1. Lecture 6 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A AA

2. First lets review how we build a SUSY theory…

3. Irreducible superfield representations of SUSY = Building blocks of SUSY theories Superfields Chiral Superfields scalar spinor Auxilliary fields (In chiral representation) Vector Superfields Gauge bosonGaugino Auxilliary D (In the Wess-Zumino gauge)

4. And obtain the kinetic parts from (Vector superfields) SUSY invariant Lagrangian for a chiral superfields where (Kahler potential) From superpotential:

5. General SUSY invariant Lagrangian density Superpotential: Supersmymetric field strengths Gauge invariant Kahler potential

6. OR Recall: Spontaneous SUSY breaking

7. Gravity Mediation (for example)

8. 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!

9. 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…

10. Superfield content of the MSSM Gauge group is that of SM: StrongWeakhypercharge Vector superfields of the MSSM

11. Structure of the MSSM Gauge group is that of SM: StrongWeakhypercharge 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

12. 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

13. 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.

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

15. - 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.

16. MSSM Lagragngian density Superpotential 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!

17. MSSM Lagragngian density Superpotential 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

18. 4.2 MSSM Lagragngian density Superpotential 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

19. 4.2 MSSM Lagragngian density Superpotential With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.

20. Scalar covariant derivative Usual gauge-fermion- fermion vertex Gaugino interactions from Kahler potential

21. A SUSY signature at the LHC Contributes to: Superfield strength Kahler potential R-parity conservation signal Lightest supersymmetric particle (LSP)

22. - 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.