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Lecture 7

Lecture 7. Tuesday…. Superfield content of the MSSM. Strong. Weak. hypercharge. Gauge group is that of SM:. Vector superfields of the MSSM. MSSM Chiral Superfield Content. Left handed quark chiral superfields. Conjugate of right handed quark superfields.

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Lecture 7

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  1. Lecture 7

  2. Tuesday…

  3. Superfield content of the MSSM Strong Weak hypercharge Gauge group is that of SM: Vector superfields of the MSSM

  4. MSSM Chiral Superfield Content Left handed quark chiral superfields Conjugateof 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!

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

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

  7. 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.

  8. Electroweak Symmetry Breaking (EWSB) Recall in the SM the Higgs potential is: Vacuum Expectation Value (vev) Underlying SU(2) invariance ) the direction of the vev in SU(2) space is arbitrary. 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

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

  10. EWSB And after a lot of algebra… The Higgs Potential

  11. 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: B¹ term unfavorable for stable EWSB minima

  12. EWSB conditions Only phase in potential First consider: To ensure potential is bounded from below: Choosing phase to maximise contribution of B¹ reduces potential: For the origin in field space, we have a Hessian of,

  13. EWSB conditions For successful EWSB: With:

  14. 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:

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

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

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

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

  19. Charged Higgs mass matrix Massless Goldstone boson Charged Higgs

  20. 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)

  21. 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

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