What is SUSY

1
What is SUSY

• Supersymmetry is a boson-fermion symmetry
• that is aimed to unify all forces in Nature
  including
• gravity within a singe framework
• Modern views on supersymmetry in particle
  physics
• are based on string paradigm, though low energy
• manifestations of SUSY can be found (?) at modern
• colliders and in non-accelerator experiments

2
Motivation of SUSY in Particle Physics

• Unification with Gravity

• Unification with Gravity
• Unification of gauge couplings
• Solution of the hierarchy problem
• Dark matter in the Universe
• Superstrings

Unification of matter (fermions) with forces
(bosons) naturally arises from an attempt to
unify gravity with the other interactions
Local translation general
relativity !
3
Motivation of SUSY in Particle Physics

• Unification of gauge couplings

Running of the strong coupling
4
Motivation of SUSY
RG Equations
Unification of the Coupling Constants in the SM
and in the MSSM
Input
Output
SUSY yields unification!
5
Motivation of SUSY

• Solution of the Hierarchy Problem

Cancellation of quadratic terms
Destruction of the hierarchy by radiative
corrections
SUSY may also explain the origin of the
hierarchy due to radiative mechanism
6
Motivation of SUSY

• Dark Matter in the Universe

The flat rotation curves of spiral galaxies
provide the most direct evidence for the
existence of large amount of the dark matter.
Spiral galaxies consist of a central bulge and a
very thin disc, and surrounded by an
approximately spherical halo of dark matter
SUSY provides a candidate for the Dark matter
a stable neutral particle
7
Cosmological Constraints
New precise cosmological data

• Supernova Ia explosion
• CMBR thermal fluctuations

(news from WMAP )
Hot DM (not favoured by galaxy formation)
Dark Matter in the Universe
Cold DM (rotation curves of Galaxies)
SUSY
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Supersymmetry
Grassmannian parameters
SUSY Generators
This is the only possible graded Lie algebra that
mixes integer and half-integer spins and changes
statistics
9
Basics of SUSY
Quantum states
Vacuum
Energy helicity
State Expression of states
vacuum 1
1-particle
2-particle

N-particle
Total of states
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SUSY Multiplets
scalar
spinor
helicity
-1/2 0 1/2
Chiral multiplet
of states
1 2 1
helicity
Vector multiplet
-1 -1/2 1/2 1
of states
1 1 1 1
spinor
vector
Members of a supermultiplet are called
superpartners
Extended SUSY multiplets
N4 SUSY YM helicity -1 1/2 0 1/2 1
? -1 of states 1 4 6 4 1
N8 SUGRA helicity -2 3/2 1 1/2 0 1/2 1 3/2 2
? -2 of states 1 8 28 56 70 56 28 8 1
For renormalizable theories (YM)
spin
For (super)gravity
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Matter Superfields
- general superfield reducible representation
chiral superfield
component fields
spin0
spin1/2
auxiliary
SUSY transformation
Superpotential
is SUSY invariant
F-component is a total derivative
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Gauge superfields
real superfield
Covariant derivatives
Gauge transformation
Wess-Zumino gauge
Field strength tensor
physical fields
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SUSY Lagrangians
Superfields
Components
no derivatives
Constraint
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Superfield Lagrangians
Grassmannian integration in superspace
Matter fields
Gauge fields
Superpotential
Gauge transformation
Gauge invariant interaction
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Gauge Invariant SUSY Lagrangian
Superfields
Components
Potential
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Spontaneous Breaking of SUSY
Energy
if and only if
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Mechanism of SUSY Breaking
Fayet-Iliopoulos (D-term) mechanism
(in Abelian theory)
ORaifertaigh (F-term) mechanism
D-term
F-term
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Minimal Supersymmetric Standard Model (MSSM)
SUSY of fermions of bosons
N1 SUSY
SM 28 bosonic d.o.f. 90 (96) fermionic d.o.f.
There are no particles in the SM that can be
superpartners
SUSY associates known bosons with new fermions
and known fermions with new bosons
Even number of the Higgs doublets min 2
Cancellation of axial anomalies (in each
generation)
Higgsinos
-110
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Particle Content of the MSSM
sleptons
leptons
squarks
quarks
higgsinos
Higgses
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SUSY Shadow World
One half is observed!
One half is NOT observed!
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The MSSM Lagrangian
The Yukawa Superpotential
superfields
Yukawa couplings
Higgs mixing term
R-parity
These terms are forbidden in the SM
B - Baryon Number L - Lepton Number S - Spin
The Usual Particle R 1 SUSY Particle
R - 1
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R-parity Conservation
The consequences

