Minimal supersymmetric standard...
Transcript of Minimal supersymmetric standard...
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Minimal supersymmetricstandard model
Yasaman FarzanIPM, Tehran
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Standard model
Building blocks of nature
Bosons
Fermions
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Elementary particlesMain forces in Standard Model (SM):
Gravitation
Electrodynamics
Weak interaction
Strong interaction
Higgs ?!
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Fermions of the SM
Leptons Quarks
1st generation
2nd generation
3rd generation
Notation:
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Lagrangian of the leptonsEM
NC:
CC:
Mass:
In Old SM:
In the general basis
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Reminder Quantum mechanics(schrodinger equation)
Special relativity
Quantum field theory (Dirac Equation for fermions)
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Quantum Field Theory
Matter Antimatter
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What is the anti-particle of the electron?What is the anti-particle of the muon?What is the anti-particle of the tau?What is the anti-particle of the up-quark?What is the anti-particle of photon?What is the anti-particle of the Z boson? What is the anti-particle of the neutrino?
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Modern question: Are the neutrino and antineutrino the same particles?More technically: Are neutrinos of Majorana nature ?
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Supersymmetry
Each particle has superpartner with exactly the same quantum numbers but with different spin.
Fermion sfermion
Boson name+ino
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Naming the super-partners of the superpartners
Electron SelectronMuon Smuon
Tau StauTop Stop
Neutrino Sneutrino
squarkslepton
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How many degrees of freedom does a Dirac fermion such as electron have?
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Naming the superpartners of the bosons Higgs Higgsino Gluon Gluino W Wino Photon ??? Z ???
Neutralino sneutrino Chargino
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Why beyond Standard Model
Theoretical motivation- Hierarchy problem- Quest for Unification
Observational Motivation
- Dark matter candidate- Neutrino mass
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References
Martin, A supersymmetric primer, Hep-ph/9709356 (last update)
Peskin’s lecture noteshttp://www.slac.stanford.edu/~mpeskin
With his permission, I shall Adwidely use his material in the following but I have ded some other material of my own, too.
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Higgs mechanism
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Hierarchy problem
Cutoff
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Solutions
Technicolor Electroweak precision data
Cancelation because of a new symmetry
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Unification
Electric force Magnetic force
Electromagnetism (prediction??)
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Unification
Electromagnetism
Weak interaction
Electroweak interactions
Prediction??
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Grand unification Electroweak
Strong interaction
Grand Unification
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Susy
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Already lots of implications!
Generalized JacobianIdentity
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Implication of Lorentz symmetry
Can vanish?
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Consider an arbitrary state
Either charges nullify all states or isa non-zero conserved vector field.
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For a one-particle system:
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Conservation:
Conservation :
Coleman and Mandula:If , .
Thus,
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Important lesson
You cannot be selective when you supersymmetrize a theory.
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More than one pair of Q
More than a pair:
Central charge:
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Possible values of Chiral,vector super-multiplet
Other possibilities with closed representation
requires spin larger than 2
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Spin half representation of Lorentz group
Two spin half representation:
A Lorentz invariant:
transforms like right-handed
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Mass term
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Algebra
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Chiral supermultiplet
Consistent Lagrangian?? Consistent transformation??
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We must check if the following is invariant up to a total derivative:
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Superpotential An analytical function
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Notice the sign
Eliminating Auxiliary F
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Vacuum energy vanishes if and only if
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Vacuum energy vanishes!
Unbroken SUSY implies
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An example
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Radiative correction to fermionmass
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Radiative correction to scalar mass
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Renormalization of other terms from super-potential
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Non-renormalization theorem
Super-potential does not get renormalized!
(As far as SUSY is exact!) However, field strength does
We should then renormalize the fields.
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Superspace
Super-field
How can we define susy transformation?
Simplest guess:
But does not work
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Supersymmetry transformation
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Let us define
and
Definition of chiral superfield
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Chiral superfield
Taylor expansion:
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Lagrangian
Kahler potetial
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Supergraphs
Feynman rules in superspace
Radiative correction
Non-renormalizability of the superpotential