Supersymmetry breaking ,R-symmetry breaking ,and metastable vacua in supergravity

1. Yuji Omura (Kyoto Univ.) Hiroyuki Abe (YITP,Kyoto Univ.) Tatsuo Kobayashi(Kyoto Univ.) Supersymmetry breaking ,R-symmetry breaking ,and metastablevacua in supergravity

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.” Introduction • We discuss SUSY Models • with a global U(1)R symmetry.

3. U(1)R symmetry must be broken to make nonvanishingMajoranagaugino masses . Nelson and Seiberg’sargument in global SUSYis But spontaneous R symmetry breaking causes massless Goldstone boson ,R-axion. The SUSY Models with U(1)R symmetry In global SUSY R-symmetry breaking SUSY breaking explicit R-symmetry breaking Intriligator,Seiberg and Shih showed in global SUSY SUSY breaking vacuum is metastable in O’Raifeartaigh Model.

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 R-symmetry should be broken for Majoranagaoujino masses to exist. Are there relations between R-breaking and SUSY breaking like the Nelson and Seiberg’s argument? 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 vacuametastable ?

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

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 vacuametastable in O’Raifeartaigh Model. Before the main topic, Introduction of generic O’Raifeartaigh Model : 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 nosupersymmetric vacuum. 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. V R-symmetric Explicit R-breaking SUSY SUSY breaking vacuum is metastable! X SUSY

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

11. The metastability in SUGRA This potential can be negative • 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. 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 the solutions of these equations exist. The points satisfying the F-flat conditions are in V<0. This adding makes SUSY breaking vacuum metastable!

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. SUSY vacua appear like the analyses in global SUSY. If c is small, this is the same as in global SUSY! There is a possibility the SUSY breaking Minkowski vacuum is not metastable .

14. Example (1) 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!

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 InPolonyi –like Model, SUSY breaking vacuum(V=0): ,this condition is SUSY vacua can’t exist.

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

17. That is,…… R 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. 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 ,IntriligatorSeiberg and Shih showed the requirements cause the metastability of SUSY breaking vacua. We discussed the metastability in supergravity.

20. .. Explicit R-symmetry breaking terms are required not only to avoid R-axion but also make Minkowskivacua. If Kahler potential is canonical, V >0 in O’Raifeartaigh Model in supergravity. The explicit R-symmetry breaking causes the metastableMinkowski 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. Appendix A solution which doesn’t satisfy the NS condition. • There is a R solution satisfying SUSY stational conditions in the case R-charge of X is negative. V SUSY : qx<0 SUSY X SUSY :