Title: What is SUSY
1What is SUSY
 Supersymmetry is a bosonfermion 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 nonaccelerator experiments
2Motivation of SUSY in Particle Physics
 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 !
3Motivation of SUSY in Particle Physics
 Unification of gauge couplings
Running of the strong coupling
4Motivation of SUSY
RG Equations
Unification of the Coupling Constants in the SM
and in the MSSM
Input
Output
SUSY yields unification!
5Motivation 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
6Motivation 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
7Cosmological 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
8Supersymmetry
Grassmannian parameters
SUSY Generators
This is the only possible graded Lie algebra that
mixes integer and halfinteger spins and changes
statistics
9Basics of SUSY
Quantum states
Vacuum
Energy helicity
State Expression of states
vacuum 1
1particle
2particle
Nparticle
Total of states
10SUSY 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
11Matter Superfields
 general superfield reducible representation
chiral superfield
component fields
spin0
spin1/2
auxiliary
SUSY transformation
Superpotential
is SUSY invariant
Fcomponent is a total derivative
12Gauge superfields
real superfield
Covariant derivatives
Gauge transformation
WessZumino gauge
Field strength tensor
physical fields
13SUSY Lagrangians
Superfields
Components
no derivatives
Constraint
14Superfield Lagrangians
Grassmannian integration in superspace
Matter fields
Gauge fields
Superpotential
Gauge transformation
Gauge invariant interaction
15Gauge Invariant SUSY Lagrangian
Superfields
Components
Potential
16Spontaneous Breaking of SUSY
Energy
if and only if
17Mechanism of SUSY Breaking
FayetIliopoulos (Dterm) mechanism
(in Abelian theory)
ORaifertaigh (Fterm) mechanism
Dterm
Fterm
18Minimal 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
19Particle Content of the MSSM
sleptons
leptons
squarks
quarks
higgsinos
Higgses
20SUSY Shadow World
One half is observed!
One half is NOT observed!
21The MSSM Lagrangian
The Yukawa Superpotential
superfields
Yukawa couplings
Higgs mixing term
Rparity
These terms are forbidden in the SM
B  Baryon Number L  Lepton Number S  Spin
The Usual Particle R 1 SUSY Particle
R  1
22Rparity 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
23Interactions in the MSSM
MSSM
SM
Vertices
24Creation of Superpartners at colliders
LEP II
Experimental signature missing energy and
transverse momentum
25SUSY 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
26Decay of Superpartners
squarks
sleptons
neutralino
Final sates
chargino
gluino
27Soft SUSY Breaking
Hidden sector scenario
 four scenarios
 Gravity mediation
 Gauge mediation
 Anomaly mediation
 Gaugino mediation
SUGRA
Sdilaton, Tmoduli
gravitino mass
28Soft SUSY Breaking Contd
Gauge mediation
Scalar singlet S
Messenger F
gaugino
squark
gravitino mass
LSPgravitino
Anomaly mediation
Results from conformal anomaly ß function
LSPslepton
29Soft 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
30We like elegant solutions
31 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
32 Mass Spectrum
Chargino
Neutralino
33Mass Spectrum
Squarks Sleptons
34SUSY Higgs Bosons
SM
42231
MSSM
84435
35The Higgs Potential
Minimization
Solution
At the GUT scale
No SSB in SUSY theory !
36Renormalization Group Eqns
The couplings
Soft Terms
37RG Eqns for the Soft Masses
38Radiative 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 nontrivial
minimum leading to spontaneous breaking of EW
symmetry  this is called Radiative EWSB
39The Higgs Bosons Masses
CPodd neutral Higgs A CPeven charged Higgses H
CPeven neutral Higgses h,H
Radiative corrections
40Constrained 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
41SUSY Fits
Minimize
Exp.input data Fit low tan? Parameters high tan?
42Low 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
43Allowed Regions in Parameter Space
All the requirements are fulfilled
simultaneously !
 µ is defined
 from the EWSB

?  is the best fit value
44Masses of Superpartners
45Allowed 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
46Mass 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
47The Lightest Superparticle
property
signature
stable
jets/leptons
stable
photons/jets
lepton
stable
lepton
stable
LSP is unstable ? SM particles
Rare decays Neutrinoless double ? decay
48The Higgs Mass Limit
 Indirect limit from radiative corrections
 Direct limit from Higgs nonobservation
at LEP II (CERN)
113 lt mH lt 200 GeV
At 95 C.L.
49Higgs Searches
mH ? 113.4 GeV at 95 C.L.
114 115 GeV Event
50The Higgs Mass Limit (Theory)
 The SM Higgs
 mH ? 134 GeV
? SUSY Higgs mH ? 130 GeV
51SUSY Searches at LEP
neutralinos
m?0 ? 40 GeV
charginos
m? ? 100 GeV
squarks
sleptons
ml ? 100 GeV
52SUSY Searches at Tevatron
The reach of Tevatron in
plane
Exclusion Worlds Best Limits
Dilepton Channel
mq ? 300 GeV mg ? 195 GeV
3 jet channel
53Tevatron Discovery Reach
54SUSY Searches at LHC
Reach limits for various channels at 100 fb
5 s reach in jets
channel
1
55Superparticles
Discovery of the new world of SUSY
Back to 60s New discoveries every year
56PART II EXTRA DIMENSIONS
1. The main idea 2. KaluzaKlein Approach 3.
Braneworld models 4. Possible experimental
signatures of ED
57Why dont we see extra dimensions
58KaluzaKlein Approach
compact space
PseudoEuclidean space
Minkowski space
Metrics
Fields
Eigenfunctions of Laplace operator on internal
space K
d
Masses
KK modes
Radius of the compact space
Couplings
59Multidimensional Gravity
Action
KK Expansion
Newton constant
Plank Mass
Reduction formula
60Low Scale Gravity
10
10
10
Modified Newton potential
61Brane World
Compact Dimensions
Noncompact dimensions
Kink soliton
R
Energy density
brane
Localization on the brane
(Potential well)
D4brane
New
D4brane
SM
Bulk
Spacetime of Type I superstring
62The ADD Model
graviton
metric
SM
KK gravitons
Interactions with the fields on the brane
The of KK gravitons with masses
Emission rate
63Particle content of ADD model
 (4d)dimensional picture
 (4d)dimensional massless graviton matter
 4dimensional picture
 1 massless graviton (spin 2) matter
 KK tower of massive gravitons (spin 2)
 (d1) 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
64HEP Phenomenology
New phenomena graviton emission virtual
graviton exchange
bg
LHC
65HEP Phenomenology II
 Virtual graviton exchange
q
Spin2

q
SM
Angular distribution
66RandallSandrum Models
D4brane
D4brane
Plank
TeV
Bulk
Positive tension
Negative tension
Metric
Matter
warp factor
graviton
radion
Perturbed Metric
67RandallSandrum Model contd
Brane 2
Brane 1
Wrap factor
 Massless graviton
 massive KK gravitons

 massless radion
Hierarchy Problem !
 Massless graviton
 massive KK gravitons
 massless radion
68HEP Phenomenology
The first KK graviton mode M 1 TeV
 DrellYan process
 Excess in dijet process
Exclusion plots for resonance production
Excluded
Excluded
Run I
Dj
DY
Run II
DY
Tevatron
LHC
69HEP Phenomenology II
The xsection of DY production
First KK mode
First and subsequent KK modes
Tevatron (M 700 GeV)
LHC (M 1500 GeV)
70HEP Phenomenology III
Angular dependence
LHC
LHC
71ED 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)
72What comes beyond the Standard Model ?
SM