfactory. There must be more fundamental theory.

Phenomena of string phenomenology

- 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 of string phenomenology

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 of string phenomenology

- electroweak scale 100 GeV
- Planck scale 10^18 GeV

Naturalness problem (gauge hierarchy problem)

Proposals of string phenomenology

- 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 of string phenomenologyscale)

- 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) of string phenomenologyContribution 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 of string phenomenology

Exchange of X boson lepton flavor violation

Flavor Problem in Beyond-SM of string phenomenology

- 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 of string phenomenology

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.

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