• The superpartners are created in pairs
• The lightest superparticle is stable

Physical output
The lightest superparticle (LSP)
should be neutral - the best
candidate is
neutralino (photino or higgsino)
It can survive from the Big Bang
and form the
Dark matter in the Universe
23
Interactions in the MSSM
MSSM
SM
Vertices
24
Creation of Superpartners at colliders
LEP II
Experimental signature missing energy and
transverse momentum
25
SUSY Production at Hadron Colliders
Annihilation channel
Gluon fusion, qq scattering and qg scattering
channels
No new data so far due to insufficient
luminosity at the Tevatron
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Decay of Superpartners
squarks
sleptons
neutralino
Final sates
chargino
gluino
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Soft SUSY Breaking
Hidden sector scenario

• four scenarios
• Gravity mediation
• Gauge mediation
• Anomaly mediation
• Gaugino mediation

SUGRA
S-dilaton, T-moduli
gravitino mass
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Soft SUSY Breaking Contd
Gauge mediation
Scalar singlet S
Messenger F
gaugino
squark
gravitino mass
LSPgravitino
Anomaly mediation
Results from conformal anomaly ß function
LSPslepton
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Soft SUSY Breaking Contd
Gaugino mediation
All scenarios produce soft SUSY breaking terms
Soft operators of dimension
Net result of SUSY breaking
scalar fileds
gauginos
SUSY spectra for various mediation mechanisms
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We like elegant solutions
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Parameter Space of the MSSM

• Three gauge coupligs
• Three (four) Yukawa matrices
• The Higgs mixing parameter
• Soft SUSY breaking terms

SUGRA Universality hypothesis soft terms are
universal and repeat the
Yukawa potential
Five universal soft parameters
and
and
in the SM
versus
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Mass Spectrum
Chargino
Neutralino
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Mass Spectrum
Squarks Sleptons
34
SUSY Higgs Bosons
SM
42231
MSSM
84435
35
The Higgs Potential
Minimization
Solution
At the GUT scale
No SSB in SUSY theory !
36
Renormalization Group Eqns
The couplings
Soft Terms
37
RG Eqns for the Soft Masses
38
Radiative EW Symmetry Breaking
Due to RG controlled running of the mass terms
from the Higgs potential they may change sign
and trigger the appearance of non-trivial
minimum leading to spontaneous breaking of EW
symmetry - this is called Radiative EWSB
39
The Higgs Bosons Masses
CP-odd neutral Higgs A CP-even charged Higgses H
CP-even neutral Higgses h,H
Radiative corrections
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Constrained MSSM
Requirements

• Unification of the gauge couplings
• Radiative EW Symmetry Breaking
• Heavy quark and lepton masses
• Rare decays (b -gt s?)
• Anomalous magnetic moment of muon
• LSP is neutral
• Amount of the Dark Matter
• Experimental limits from direct search

Allowed region in the parameter space of the MSSM
Parameter space
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SUSY Fits
Minimize
Exp.input data Fit low tan? Parameters high tan?

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Low and High tanß Solutions

• Requirements
• EWSB
• bt unification

Low tanß solution
High tanß solution

• bt unification is the
• consequence of GUT
• Non working for the
• light generations

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Allowed Regions in Parameter Space
All the requirements are fulfilled
simultaneously !

• µ is defined
• from the EWSB

? - is the best fit value
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Masses of Superpartners
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Allowed regions of parameter space
From the Higgs searches
measurement
From
Fit to all constraints
In allowed region one fulfills all the
constraints simultaneously and has the suitable
amount of the dark matter
Fit to Dark Matter constraint
46
Mass Spectrum in CMSSM
SUSY Masses in GeV
Symbol Low tan ? High tan ?
214, 413 170, 322
1028, 1016 481, 498
413, 1026 322, 499
1155 950
303, 270 663, 621
290 658
1028, 936 1040, 1010
279, 403 537, 634
953, 1010 835, 915
727, 1017 735, 906
h, H 95, 1344 119, 565
A, H 1340, 1344 565, 571
Fitted SUSY Parameters
Symbol Low tan ? High tan ?
tan ? 1.71 35.0
m 0 200 600
m 1/2 500 400
?(0) 1084 -558
A(0) 0 0
1/? GUT 24.8 24.8
M GUT 16 1.6 10 16 1.6 10
47
The Lightest Superparticle
property
signature
stable

