# Presentation: 711022

## Basic Supersymmetry

*Aldo F. Saavedra *
*LBL*

## Outline:

- Motivation
- A bit of algebra
- Signals

## Some Shortcomings of the Standard Model

**Hierarchy problem:**

- For spontaneous symmetry breaking one needs:

- Where H and  are higgs field responsible for symmetry breaking of SU(2) and GUT groups.
- The first question is how to get such a small number.  The only way is to tune coupling constants.
- A radiative correction will certainly disrupt the fore metioned hierarchy.

## The feynman diagram for a the radiative correction

-  to a ligh higgs mass is shown and is proportional to the squared mass of the particle

- Not cancelled will disrupt the hierachy

- In supersymmetry the contribution of the superpartners of the higgs particle perform the cancellation:

## Unification of the Couplings of Electromagnetic, Weak and Strong Forces

- D.I. Kazakov Phys. Rept. 344, 309, (2001)

## Muon Anomalous Magnetic Moment:

- Collaboration E821 at Brookhaven measured a value for
-  a = (g -2) /2  which deviates by 2.6 from the Standard
- Model.

## Slide 7

## The collaboration claims that the difference can be

- accounted for in a number particle physics models
- employing weak scale supersymmetry.
- In hep-ph/0103280 different SUSY models are compared.
- Some are favoured and some are not.

## The only possible extension of symmetry beyond Lie symmetries. Coleman- Mandula Theorem.(1967).

- This came from an attempt to combine internal and Lorentz symmetries and it states that:
**The only conserved quantities that transform as tensors under Lorentz transformation in a theory with non-zero scattering amplitudes in 4 dimensions are the generators of Poincare group and Lorentz invariant quantum numbers(scalar charges)**

## Q| Boson = | Fermion                  Q| Fermion = | Boson 

-            [Q,*H*] = 0               [{Q, Q*},H] = 0
- {Q, Q*} = 2*P           {Q, Q} = 0        {Q*, Q*} = 0
-        Translation
- Supersymmetry relates particles of different spin with equal quantum numbers of identical masses

- 1/2

- 0

- 

- q (quark)

- q (squark)

- 1

- 1/2

- 

- g (gluon)

- g (gluino)

- Chiral supermultiplet

- Gauge supermultiplet

- But it does not forbid conserved of spinor charges,
- Q.  (Graded Lie algebra)

## Slide 11

| SM | Superpartner | Quantum
Number | SM | Superpartner
 | Quantum Number |
| --- | --- | --- | --- | --- | --- |
| QL | squark doublet 
QL |    (3,2,1/6) | LL | slepton doublet
LL |  (1,2,-1/2) |
| uR | up squarl singlet
uR  | (3,1,2/3) | dR | sdown singlet
dR |  (3,1,-1/3) |
| eR | selectron singlet
eR | (1,1,-1) | R | Sneutrino right
R |  (1,1,0) |
| H1 | down higgsino
H1 | (1,2,-1/2) | H2 | Up higgsino
H2 |  (1,2,1/2) |
| g | gluino
g | (8,1,0) | W | Wino
W |  (1,3,0) |
| B | bino
B | (1,1,0) |  |  |  |

## R-parity

- Consequences:
- SUSY particles produced in pairs.
- Lightest SUSY particle (LSP) must be neutral
- 	and colourless (from cosmological constraints).
- LSP is stable.
- No theoretical argument requires R-parity.
- Some models conserve, others violate R-parity.

## References:

-  Jose Miguel Figueroa-O’Farrill ,
-  BUSSTEPP Lectures on supersymmetry, hep-th/0109172 21 sep 2001.
-   Stephen P. Martin, A Supersymmetry Primer, hep-ph/9709356.
-  Marco Battaglia, Ian Hinchliffe, Daniel Tovey,
-   Cold Dark Matter and the LHC, hep-ph/0406147
-  M. Biglietti *et al* , Full Supersymmetry Simulation for ATLAS in DC1,
-   ATL-PHYS-2004-011.