Transcript Slide 1
Lecture 6 First lets review how we build a SUSY theory… Superfields Irreducible superfield representations of SUSY = Building blocks of SUSY theories Chiral Superfields scalar spinor scalar Auxilliary fields (In chiral representation) Vector Superfields Gauge boson Gaugino (In the Wess-Zumino gauge) Auxilliary D SUSY invariant Lagrangian for a chiral superfields where From superpotential: And obtain the kinetic parts from (Vector superfields) (Kahler potential) General SUSY invariant Lagrangian density Superpotential: Supersmymetric field strengths Gauge invariant Kahler potential Spontaneous SUSY breaking Recall: OR 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 Strong Weak hypercharge Gauge group is that of SM: Vector superfields of the MSSM Structure of the MSSM Strong Weak hypercharge Electric charge Gauge group is that of SM: EWSB We want EWSB to take place via the usual Higgs mechanism, with fundamental Higgs fields: But SM quarks get masses from Yukawa interactions: with So all fermions get masses from same Higgs doublet ) MSSM has TWO Higgs doublets: couples to “up-type “ chiral superfields, to “down-type” chiral superfields MSSM Chiral Superfield Content Left handed quark chiral superfields Conjugate of right handed quark 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! MSSM R-parity Strong constraints on L and B violating operators. Tightest constraint comes from non-observation of proton decay Lepton number violating Baryon number violating Problem: 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 density Superpotential 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 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! 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 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 4.2 MSSM Lagragngian density Superpotential With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian. Usual gauge-fermionfermion vertex Scalar covariant derivative Gaugino interactions from Kahler potential A SUSY signature at the LHC Superfield strength Kahler potential Lightest supersymmetric particle (LSP) R-parity conservation signal Contributes to: - 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.