Basics of SUSY

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Basics of SUSY
phenomenology
Dmitri Kazakov
JINR / ITEP
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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

First papers in 1971-1972 No evidence in
particle physics yet
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Motivation of SUSY in Particle Physics

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

• Unification with Gravity

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

• Unification of gauge couplings

Running of the strong coupling
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Motivation of SUSY
RG Equations
Unification of the Coupling Constants in the SM
and in the MSSM
Input
Amaldi, de Boer, Fuerstenau91
Output
SUSY yields unification!
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Motivation of SUSY

• Solution of the Hierarchy Problem

Cancellation of quadratic terms
Destruction of the hierarchy by radiative
corrections
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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
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Cosmological Constraints
New precise cosmological data

• Supernova Ia explosion
• CMBR thermal fluctuations

Hot DM (not favoured by galaxy formation)
Dark Matter in the Universe
Cold DM (rotation curves of Galaxies)
SUSY
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Superalgebra
Grassmannian parameters
SUSY Generators
This is the only possible graded Lie algebra that
mixes integer and half-integer spins and changes
statistics
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Quantum States
Quantum states
Vacuum
Energy helicity
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
For renormalizable theories (YM)
spin
For (super)gravity
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Simplest (N1) SUSY Multiplets
Bosons and Fermions come in pairs
Spin 0
Spin 1/2
Spin 1
Spin 1/2
Spin 3/2
Spin 2
scalar
gravitino
chiral fermion
graviton
vector
mayorana fermion
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SUSY Transformation
N1 SUSY Chiral supermultiplet
parameter of SUSY transformation (spinor)
spin0
spin1/2
Auxiliary field
(unphysical d.o.f. needed to close SYSY algebra )
SUSY multiplets
Superfiled in Superspace
Expansion over grassmannian parameter
superfield
component fields
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Gauge superfields
Gauge superfield
Field strength tensor
Gauge transformation
Wess-Zumino gauge
Covariant derivatives
physical fields
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How to write SUSY Lagrangians
1st step
Take your favorite Lagrangian written in terms of
fields
2nd step
Replace
3rd step
Replace
Grassmannian integration in superspace
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SUSY Lagrangian (Matter)
Superfields
Superpotential
Kinetic term
Components
no derivatives
Constraint
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SUSY Lagrangians (gauge)
Gauge fields
Gauge transformation
Gauge invariant interaction with matter
(covariant derivative)
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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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The MSSM Lagrangian
The Yukawa Superpotential
Superfields
Yukawa couplings
Higgs mixing term
These terms are forbidden in the SM
Violate
Lepton number
Baryon number
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R-parity
B - Baryon Number L - Lepton Number S - Spin
The Usual Particle R 1 SUSY Particle
R - 1
The consequences

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

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
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Interactions in the MSSM
MSSM
SM
Vertices
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Creation of Superpartners at colliders
Annihilation channel
Gluon fusion, ee, qq scattering and qg scattering
channels
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Decay of Superpartners
squarks
sleptons
neutralino
Final sates
chargino
gluino
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Soft SUSY Breaking
Hidden sector
MSSM
SUSY
Messengers Gravitons, gauge,
gauginos, etc
Breaking via F and D terms in a hidden sector
gauginos
scalar fields
Over 100 of free parameters !
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We like elegant solutions
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MSSM Parameter Space

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

mSUGRA
Universality hypothesis (gravity is colour and
flavour blind) Soft parameters are equal at
Planck (GUT) scale
Five universal soft parameters
in the SM
versus
and
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Mass Spectrum
Chargino
Neutralino
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Mass Spectrum
Squarks Sleptons
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Renormalization Group Eqns
The couplings
Soft Terms
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RG Eqns for the Soft Masses
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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
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SUSY Higgs Bosons
SM
42231
MSSM
84435
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The Higgs Potential
Minimization
Solution
At the GUT scale
No SSB in SUSY theory !
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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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The Higgs Mass Limit

• The SM Higgs
• mH ? 134 GeV

? SUSY Higgs mH ? 130 GeV
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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
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Constrained MSSM (Choice of constraints)
Experimental lower limits on Higgs and
superparticle masses
Regions excluded by Higgs experimental limits
provided by LEP2
tan ß 35
tan ß 50
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Constrained MSSM (Choice of constraints)
Data on rare processes branching ratios
Regions excluded by experimental limits (for
large tanß)
tan ß 50
tan ß 35
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Constrained MSSM (Choice of constraints)
Muon anomalous magnetic moment
Regions excluded by muon amm constraint
tan ß 50
tan ß 35
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Constrained MSSM (Choice of constraints)
The lightest supersymmetric particle (LSP) is
neutral.
This constraint is a consequence of R-parity
conservation requirement
Regions excluded by LSP constraint
tan ß 35
tan ß 50
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Favoured regions of parameter space
Pre-WMAP allowed regions in the parameter space.
From the Higgs searches tan ß gt4, from aµ
measurements µ gt0
tan ß 35
tan ß 50
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Allowed regions after WMAP
In allowed region one fulfills all the
constraints simultaneously and has the suitable
amount of the dark matter
WMAP
LSP charged
Narrow allowed region enables one to predict the
particle spectra and the main decay patterns
Higgs
EWSB
Phenomenology essentially depends on the region
of parameter space and has direct influence on
the strategy of SUSY searches
tan ß 50
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Mass Spectrum in CMSSM
SUSY Masses in GeV
(Sample)
Fitted SUSY Parameters
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Superparticles
Discovery of the new world of SUSY
Back to 60s New discoveries every year