SUSY breaking by metastable state Color fields on the light shell Chia-Hung V. Chang at AS on May 29 ‘10

SUSY vacuum

Put everything together: with the all (and the only) important scalar potential:

Spontaneous SUSY breaking SUSY ground state has zero energy! Ground state energy is the order parameter. SUSY will be broken if all the auxiliary fields can not be made zero simultaneously!

F-type SUSY breaking O’Raifeartaigh Type Model (OR) There are as many F-terms as superfield. In general, there will be a solution for all the F-terms to vanish unless the superpotential is special-designed. Three chiral superfields: X,Φ2 don’t talk to each other. Generically we can’t make both vanish. SUSY is borken.

There is a mass relation for the fields spontaneously breaking SUSY. Spontaneous SUSY breaking can’t be generated in SM or one of the squarks will be too light. Hidden SUSY Breaking Sector SM Weak Mediating sector The mediation control the phenomenology. It could be gravity, gauge interaction, anomaly etc.

U(1)R symmetry O’Raifeartaigh Model (OR) has an unbroken U(1)R symmetry. This is a serious problem. Boson and its superpartner have opposite charges. Superpotential W needs to be charge 2 to preserve U(1)R The R charges of the three chiral superfields: An unbroken U(1)R symmetry will prohibit Majorana gaugino masses and render model-building very difficult.

Generically it can be proven: An unbroken U(1)R symmetry will prohibit Majorana gaugino masses and render model-building very difficult. The issue of R symmetry is just one among several other strict constraints preventing SUSY breaking to appear easily.

Witten Index (1982) Every bosonic state of non-vanishing energy pair with a fermionic state. If the Witten index is non-zero, there must be a state with zero energy and hence SUSY is unbroken! SUSY is unbroken. (The reverse is not true.) Witten index is invariant under changes of the Hamiltonian that do not change the far away behavior of the potential!

It is possible to calculate Witten index at weak coupling while applying the conclusion to strong coupling. Witten index is non-zero for pure SUSY Yang-Mills theory. Gauge theories with massive vector-like matter, which flows to pure Yang-Mills at low energy, will also have a non-zero Witten indices. For these two theories, SUSY is unbroken. SUSY breaking seems to be a rather non-generic phenomenon. “The issue of SUSY breaking has a topological nature: it depends only on asymptotics and global properties of the theory.”

Enters Meta-Stable Vacua

“Breaking SUSY by long-living metastable states is generic.” Using metastable state to break SUSY while keeping a SUSY ground state could help evade a lot of constraints such as Witten Index. “Breaking SUSY by long-living metastable states is generic.” Intrilligator, Seiberg, Shih (2006)

Modify OR model by adding a small mass term for φ2 (Deformation) Now 3 equations for 3 unknowns, a solution can be found: This is a SUSY vacuum. U(1)R has been broken by the small mass term as expected.

At A, At B, Metastable state breaking SUSY As ε becomes smaller, SUSY vacuum A will be pushed further and further, diminishing the tunneling rate as small as you like, until disappear into infinity at ε=0. With a SUSY vacuum, R symmetry is explicitly broken.

Dienes and Thomas Model nest Achieve a SUSY breaking metastable state perturbatively (tree level calculation).

The recipe is to put a Wess-Zumino and a Fayet-Illiopoulos together! Three Chiral Superfields A Wess-Zumino Superpotential Two Abelien U(1) with FI terms: Massive vector matter with opposite charges in FI Together, you also need to assign appropriate charges to

The extrema are determined by the conditions: Solutions is a local minimum if the following mass matrix contains only positive eigenvalues! This is the hard part!

As an example, choose A is a SUSY true vacuum, with R symmetry and a U(1) gauge symmetry. B is a SUSY breaking metastable local minimum, with broken R symmetry and broken U(1) gauge symmetry.

Lifetime of the metastable state The metastable state tunnels to the true vacuum through instanton transition. The decay rate per unit volume is B is calculated from the distances in field space between barrier top (C) and metastable state (B) or true vacuum (A): and the potential differences between similar combinations:

Our Model I: To simplify Dienes & Thomas Model We throw away U(1)b As an example: We again find structures of minima:

B A The metastable minimum is a bit shallow! It will decrease the lifetime of B, but it turns out still OK.

B

Our Model II: we simplify our Model I even further: We throw away one superfield and U(1)b As an example: We again find structures of minima:

A B

A C B

C B A We have constructed a model which is one field and one Abelien Gauge symmetry short of the Dienes Thomas Model, but achieves the same ground state structure. The metastable local minimum is about as deep in DT and the distance between A,B is also about the same order. We expect the lifetime of metastable to exceed the age of the universe.

How about a model without mass terms?

Anomalous U(1) as a mediator of SUSY breaking Dvali and Pomarol 1996 We have anomalous U(1) in our model. The anomaly ca be cancelled by Green-Schwarz mechanism. This requires both hidden and visible sector carry U(1) charge! D term contribution: When D get a nonzero VEV, the squarks get a mass proportional to their charge! We are studying the realization of this mechanism in our model.

Field of a charge start to move from rest.

Light shell Color electric and magnetic fields vanish outside the light shell!

Light shell Color electric and magnetic fields also vanish inside the light shell!

Light shell Color electric and magnetic fields are concentrated on the 2D light shell!

Light shell Color gauge fields Field strength Maxwell Equation Color field strength on the light shell are tangent to the light shell!

Maxwell Eqs. become It is an equation totally written in terms of quantities on the light shell! Could we define a field on light shell that can determine its own fate? Start with Define a field that is a function only of by setting t = r Let’s pile up the 2D light shell fields and construct a 3D field:

Start with Define a field that is a function only of by setting t = r It’s like piling up r stacking up the 2D light shell fields to become a 3D field: Light shell field e depends on r also through ξ’s dependence on t. Gauss law of light shell fields, static, in 3D r direction is actually t

It’s transverse. From the condition that fields vanish inside light shell: From this, we can derive that e scales trivially:

The first three eqs can be solved by introducing a 3 by 3unitary matrix: The Lagrangian is here the energy: Non-linear σ model