• Gravity mediation

jets/leptons

• Gauge mediation

stable
photons/jets
lepton
stable

• Anomaly mediation

lepton
stable

• R-parity violation

LSP is unstable ? SM particles
Rare decays Neutrinoless double ? decay

• Modern limit

48
The Higgs Mass Limit

• Indirect limit from radiative corrections
• Direct limit from Higgs non-observation
  at LEP II (CERN)

113 lt mH lt 200 GeV
At 95 C.L.
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Higgs Searches
mH ? 113.4 GeV at 95 C.L.
114 -115 GeV Event
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The Higgs Mass Limit (Theory)

• The SM Higgs
• mH ? 134 GeV

? SUSY Higgs mH ? 130 GeV
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SUSY Searches at LEP
neutralinos

m?0 ? 40 GeV
charginos

m? ? 100 GeV
squarks
sleptons

ml ? 100 GeV
52
SUSY Searches at Tevatron
The reach of Tevatron in
plane
Exclusion Worlds Best Limits
Dilepton Channel

mq ? 300 GeV mg ? 195 GeV

3 jet channel
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Tevatron Discovery Reach
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SUSY Searches at LHC
Reach limits for various channels at 100 fb
5 s reach in jets
channel
-1
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Superparticles
Discovery of the new world of SUSY
Back to 60s New discoveries every year
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PART II EXTRA DIMENSIONS
1. The main idea 2. Kaluza-Klein Approach 3.
Brane-world models 4. Possible experimental
signatures of ED
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Why dont we see extra dimensions
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Kaluza-Klein Approach
compact space
Pseudo-Euclidean space
Minkowski space
Metrics
Fields
Eigenfunctions of Laplace operator on internal
space K
d
Masses
K-K modes
Radius of the compact space
Couplings
59
Multidimensional Gravity
Action
K-K Expansion
Newton constant
Plank Mass
Reduction formula
60
Low Scale Gravity
10
10
10
Modified Newton potential
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Brane World
Compact Dimensions
Non-compact dimensions
Kink soliton
R
Energy density
brane
Localization on the brane
(Potential well)
D4-brane
New
D4-brane
SM
Bulk
Space-time of Type I superstring
62
The ADD Model
graviton
metric
SM
K-K gravitons
Interactions with the fields on the brane
The of KK gravitons with masses
Emission rate
63
Particle content of ADD model

• (4d)-dimensional picture
• (4d)-dimensional massless graviton matter

• 4-dimensional picture
• 1 massless graviton (spin 2) matter
• KK tower of massive gravitons (spin 2)
• (d-1) KK spin 1 decoupling fields
• KK tower of real scalar
  decoupling fields
• KK tower of scalar fields (zero mode radion)

The SM fields are localized on the brane, while
gravitons propagate in the bulk
The gravitational coupling is
64
HEP Phenomenology
New phenomena graviton emission virtual
graviton exchange

• KK states production

bg
LHC
65
HEP Phenomenology II

• Virtual graviton exchange

q
Spin2
-
q
SM
Angular distribution
66
Randall-Sandrum Models
D4-brane
D4-brane
Plank
TeV
Bulk
Positive tension
Negative tension
Metric
Matter
warp factor
graviton
radion
Perturbed Metric
67
Randall-Sandrum Model contd
Brane 2
Brane 1
Wrap factor

• Massless graviton
• massive K-K gravitons
• massless radion

Hierarchy Problem !

• Massless graviton
• massive K-K gravitons
• massless radion

68
HEP Phenomenology
The first KK graviton mode M 1 TeV

• Drell-Yan process
• Excess in dijet process

Exclusion plots for resonance production
Excluded
Excluded
Run I
Dj
D-Y
Run II
D-Y
Tevatron
LHC
69
HEP Phenomenology II
The x-section of D-Y production
First KK mode
First and subsequent KK modes
Tevatron (M 700 GeV)
LHC (M 1500 GeV)
70
HEP Phenomenology III
Angular dependence
LHC
LHC
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ED Conclusion

• ADD Model
• The MEW/MPL hierarchy is replaced by
• The scheme is viable
• For M small enough it can be checked at modern
• and future colliders
• For d2 cosmological bounds on M are high (gt 100
  TeV),
• but for dgt2 are mild

• RS Model
• The MEW/MPL hierarchy is solved without new
  hierarchy
• A large part of parameter space will be studied
  in future
• collider experiments
• With the mechanism of radion stabilization the
  model is viable
• Cosmological scenarios are consistent (except
  the cosmological
• constant problem)

72
What comes beyond the Standard Model ?
SM