Memorial Conference in Honor of Julius Wess

1. Memorial Conference in Honor of Julius Wess

2. Topics in Gauge Mediation Nathan Seiberg IAS Based on: Meade, NS and Shih, arXiv:0801.3278 NS, Volansky and Wecht, arXiv:0809.4437 Buican, Meade, NS and Shih, to appear

3. The LHC is around the corner

4. What will the LHC find? • Of course, we do not know. • Among the known suggestion I view supersymmetry as the most conservative and most conventional possibility for LHC physics. It is also the most concrete one. • We need to understand: • How is supersymmetry broken? • How is the information about supersymmetry breaking mediated to the MSSM? • Predict the soft breaking terms.

5. Assuming SUSY is Discovered • We will have a handful of measured numbers: masses of some gauginos, sfermions and Higgs fields… • What will these numbers tell us about shorter distance physics? • How is SUSY broken? • How is the information about SUSY breaking mediated to the MSSM?

6. Roadmap to SUSY Models Single sector Gravity mediation Gauge mediation

7. MSSM SUSY SUSY Breaking Mediation mediation

8. Roadmap to SUSY Models Gauge mediation Gravity mediation Single sector Direct mediation Messengers

9. Minimal Gauge Mediation – Models With Messengers[Dine, Nelson, Nir, Shirman, …] couples to the SUSY breaking sector. Its vev is the only source of SUSY breaking. It can be treated classically. are messengers in a real representation of the MSSM gauge group. The messengers’ spectrum is not SUSY. Their coupling to the MSSM gauge fields feeds SUSY breaking to the rest of the MSSM (more below).

10. Original Gauge Mediation Models – Direct Mediation [Dine, Fischler, Nappi, Ovrut, Alvarez-Gaume, Claudson, Wise…] • Start with the O’Raifeartaigh model • Let be in a real representation of the MSSM gauge group. (Need to extend it to break its R-symmetry.) • Similar to the previous case but: • The spontaneous SUSY breaking mechanism is manifest (explicit). • The messengers participate in SUSY breaking – more economical.

11. Dynamical SUSY Breaking • Dynamical SUSY breaking and therefore SUSY breaking is naturally small [Witten]. • Need a tiny nonperturbative effect in a gauge theory. • Original hope: all dimensionful parameters are generated this way. • Alternative: can use high dimension operators suppressed by the Planck scale. Using dynamically generated scales, these can lead to mass terms.

12. Example of DSB[Affleck, Dine, NS] gauge theory with matter and superpotential squark vevs ensures large vevs = weak coupling

13. Direct Mediation of Dynamical SUSY Breaking • Combine DSB with direct mediation [Affleck, Dine, NS]. • Messengers participate in SUSY breaking or might not even be well defined (strongly coupled messengers). • More elegant, but: • Landau poles in MSSM • R-symmetry problem • Complicated models • Hard to compute • These difficulties are made easier or even avoided using metastable DSB[… Intriligator, NS, Shih …].

14. Definition: Gauge Mediation MSSM Hidden sector • In the limit the theory decouples to two sectors. • The hidden sector includes • the SUSY breaking sector • messengers if they exist • other particles outside the MSSM • For small the gauge fields of the MSSM couple to the hidden sector and communicate SUSY breaking. MSSM gauge fields with couplings

15. General mild assumptions about the hidden sector: It is characterized by a scale . It has a global symmetry which is identified with the MSSM gauge symmetry. It is easy to derive general results… General gauge mediation

16. The three gaugino masses are unrelated. Sfermions with the same quantum numbers are degenerate (no FCNC). Two mass relations: (These should be renormalized from .) Imposing CP, the general model has 6 real parameters (determining the gauginos and sfermion masses). Small A-terms are challenging Gravitino LSP General gauge mediation

17. Parameters • The general model has 6 real parameters. • The simplest model with messengers has only one real parameter. • More elaborate spectrum of messengers allows us to cover larger parts of, and even the entire parameter space, while satisfying all phenomenological requirements [Carpenter, Dine, Festuccia and Mason; Buican, Meade, NS and Shih]. • Hence, generically there cannot be additional relations. • Measuring these numbers will tell us something about the higher energy physics. • Additional couplings and parameters are needed to explain

18. Roadmap to SUSY Models Gravity mediation Single sector Gauge mediation Direct mediation Messengers The messengers couple to the SUSY breaking sector via… Semi-direct gauge Mediation [also Ibe, Nakayama, Yanagida] Yukawa interactions– ordinary (minimal) gauge mediation Gauge fields [Randall]

19. Semi-direct Gauge MediationExample: the 3-2 Model Recall the 3-2 model: gauge theory with matter and superpotential Add massive messengers which are doublets. Now and

20. The 3-2 Model with Additional Doublets [More details in the paper] • Clearly, for the messengers do not affect the supersymmetry breaking vacuum: • The messengers get supersymmetry breaking masses (up to numerical coefficients): tree one loop

21. Couple to the MSSM [More details in the paper] • The model is automatically CP invariant. • The model has messenger parity and hence there are no dangerous FI-terms. • All the soft terms are calculable. • Even though the messenger mass matrix has off-diagonal (R-breaking) terms, the gaugino masses vanish at leading order. They are nonzero at higher orders. • The sfermions masses receive several contributions of different signs and different parametric dependence on the coupling constants. • A more detailed analysis is needed to determine whether the model is viable.

22. Conclusions • Generic predictions of gauge mediation • Sfermion degeneracy (no FCNC) • Two mass relations • Small A-terms • are challenging • Gravitino LSP • Specific models with messengers have additional relations. • Semi-direct gauge mediation • More work is needed to find the right model