1. Center for theoretical Physics at BUE
Supersymmetry at LHC
Shaaban Khalil
Center for theoretical Physics at BUE
& Ain Shams University
Outline
1- Introduction
2- Motivation for supersymmetry
3- What is supersymmetry
3- Supersymmetry breaking
4- The minimal supersymmetric standard model
5- Searches for Supersymmetry
6- Conclusions.

2. Introduction
The SM, based on the gauge symmetry SU(3)C x SU(2)L x U(1)Y , is in excellent agreement with experimental results.
Strong indications that it is just an effective of fundamental one:
1) In the SM we can not predict a particle mass.
2) We do not know why there are six kinds of quarks and leptons
3) The electroweak and the strong forces are partially unified and gravity is not included.
4) In the SM neutrinos are massless & why matter dominates antimatter.
6) In the SM we do not know what is the dark matter made of.

3. Motivation For Supersymmetry
Supersymmetric theories are promising candidate for unified theory beyond the SM.
SUSY is a generalization of the space-time symmetries that links the matter particles with the force carrying particles, and leads to additional 'superparticles'.
SUSY is a new symmetry which relates boson and fermions
SUSY ensures the stability of hierarchy between the week and the Planck scales.

4. Local supersymmetry leads to a partial unificationof gravity of the SM with gravity 'supergravity'.
In supersymmetric theories, the mechanism of the electroweak symmetry breaking is natural.
Supersymmetry is a necessary ingredient in string theory.
With supersymmetry, the SM gauge couplings are unified at GUT scale MG ≈ 2 x1016 GeV.

5. Hierarchy problem and SUSY
String and GUT unification -> A cutoff scale ~ Planck scale (1019 GeV).
SUSY is a symmetry to avoid the fine tuning in the renormalization of the Higgs boson mass at the level of O(1034).
In SUSY, the loop diagrams that are quadratically divergent cancel, term by term against the equivalent diagrams involving superpartners.
If mH ~ O(100) GeV, the masses of superpartners should be ≤ O(1) TeV.
Thus, some of the superpartners will be detected at the LHC.

6. What is Supersymmetry
Supersymmetry (SUSY): a symmetry between bosons and fermions.
Introduced in 1973 as a part of an extension of the special relativity.
Super Poincare algebra.
SUSY = a translation in Superspace.
Supergravity was formulated in 1976.

7. Superfields
We define superfied as function of the superspace coordinates.
1- Chiral Superfields :
2- Vector Superfields V=V+:
3- Linear Superfields DDL=0: contains a real scalar field, a Majorana spinor and antisymmetric tensor. It represents the gravity multiplet of superstrings which contains antisymmetric tensor & dilaton and dilataino.

8. Supersymmetric Lagrangian
The most general supersymmetric lagrangian takes the form:
Eliminating the Da and Fi fields give rise to the scalar potential

9. Supersymmetry Breaking
From the definition of the SUSY algebra:
If the vacuum is supersymmetric the Evac=<0|H|0>=0 and if SUSY is broken Then Evac >0. Hence SUSY is broken if <0|F|0>≠0 or <0|D|0> ≠0
SUSY must be broken symmetry or else SUSY particles should have been observed (with same mass as SM-partners)
What happens to the cancellation of quadratic divergences?
SUSY partners must be not heavier than ~TeV.

10. Spontaneous SUSY breaking
One may introduce terms in the Lagrangian which break SUSY softly.
The general structure for the SUSY breaking includes three sectors:
1) Observable sector: which comprises all the ordinary particle and their SUSY particles,
2) Hidden sector: where the breaking ofSUSY occurs,
3) The messengers of the SUSY breakingfrom hidden to observable sector.
The soft SUSY breaking terms are: Masses for the scalars, Masses for the gauginos, cubic couplings for scalars.

11. The minimal supersymmetric standard model
The MSSM is a straightforward supersymmetrization of the SM with minimal number of new parameters.
The particle content of MSSM = Two Higgs doublet SM + scalar SUSY partners and fermionic SUSY partners
Two Higgs doublets are necessary for fermion Yukawa couplings.
H1: down-type-quark and lepton Yukawa couplings
H2: up-type-quark Yukawa couplings
Different assumptions about SUSY breaking are often made. This leads to quite different phenomenological predictions.
A new symmetry, called R-symmetry is introduced to rule out the terms violate baryon and lepton number explicitly and lead to proton decay at unacceptable rates.

12. SUSY Particle Spectrum

13. MSSM Lagrangian
SUSY invariant Lagrangian: Coupling constants g1,g2,g3 & yij
The potential of the Higgs neutral components is given by:
m1& m2 are soft scalar masses. The running from MGUT to weak scale reduce their squared values until the condition of the EW symmetry breaking are satisfied.

14. Constrained MSSM Can predict SUSY spectrum at our energies
Unconstrained SUSY would bring in 105 parameter (on top of the SM ones)
mSUGRA: simple boundary conditions at GUT scale reduce the number of parameters to ~5!
Common scalar mass m0
Common gaugino mass m1/2
Common trilinear scalar interaction A
Ratio of vevs of two Higgs fields tanb
Sign of Higgs mass parameter m
Can predict SUSY spectrum at our energies

15. The RGE are used to calculate the parameters at the electrweak scale.
In CMSSM (mSUGRA), universality of soft SUSY breaking terms is assumed at GUT scale.
The RGE are used to calculate the parameters at the electrweak scale.

16. Higgs in MSSM M2H±= M2A + M2W => MH± > MW
The SM Higgs mechanism is very economical
In SUSY, two Higgs doublets are needed.
This means: 8 degrees of freedom, 3 eaten up by the W± and Z => 5 Higgs fields: h0,A0,H0,H±
Connection between Higgs masses and gauge boson masses:
M2H±= M2A + M2W => MH± > MW
MA2 =m12+m22
M2H,h =1/2 [M2A+M2Z ± ((M2A+M2Z)2- 4 M2AM2Z cos2β)0.5]
 Mh < MZ
This is only true at tree level. When including higher order contributions: Mh < ~ 130 GeV (or so…)

17. R-parity and the LSP
A totally unconstrained SUSY would lead to the proton decaying with lifetime of ~hours!!!
Introduce R-parity
R = (-1)3(B-L)+2s
All SM particles have R=+1, all sparticles R=-1
R-parity conservation implies that:
SUSY particles are produced or destroyed only in pairs
The LSP is absolutely stable and it is a candidate for Dark Matter.

18. Interactions of SUSY particles
A major signature for R-parity conserving models is represented by events with missing Energy:
For instance e+ e-  jet + missing energy

19. Search for SUSY particles
Today's negative SUSY search provide the following lower maas limits.
The LHC at CERN is the machine that will take particle physics into a new phase of discovery.
The LHC is a proton-proton collider which will explore energies around 1 TeV.
The Higgs boson is the last missing particle in the SM and its discovery is in favoured of SUSY.
At LHC, the search for the Higgs boson will be one of the primary goals

21. Summary
Supersymmetry is one of the most interesting candidate for physics beyond standard model.
SUSY is a key to unification and cosmology.
Discovery of SUSY, if it occurs, would be a revolution of physics in 21st century.
If SUSY exists at the electroweak scale, then these particles could be easily observed at the LHC.