Memorial Conference in Honor of Julius Wess

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?

Roadmap to SUSY Models

Gravity mediation Gauge mediation Single sector

SUSY Breaking Mediation

mediation

MSSMSUSY

Gravity mediation Gauge mediation

Coupling to MSSMThrough Planck

suppressed ops.MSSM gauge interactions

FCNC ChallengingNaturally suppressed

Dark matter Simple Challenging

problem Simple Challenging

Roadmap to SUSY Models

Gravity mediation Single sector

MessengersDirect mediation

Gauge mediation

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 MSSMgauge group.

The messengers’ spectrum is not SUSY. Their coupling to the MSSM gauge fields feeds SUSYbreaking 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 ensures large vevs = weak

coupling

Example of DSB [Affleck, Dine, NS]

gauge theory with matter

and superpotential

squarkvevs

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

• 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.

MSSMHidden sector

MSSM gauge fields with couplings

15

General gauge mediation

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…

16

General gauge mediation

• 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

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

Roadmap to SUSY Models

Gravity mediation Single sector

MessengersDirect mediation

Semi-direct gauge Mediation

[also Ibe, Nakayama, Yanagida]

The messengers couple to the SUSY breaking sector via…

Yukawa interactions – ordinary (minimal) gauge mediation

Gauge fields [Randall]

Gauge mediation

19

Recall the 3-2 model:

gauge theory with matter

and superpotential

Add massive messengers which are doublets.

Now

and

Semi-direct Gauge MediationExample: the 3-2 Model

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