1. Yuji Omura (Kyoto Univ.) Hiroyuki Abe (YITP,Kyoto Univ.) Tatsuo Kobayashi(Kyoto Univ.)

2.  Supersymmetry(SUSY) is one of the key ingredients to study physics beyond the SM :the hierarchy between the Planck scale and the weak scale, dark matters, and etc……  On the other hand,SUSY must be broken.  Nelson and Seiberg showed “Generally there is broken SUSY if there is an R-symmetry.”  We discuss SUSY Models with a global U(1) R symmetry.

3.  U(1) R symmetry must be broken to make nonvanishing Majorana gaugino masses. Nelson and Seiberg’s argument in global SUSY is But spontaneous R symmetry breaking causes massless Goldstone boson,R-axion. SUSY breaking vacuum is metastable in O’Raifeartaigh Model. R-symmetry breaking SUSY breaking explicit R-symmetry breaking In global SUSY Intriligator,Seiberg and Shih showed in global SUSY

4.  SUSY breaking vacuum has a positive vacuum energy in global SUSY. supergravity effect should be considered to realize a Minkowski vacuum (V=0). R-symmetry in supergravity 1.Are there relations between R-breaking and SUSY breaking like the Nelson and Seiberg’s argument? R-symmetry should be broken for Majorana gaoujino masses to exist. R-symmetry should be broken explicitly to avoid R-axion and …. 2. In O’Raifeartaigh Model,which generally has SUSY breaking vacua,are SUSY breaking vacua metastable ?

5. Contents of our study and this talk 1. the relation between R-symmetry and Supersymmetry breaking in supergravity(SUGRA) (based on the study of Nelson and Seiberg) 2. the metastability of a supersymmetry breaking Mikowski vacuum in O’Raifeartaigh Model in SUGRA. (Intriligator,Seiberg and Shih argued this metastability in global SUSY.) 3. Conclusion We discuss,

6. “The Nelson and Seiberg argument in global SUSY” the generic R-symmetric superpotential is rewritten ; R[W]=2,R[X] =q X. If there are R-breaking SUSY vacua( ), There is not a solution of these equations. R-symmetry breaking SUSY breaking N+1 equations with N unknowns (i=1,2,…,N)

7.  In SUGRA,F-flat conditions are modified That is,as long as, Nelson and Seiberg’s argument still holds. For example, in the model with and, R-symmetry breaking SUSY breaking. But most of R-symmetric Models don’t cause R-breaking. We considered O’Raifeartaigh Model which is known as the R-symmetric Model drawing SUSY breaking.

8. 3.The metastability of SUSY breaking vacua We argue explicit R-symmetry breaking makes SUSY breaking vacua metastable in O’Raifeartaigh Model. Before the main topic, : a=1,2,…,r and i=1,2,…,s. And r>s. In global SUSY, F-flat conditions for X are so that there is no supersymmetric vacuum. Introduction of generic O’Raifeartaigh Model r equations with s(<r) unknowns

9. Intriligator,Seiberg and Shih’s argument They added explicit R breaking terms to the generic O’Raifeartaigh Model to avoid R-axion. In global SUSY, F-flat conditions for X are There are solutions depending on f. SUSY breaking vacuum is metastable! Explicit R-breaking V X R-symmetric SUSY

10. and add SUSY breaking vacuum: SUSY vacuum: The SUSY breaking vacuum is metastable and long-lived for. Example in global SUSY V X SUSY

11. The metastability in SUGRA Generic O’Raifeartaigh Model in SUGRA F-term flat conditions for X are If there is no solution of, there is no SUSY vacuum.For example, K is canonical. This potential can be negative r equations with s(<r) unknowns

12. And if Kahler is canonical, V>0. Explicit R-breaking terms are required not only to avoid R- axion but also to make a Minkowski vacuum under this condition about K. This adding makes SUSY breaking vacuum metastable! This adding makes the solutions of these equations exist. The points satisfying the F-flat conditions are in V<0...

13. By adding more generic explicit R-breaking terms, Even if SUSY vacuua actually exist. But this constant |c| must be set to tune V to 0. There is a possibility the SUSY breaking Minkowski vacuum is not metastable. SUSY vacua appear like the analyses in global SUSY. If c is small,this is the same as in global SUSY!

14. case 1 : By integrating out and, SUSY breaking vacuum(V=0): SUSY vacuum: case 2 : SUSY breaking vacuum (V=0) : SUSY vacuum : ( ) In these cases, SUSY vacuum cannot exist!Example (1)

15. The situations to avoid the metastable More generally,the solutions of F-flat conditions can be expressed.In this case, the condition for SUSY vacua to exist is In Polonyi –like Model, SUSY breaking vacuum(V=0):,this condition is SUSY vacua can’t exist.

16. (2) The parameters are set ; SUSY breaking vacuum(V=0) SUSY vacuum V X SUSY This term is added to (1). Example 2

17. SUSY vacua appear,. 0 makes the SUSY breaking vacuum long- lived. Even if = 0, It is possibile that a SUSY vacuum exist. But the constant |c| is fixed to tune V to 0, so that there is a possibility that a SUSY Minkowski vacuum is stabilized. That is,…… R We found Polonyi-like models can avoid the metastable.

18. 4.Conclusion  Nelson and Seiberg argument “In the model with global U(1) R symmetry, R-symmetry breaking SUSY breaking “  This argument is also satisfied in SUGRA under the special condition,.(R[X]= ) For example, The R-charges of all fields are positive, and.

19. We considered R-symmetric Model with SUSY breaking dynamics, O’Raifeartaigh Model. To make gauginos massive and avoid R-axion, R-symmetry should be broken explicitly. In global SUSY,Intriligator Seiberg and Shih showed the requirements cause the metastability of SUSY breaking vacua. We discussed the metastability in supergravity.

20. If Kahler potential is canonical, V >0 in O’Raifeartaigh Model in supergravity. Explicit R-symmetry breaking terms are required not only to avoid R-axion but also make Minkowski vacua. The explicit R-symmetry breaking causes the metastable Minkowski vacuum under the condition. We verified there are the points which satisfy SUSY stational conditions in the explicit R-symmetry breaking models. It is possible that the metastability of the SUSY breaking Minkowski vacuum is avoided,for example, in Polonyi-like Model. Fin..

21.  There is a R solution satisfying SUSY stational conditions in the case R-charge of X is negative. A solution which doesn’t satisfy the NS condition. SUSY : X V SUSY q x <0