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Lecture 7 (Theory Part 6 )

Lecture 7 (Theory Part 6 ). SUSY BREAKING Gravity Mediation example. (Recap of Part 6). Soft SUSY breaking Lagrangian. (Recap of Part 6). [Shown to be soft to all orders, L. Girardello , M. Grisaru ]. All dimension 3 or less, ) all coefficients have mass dimension!.

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Lecture 7 (Theory Part 6 )

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  1. Lecture 7 (Theory Part 6 )

  2. SUSY BREAKING Gravity Mediation example (Recap of Part 6)

  3. Soft SUSY breaking Lagrangian (Recap of Part 6) [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!

  4. (Recap of Part 6) Minimal Supersymmetric Standard Model (MSSM) Strong Weak hypercharge Gauge group is that of SM: Vector superfields of the MSSM

  5. MSSM ChiralSuperfield Content (Recap of Part 6) Left handed quark chiralsuperfields Conjugateof right handed quark superfields Two Higgs doublets

  6. MSSM (Recap of Part 6) Lepton number violating Baryon number violating Evade proton decay: All SM particles + Higgs bosons: R-parity All SUSY particles: Superpotential ) SUSY particles appear in even numbers ) SUSY pair production ) Lightest Supersymmetric Particle (LSP) is stable! Gives rise to a Dark Matter candidate.

  7. Part 6

  8. 4.2 MSSM Lagragngian density Superpotential With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian. Higgs-squark-quark couplings with same Yukawa coupling! SM-like Yukawa coupling H-f-f

  9. 4.2 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

  10. 4.2 MSSM Lagragngian density Superpotential With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian. Gauge-gaugino-gaugino SUSY version of this Auxialliary D-term Non-abelianself interactions from gauge-kinetic term [See page 86 of Drees, Godbole, Roy]

  11. 4.2 MSSM Lagragngian density Superpotential With the gauge structure, superfield content and Superpotential now specified we can construct the MSSM Lagrangian.

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

  13. 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.

  14. 4.3 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)Ygenererators broken: But for this choice Showing the components’ charge under unbroken generator Q

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

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

  17. 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

  18. 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,

  19. EWSB conditions For successful EWSB: With:

  20. 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 chiralsuperfields all transform together: Idea: Single scale for universalities, determined from gauge coupling unification! Constrained MSSM:

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

  22. 4.3 Higgs Bosons in the MSSM 3 longitudinal modes for 5 Physical Higgs bosons 8 scalar Higgs degrees of freedom

  23. 4.3 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

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

  25. Charged Higgs mass matrix Massless Goldstone boson Charged Higgs

  26. 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)

  27. 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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