lecture 6
DESCRIPTION
Lecture 6. TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A A A. First lets review how we build a SUSY theory…. Superfields. Irreducible superfield representations of SUSY = Building blocks of SUSY theories. Chiral Superfields. scalar. spinor. - PowerPoint PPT PresentationTRANSCRIPT
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Lecture 6
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First lets review how we build a SUSY theory…
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Irreducible superfield representations of SUSY = Building blocks of SUSY theories
Superfields
Chiral Superfields
scalar scalarspinor
Auxilliary fields
(In chiral representation)
Vector Superfields
Gauge boson Gaugino Auxilliary D
(In the Wess-Zumino gauge)
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And obtain the kinetic parts from (Vector superfields)
SUSY invariant Lagrangian for a chiral superfields
where
(Kahler potential)
From superpotential:
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General SUSY invariant Lagrangian density
Superpotential:
Supersmymetric field strengths
Gauge invariant Kahler potential
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OR
Recall:
Spontaneous SUSY breaking
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Gravity Mediation (for example)
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3.2 Terms in the soft SUSY breaking Lagrangian[Shown to be soft to all orders, L. Girardello, M. Grisaru]
All dimension 3 or less,) all coefficients have mass dimension!
) relationships between dimensionless couplings maintained!
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Minimal Supersymmetric Standard Model (MSSM)
The MSSM = minimal particle content compatible with known physics, i.e Standard Model particles and properties.
Basic idea: take SM and supersymmetrise:
Warning: Image not totally accurate as we will see…
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Superfield content of the MSSM
Gauge group is that of SM:
Strong Weak hypercharge
Vector superfields of the MSSM
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Structure of the MSSM
Gauge group is that of SM:
Strong Weak hypercharge
EWSB
Electric charge
) MSSM has TWO Higgs doublets: couples to “up-type “ chiral superfields,
to “down-type” chiral superfields
We want EWSB to take place via the usual Higgs mechanism, with fundamental Higgs fields:
But SM quarks get masses from Yukawa interactions:
So all fermions get masses from same Higgs doublet
with
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MSSM Chiral Superfield Content
Left handed quark chiral superfields
Note: left handed fermions are described by chiral superfields, right handed fermions by anti-chiral superfields. Superpotential is a function of chiral superfields only so we include right handed fermions by taking the conjugate, which transforms as a left handed superfield!
Conjugate of right handed quark
superfields
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MSSM R-parity
Problem: proton decay
Lepton number violating
Baryon number violating
Strong constraints on L and B violating operators.
Tightest constraint comes from non-observation of proton decay
Solution: Impose R-parity.
All SM particles + Higgs bosons:
All SUSY particles:
) SUSY particles appear in even numbers
) SUSY pair production
) Lightest Supersymmetric Particle (LSP) is stable!
Gives rise to a Dark Matter candidate.
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MSSM Lagragngian densitySuperpotential
With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.
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- MSSM is phenomenologically viable model currently searched for at the LHC-Predicts many new physical states:
- Very large number of parameters (105)!- These parameters arise due to our ignorance of how SUSY is broken.
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MSSM Lagragngian densitySuperpotential
With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.
SM-like Yukawa coupling H-f-f
Higgs-squark-quark couplings with same Yukawa coupling!
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MSSM Lagragngian densitySuperpotential
With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.
Quartic scalar couplings again from the same Yukawa coupling
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4.2 MSSM Lagragngian densitySuperpotential
With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.
Non-abelian self interactions from gauge-kinetic term
Gauge-gaugino-gaugino SUSY version of this
[See page 86 of Drees, Godbole, Roy]
Auxialliary D-term
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4.2 MSSM Lagragngian densitySuperpotential
With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.
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Scalar covariant derivative Usual gauge-fermion-
fermion vertex
Gaugino interactions from Kahler potential
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A SUSY signature at the LHC
Contributes to:
Superfield strength
Kahler potential
R-parity conservation
signal
Lightest supersymmetric
particle (LSP)
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- MSSM is phenomenologically viable model currently searched for at the LHC-Predicts many new physical states:
- Very large number of parameters (105)!- These parameters arise due to our ignorance of how SUSY is broken.