Lecture 7

Tuesday…

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

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

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.

Electroweak Symmetry Breaking (EWSB) Recall in the SM the Higgs potential is: Underlying SU(2) invariance ) the direction of the vev in SU(2) space is arbitrary. Vacuum Expectation Value (vev) Any choice breaks SU(2) £ U(1) Y in the vacuum, choosing All SU(2) £ U(1) Y genererators broken: But for this choice Showing the components’ charge under unbroken generator Q

EWSB Recall in the SM the Higgs potential is: In the MSSM the full scalar potential is given by: Extract Higgs terms:

EWSB And after a lot of algebra… The Higgs Potential

EWSB conditions As in the SM, underlying SU(2) W invariance means we can choose one component of one doublet to have no vev: Choose: B ¹ term unfavorable for stable EWSB minima

EWSB conditions First consider: To ensure potential is bounded from below: Only phase in potential Choosing phase to maximise contribution of B ¹ reduces potential: For the origin in field space, we have a Hessian of,

EWSB conditions For successful EWSB: With:

Recall from SUSY breaking section, gravity mediation implies: Take minimal set of couplings: (warning: minimal flavour diagonal couplings not motivated here, just postulated) Universal soft scalar mass: Universal soft gaugino mass: Universal soft trilinear mass: Universal soft bilinear mass: Fits into a SUSY Grand unified Theory where chiral superfields all transform together: Idea: Single scale for universalities, determined from gauge coupling unification! Constrained MSSM:

Radiative EWSB Renormalisation group equations (RGEs) connect soft masses at M X to the EW scale. RGEs naturally trigger EWSB: Runs negative

Constrained MSSM (cMSSM) (Slope 1 from Snowmass points and slopes)

Higgs Bosons in the MSSM 8 scalar Higgs degrees of freedom 3 longitudinal modes for 5 Physical Higgs bosons Note: no mass mixing term between neutral and charged components, nor between real and imaginary components. Goldstone bosons CP-even Higgs bosons Charged Higgs boson CP-odd Higgs boson

CP-odd mass matrix Included for vevs Eigenvalue equation Massless Goldstone boson CP-odd Higgs

Charged Higgs mass matrix Massless Goldstone boson Charged Higgs

CP-Even neutral Higgs mass matrix Taylor expand: Upper bound: Consequence of quartic coupling fixed in terms of gauge couplings ( compare with free ¸ parameter in SM)

Upper bound: Consequence of quartic coupling fixed in terms of gauge couplings (compare with free ¸ parameter in SM) Radiative corrections significantly raise this Including radiative corrections