1. Supersymmetry in Particle Physics
Outline
1. What is SUSY
2. Basics of SUSY
3. The MSSM
4.Constrained MSSM
5. SUSY Searches
6. SUSY DM

2. Unification Paradigm
GUT
Unification of strong, weak and electromagnetic interactions within Grand Unified Theories is the new step in unification of all forces of Nature
Creation of a unified theory of everything based on string paradigm seems to be possible
D=10

3. No evidence in particle physics yet
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
No evidence in particle physics yet

4. 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 supersymmetry = general relativity !

5. Motivation of SUSY in Particle Physics
Unification of gauge couplings
Running of the strong coupling

6. Unification of the Coupling Constants
Motivation of SUSY
RG Equations
Unification of the Coupling Constants
in the SM and in the MSSM
Input
Output
SUSY yields unification!

7. 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

8. 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

9. Cosmological Constraints
New precise cosmological data
Supernova Ia explosion
CMBR thermal fluctuations
(recent news from WMAP )
Hot DM
(not favoured by galaxy formation)
Dark Matter in the Universe:
Cold DM
(rotation curves
of Galaxies)
SUSY

10. Superalgebra SUSY Generators Grassmannian parameters
The only possible graded Lie algebra that mixes integer and half-integer spins and changes statistics

11. Quantum States Quantum states: Vacuum = State Expression # of states
Energy helicity
State
Expression
# of states
vacuum 1
1-particle
2-particle …
N-particle
Total # of states:

12. SUSY Multiplets helicity -1/2 0 1/2 Chiral multiplet # of states 1 2 1
scalar
spinor
helicity
-1/ /2
Chiral multiplet
# of states
helicity
Vector multiplet
-1 -1/2 1/2 1
# of states
spinor
vector
Members of a supermultiplet are called superpartners
N=4
SUSY YM
helicity
-1 –1/ /2 1
λ = -1
# of states
N=8
SUGRA
-2 –3/2 –1 –1/2 0 1/ /2 2
λ = -2
For renormalizable theories (YM)
spin
For (super)gravity

13. Simplest (N=1) SUSY Multiplets
Bosons and Fermions come in pairs
Spin 0
Spin 1/2
Spin 1/2
Spin 1
Spin 3/2
Spin 2
scalar
chiral fermion
gravitino
vector
graviton
majorana fermion

14. SUSY Transformation N=1 SUSY Chiral supermultiplet:
parameter of SUSY transformation
(spinor)
spin=0
spin=1/2
Auxiliary field
(unphysical d.o.f. needed
to close SYSY algebra )
SUSY multiplets
Superfiled in Superspace
Expansion over
grassmannian
parameter
superfield
component fields

15. Covariant derivatives
Gauge superfields
Gauge superfield
Field strength tensor
Gauge transformation
Wess-Zumino gauge
Covariant derivatives
physical fields

16. 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

17. Superfield Lagrangians
Grassmannian integration in superspace
Matter fields
Superpotential
Gauge fields
Gauge transformation
Gauge invariant interaction

18. Gauge Invariant SUSY Lagrangian
Superfields
Components
Potential