SUSY and Superstrings

Masahiro YamaguchiTohoku University

Asian School Particles, Strings and Cosmology (NasuLec)

September 25-28, 2006@Nasu, Japan

Phenomenology of

SUSY and Superstrings

Masahiro YamaguchiTohoku University

Asian School Particles, Strings and Cosmology (NasuLec)

September 25-28, 2006@Nasu, Japan

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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

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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?

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Approaches to Beyond SM

H.Murayama

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Approaches to Beyond SM (cont.)

H.Murayama

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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)• ………..

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Supersymmetry

• Promising solution to explain the naturalness problem in electroweak sector

• Gauge coupling Unification achieved in supersymmetric extension

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2.5 5 7.5 10 12.5 15energyscale

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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!?

2.5 5 7.5 10 12.5 15

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MSSM SM

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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?

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Superstrings (top-down approach)

• Ultimate unified theory including quantum gravity

• What implications to real world?– Obstacle: superstring is physics near Planck s

cale– many possibilities to come down to EW scale

• supersymmetry at string scale• extra dimensions 104 dim• many massless modes

– everything seems possible!?

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• 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, ….

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Talk Plan1. Introduction2. 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.

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2. Standard Model and Beyond

2.1 Great Success of Standard Model

Gauge Symmetry

Flavor Structure

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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

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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.

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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)

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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

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gauge boson mass

(coupling) x (charge)

x (order parameter)

physical degrees of freedom

Higgs boson

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Higgs Mechanism in SMGauge symmetry beraking

Minimal Standard Model:

SU(2) doublet Higgs with Y=+1

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Gauge-Higgs sector

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Masses

Higgs-gauge coupling

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

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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.

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Two Roles played by SM Higgs

1) generates W/Z gauge boson masses

spontaneous gauge symmetry breaking

2) generates quark/lepton masses

Yukawa couplings

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Quarks and Leptons

• 3 replicas (3 generations)

• gauge quantum numbers

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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 !

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3 generations

y_u and y_d : 3 x 3 matrices

generation mixing

CP violating phase (Kobayashi-Maskawa)

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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

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W-boson coupling

Cabibbo-Kobayashi-Maskawa matrix 3 physical angles 1 physical CP phase

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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

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Examples

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

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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

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• 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:

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2.2. Motivations for Beyond Standard Model

Call for Beyond SM– phenomena – SM is unsatisfactory. There must be more

fundamental theory.

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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

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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?

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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 radiativ

e corrections? ---quadratic divergence

Naturalness problem (gauge hierarchy problem)

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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 e

xtra dimensions

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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

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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 g

ive too large FCNCs.

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Suppose there is new massive vector boson X with

Exchange of X boson lepton flavor violation

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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.

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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.