1. Metastable supersymmetry breaking vacua from conformal dynamics
Yuji Omura
　(Kyoto University)
Based on
Hiroyuki Abe, Tatsuo Kobayashi, and Yuji Omura,
arXiv: [hep-ph] .

2. 1. Introduction The argument about SUSY breaking
We suggest the scenario that conformal dynamics leads to metastable supersymmetry breaking vacua.
First, let me introduce the general argument about SUSY breaking shortly.
The argument about SUSY breaking
Based on the Nelson-Seiberg argument, the models which cause SUSY breaking have U(1)R symmetry,
For examlpe, the O’Raifeartaigh model, which we discuss in this talk, is known as one of the models which cause SUSY breaking, and it has R-symmetry.

3. (NX>Nφ ) The generalized O’Raifeartaigh model is written down as
where are generic functions .
The F-flat conditions of Xa are
They don`t have solutions,
because they are NX (>Nφ )
equations with Nφ unknowns.
(NX-Nφ) Xa are flat directions.
On the other hand, R-symmetry must be broken explicitly to get nonzero gaugino masses, and to avoid massless boson (Goldstone boson).
These R-symmetry breaking terms make SUSY vacua appear and SUSY breaking vacua disappear.

4. How can we realize SUSY breaking vacua?
One-loop effective potential can stabilize a SUSY breaking vacuum near the origin. V X
On the other hand, the R-symmetry breaking terms destabilize the SUSY breaking vacuum.
If they are much smaller than the loop effect,
a metastable SUSY breaking vacuum can be realized.
　　　would also lead to SUSY vacua, but they disappear under the limit,

5. We suggest conformal dynamics to realize enough small mab λabc .
The features of our model
Our model is the SU(N) gauge theory with Nf flavors.
The flavor number, Nf, satisfies
which corresponds to the conformal window.
Our model doesn’t have R-symmetry and its superpotential is
generic at the renormalizable level.
The dynamics can lead to conformal sequestering.

6. 2. 4D conformal model Chiral matter fields are
SU(N) symmetry is imposed on these fields as follows, and each field corresponds to φ , X in the Generalized O’Raifeartaigh Model in the introduction.
Furthermore, we impose SU(Nf) flavor symmetry to make the analysis easier, but the following discussions would be valid, even if the flavor symmetry is explicitly broken.
SU(N)
SU(Nf)
The superpotential without R-symmetry, at the renormalizable level, is

7. Vacuum structure ← corresponds to WOR .
If R-symmetry is preserved, there is a SUSY breaking vacuum,
X : flat
(This SUSY breaking vacuum corresponds to the solution in the ISS model.)
If R-symmetry is not preserved,
the SUSY breaking vacuum is destabilized and SUSY vacua appear.
SUSY vacua

8. This theory is completely conformal at the fixed-point ,
Effective Lagrangian with cut-off
,which corresponds to the conformal window, is satisfied in our model, so that gauge coupling and yukawa coupling have fixed-points.
Gauge coupling fixed-point
Yukawa coupling fixed-point
This theory is completely conformal at the fixed-point ,
so that SUSY would not be broken there.
We suggest there is a parameter region which causes SUSY breaking
near the fixed-point.

9. mφ has a negative anomalous dimension, so that mφ becomes enhanced ,
“the R-symmetric superpotential”
Near the fixed-point, these R-symmetry breaking terms are estimated as,
It is important that the suppression of f is the weakest. This means even if we assume , this superpotential approximates “the R-symmetric superpotential”, which causes SUSY breaking, at low energy scale.
mφ has a negative anomalous dimension, so that mφ becomes enhanced ,
We will comment on such terms later.

10. This solution cannot be defined under the limit,V
Loop effect X
We set the parameters at as follows:
SUSY vacua are estimated as,
Under the limit, , these SUSY vacua go far away from X=0.
A metastable SUSY breaking vacuum appear, when the potential of X becomes enough flat for the one-loop mass to be efficient .
The solution is
This solution cannot be defined under the limit,

11. How long does the conformal dynamics need to last
to realize the SUSY breaking vacuum?
If we assume　　　　　　　　　　　　　　　　
the supersymmetric mass and the one-loop mass are estimated as
The supersymmetric mass is suppressed by conformal dynamics
The scale, where the supersymmetric mass becomes the same order
as the one-loop mass, is
For example, in the case ,
the one-loop mass becomes important below
SUSY can be broken below μX.

12. If is satisfied, SUSY breaking scale changes.
In the region ( m <<mX ), the F-component of is estimated as , so that the SUSY breaking scale (Λint) is
However,
If the φ mass term, , is as large as the other terms,
this SUSYbreaking scale would change.
This is because the anomalous dimension of is negative,
This term becomes bigger at low energy, so that this theory gets out of the confomal window at the scale,
where decouple with other fields .
If is satisfied, SUSY breaking scale changes.

13. Furthermore, in conformal dynamics ,
the strong coupling anomalous dimension can suppress FCNC.
Ref)M. A. Luty and R. Sundrum,
PRD65 ,066004(2002),PRD67,045007(2003)
anomalous dimension
of Ohid(Φ).
In our model the F-component of is nonzero, so the direct couplings of
with the visible sectors are suppressed by the same order as the R-symmetry breaking sectors :
scalar mass term
gaugino mass term

14. 3.5D model
We can construct simply various models within the framework of 5D orbifold theory . Renormalization group flows in the 4D theory correspond to exponential profiles of zero modes,
c: kink mass
,where R is the radius of the fifth dimension, y and c is the constant which do not have constraints. For example, we consider the 5D theory whose 5-th dimension is compactified on S1/Z2. If we suppose that the following superpotential is allowed on the fixed-points, SUSY breaking is realized.

15. 4. Summary
We argued SUSY breaking in the generalized O’Raighfeartaigh Model,
In the limit,
these terms don’t make SUSY vacua appear.
These terms destabilize SUSY breaking vacuum.
Xa are the flat directions.
One-loop effective potential stabilizes SUSY breaking vacua.
The coefficients of squared X and cubed X need to be suppressed, compared with the the coefficients of X.
If the loop effect is bigger than the R-symmetry breaking terms, SUSY can be broken.
Conformal dynamics

16. We discussed the SU(N) gauge theory with Nf flavor which has an IR fixed-point.
The number of flavor satisfies
which corresponds to the conformal window.
High energy scale ( Λ )
If we assume SUSY is preserved because the R-symmetry breaking terms are too large, compared with the mass term in the one-loop effective potential.
Low energy scale
A metastable SUSY breaking vacuum appears when R-symmetry breaking terms are suppressed, compared with mX. The suppression is caused by the positive anomalous dimension of

17. How long does the conformal dynamics need to last
to realize the SUSY breaking vacuum?
It depends on N and Nf. If Nf is close to 3N, is so small that the flow has to be as long as possible. In the case , the scale where the one-loop effective potential becomes efficient is estimated as 　　　
The SUSY breaking scale, the nonzero F-component, is
If mφ , is large, compared with other terms,
this theory removes away from the conformal windows
at the scale, ,where decouple with other fields.
In this case, SUSY breaking scale would change.
This scenario can lead to conformal sequestering.
We suggest the construction within the framework of 5D theory according to the correspondence between Renormalization group flows in the 4D theory and exponential profiles of zero modes.
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