Tetsutaro Higaki (Tohoku University)

1. KKLT type models with moduli-mixing superpotential Tetsutaro Higaki (Tohoku University) Based on article • PRD 73 : 046005, 2006 with Hiroyuki Abe (YITP) and Tatsuo Kobayashi (Kyoto Univ.) August 29, 2006 @ POSTECH, Pohang.

2. 1. Introduction • Superstring theory : • Candidate of unified theory of matter and forces. • No free continuous parameters. Vacuum expectation values of moduli (super)fields can determine parameters. : gauge/Yukawa couplings, etc. : SUSY breaking soft terms gravity mediation ( moduli mediation ) Moduli are important for particle phenomenology.

3. (Ex) moduli fields of type IIB SUGRA: : complex dilaton : volume modulus : shape moduli : volume of compact 6D space : string coupling

4. In this talk, our purpose is to change the mirage messenger scale in mirage mediation by changing a superpotential from KKLT model Then we may obtain rich and distinctive sparticle mass spectrum at TeV scale.

5. CY 3 2. KKLT model: S.Kachru, R.Kallosh, A.Linde and S.P.Trivedi, PRD 68 (2003) 046005 This model is based on type IIB O3/O7 system on warped compact Calabi-Yau (CY) threefold with ① b.g. 3-form flux Warped throat ① ・ The minimum of warp factor : K.Choi et al.

6. ② CY 3 2. KKLT model: S.Kachru, R.Kallosh, A.Linde and S.P.Trivedi, PRD 68 (2003) 046005 This model is based on type IIB O3/O7 system on warped compact Calabi-Yau (CY) threefold with ① b.g. 3-form flux Warped throat ① ・ The minimum of warp factor : ・ Non-pertuebative potential for volume modulus K.Choi et al. ②

7. ② CY 3 2. KKLT model: S.Kachru, R.Kallosh, A.Linde and S.P.Trivedi, PRD 68 (2003) 046005 This model is based on type IIB O3/O7 system on warped compact Calabi-Yau (CY) threefold with ① b.g. 3-form flux Warped throat ③ ① ・ The minimum of warp factor : ・ Non-pertuebative potential for volume modulus ・ Explicit SUSY breaking for uplifting potential K.Choi et al. ② ③

8. This model is a N=1 SUGRA + explicit SUSY breaking model which fixes all moduli.

9. This model is a N=1 SUGRA + explicit SUSY breaking model which fixes all moduli.

10. This model is a N=1 SUGRA + explicit SUSY breaking model which fixes all moduli.

11. This model is a N=1 SUGRA + explicit SUSY breaking model which fixes all moduli.

12. This model is a N=1 SUGRA + explicit SUSY breaking model which fixes all moduli.

13. This model is a N=1 SUGRA + explicit SUSY breaking model which fixes all moduli. and are heavy due to (ISD 3-form flux).

14. Below the scale of mass of S and U, we can obtain relevant potentials by integrating out S and U: We have a anti-D3-brane as a source that breaks SUSY explicitly:

15. SUSY vac.

16. SUSY vac.

17. SUSY vac.

18. SUSY vac.

19. SUSY vac.

20. SUSY vac. Mass scales K.Choi, A.Falkowski,H.P.Nilles,M.Olechowski NPB718:113,2005 ( 4D cut off scale )

21. SUSY breaking order parameters (F-term) The tree level modulus mediation is comparable to the loop-induced anomaly mediation. Anomaly / modulus ratio :

22. Mirage mediation K.Choi,K.Jeong,K.Okumura, JHEP09 (2005) 039 M.Endo,M.Yamaguchi,K.Yoshioka, PRD72:015004,2005 Gaugino mass (SM particles are living on only D7-brane) Mirage scale : Gaugino mass are unified at the mirage scale.

23. We can have similar results for A-terms and scalar masses. ● scalar mass at ● A-term at We may find distinctive pattern of sparticle spectrum at TeV scale !

24. When α=2 , ・ We can easily control SUSY flavor problem like TeV scale mSUGRA. ・ We have a solution to little SUSY hierarchy problem. K.Choi, K.Jeong, T.Kobayashi, K.OkumuraPLB 633 : 355, 2006 R.Kitano, Y.NomuraPhys.Lett.B631:58-67,2005

25. Gaugino masses at TeV scale : K.Choi,K.Jeong,K.Okumura, JHEP09 (2005) 039

26. Sfermion masses at TeV scale : K.Choi,K.Jeong,K.Okumura, JHEP09 (2005) 039

27. 3. Moduli-mixing racetrack model Racetrack model＝ double gaugino condensations. Gaugino condensations on two D7s will generate A connection of two terms can make the minimum of scalar potential. (fine-tuning : a few %)

28. F-terms Anomaly mediation is dominant.

29. Moduli-mixing gauge coupling Heterotic (M-)theory: Type IIB O3/O7, magnetized D-branes: Naturally, string models can have moduli-mixing gauge couplings .

30. SU(N) gaugino condensation (GC) on magnetized brane: Moduli-mixing superpotential Moduli-mixing racetrack model : + uplifting potential. In the following section, we will take

31. Various mirage messenger scale: Assuming that and are stabilized by ISD flux. D3-branes sit on singularity. (N=1 SUSY on them)

32. Results : Hidden holomorphic gauge coupling, A rank of Hidden gauge group

33. No fine-tuning

34. ● Remark : GC on D3 (or flux) and mD9 K.Choi and K.Jeong, hep-th/0605108 Naturally ,

38. 4. Summary • Anomaly/modulus ratio α of SUSY breaking mediation can take various values (α=1 in KKLT model). • rich sparticle spectrum • Destabilization due tohightemperature/overshooting problem may be avoided due tobelow the compactification scale.

39. Open question ・Modulus decay → gravitino problem ? Nakamura et al, Endo et al, Dine et al. ・Stabilization of exotic matter on (magnetized) brane ? ・∃D3/magnetized D9-brane→ tachyon (unstable)? ・∃Vector superfield on magnetized D9-brane → destroy the scalar mass structure of anomaly mediation ? K.Choi et al, Hebecker et al. connected by vector superfield

40. General results :

42. After all, we find

43. Example : orientifold Kachru et al.JHEP 0310:007,2003