Lecture 6

First lets review how we build a SUSY theory…

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)

And obtain the kinetic parts from (Vector superfields)

SUSY invariant Lagrangian for a chiral superfields

where

(Kahler potential)

From superpotential:

General SUSY invariant Lagrangian density

Superpotential:

Supersmymetric field strengths

Gauge invariant Kahler potential

OR

Recall:

Spontaneous SUSY breaking

Gravity Mediation (for example)

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!

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…

Superfield content of the MSSM

Gauge group is that of SM:

Strong Weak hypercharge

Vector superfields of the MSSM

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

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

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.

MSSM Lagragngian densitySuperpotential

With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.

- 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.

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!

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

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

4.2 MSSM Lagragngian densitySuperpotential

With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.

Scalar covariant derivative Usual gauge-fermion-

fermion vertex

Gaugino interactions from Kahler potential

A SUSY signature at the LHC

Contributes to:

Superfield strength

Kahler potential

R-parity conservation

signal

Lightest supersymmetric

particle (LSP)

- 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.