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Understanding the MSSM: Superfields, Gauge Structure, and Electroweak Symmetry Breaking

This lecture covers the essential components of the Minimal Supersymmetric Standard Model (MSSM), including superfield content, gauge groups, and the role of chiral and anti-chiral superfields. We discuss the construction of the MSSM Lagrangian, the significance of the superpotential, and the implications of R-parity conservation. The session also delves into the conditions necessary for electroweak symmetry breaking (EWSB), scalar potentials, and the importance of soft mass parameters in SUSY theories. Insights into Higgs bosons and their properties within the MSSM framework are provided.

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Understanding the MSSM: Superfields, Gauge Structure, and Electroweak Symmetry Breaking

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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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