1. Jun. 19, 2008SUSY 08 Axionic Mirage Mediation Tohoku Univ. Shuntaro Nakamura Collaborated with K. Okumura and M. Yamaguchi This talk is based on arXiv:0803.3725 (accepted in PRD)

2. Jun. 19, 2008SUSY 08 Plans of this talk 1.Introduction & Summary 2.The model 3. problem 4.Cosmology 5.Summary

3. Jun. 19, 2008SUSY 08 1. Introduction & Summary SUSY is an attractive candidate for new physics beyond SM solves the hierarchy problem has DM candidates However, sparticles have not been discovered yet It has to be broken Phenomenological aspects depend on how SUSY is broken To understand the SUSY mechanism is important !

4. Jun. 19, 2008SUSY 08 One is the moduli mediation Another is anomaly mediation In KKLT set-up, the modulus is stabilized with the relatively heavy mass : modulus mass Thus, the anomaly mediation is comparable to the modulus one This is known as the mirage mediation Choi, Falkowski, Nilles, Olechowski ’05 Endo, Yamaguchi, Yoshioka ’05 Kachru, Kallosh, Linde, Trivedi ’03 Some plausible mediation mechanisms are known

5. Jun. 19, 2008SUSY 08 The mirage mediation is very attractive mechanism However, it has two crucial problems In general, B parameter becomes TeV Too large ! 2. moduli problem The modulus decay produces too many gravitinos Neutralinos, if they are stable, overclose the Universe ! Endo, Hamaguchi, Takahashi ’06 SN, Yamaguchi ’06 Choi, Jeong, Okumura ’05 1. problem

6. Jun. 19, 2008SUSY 08 In this work, we showed the introduction of the axion superfield into the mirage mediation can solve these two problems ! In addition to these virtues, our model can explain strong CP problem (as it should be) SUSY CP problem present DM abundance axino with mass

7. Jun. 19, 2008SUSY 08 2. The model We introduce the axion superfield and messengers In SUSY limit, is a flat direction but it is lifted by SUSY When gets a VEV, we can integrate out From EOM of, we obtain is also smaller than by one-loop factor : singlet : messenger

8. Jun. 19, 2008SUSY 08 The scalar potential is Roughly speaking, is stabilized at a point where crosses zero From RGE of : # of messengers drives to be negative !we can find

9. Jun. 19, 2008SUSY 08 The PQ scale in axionic mirage mediation In what follows, we consider the case : modular weight of the messenger

10. Jun. 19, 2008SUSY 08 The axino mass is obtained from This is two-loop order in contrast with the other soft masses being one-loop The axino becomes LSP

11. Jun. 19, 2008SUSY 08 Let us consider the following superpotential and Kahler potential are singlets When gets VEV, we can integrate out 3. The problem These are soft mass order cf. Pomarol, Rattazzi ’99

12. Jun. 19, 2008SUSY 08 In the mirage mediation, the phases of two SUSY can be aligned Choi ’93 Endo, Yamaguchi, Yoshioka ’05 Thus, the phase of B can be rotated away simultaneously with that of and term: Because and term can be obtained as In our model, SUSY CP problem is absent !

13. Jun. 19, 2008SUSY 08 4. Cosmology We assume both and have Planck scale amp., and their coherent oscillations start before the reheating is completed The modulus decay dilutes unwanted particles saxion mainly decays into axions modulus mainly decays into gauge multiplet Therefore, it is sufficient to discuss the cosmic evolution only after the modulus decay entropy production

14. Jun. 19, 2008SUSY 08 There are four production processes of the axino

15. Jun. 19, 2008SUSY 08 This process gives the dominant contribution There are four production processes of the axino

16. Jun. 19, 2008SUSY 08 We investigated the relic abundance of the axino in various NLSP cases

17. Jun. 19, 2008SUSY 08 Contours of the density parameter of the axino For the case that the annihilation of NLSPs is not effective Spergel, et. al ’06

18. Jun. 19, 2008SUSY 08 Contours of the density parameter of the axino For the case that the annihilation of NLSPs is effective

19. Jun. 19, 2008SUSY 08 Especially, the higgsino NLSP case is very interesting ! The higgsino can decay into the Higgs and the axino, and the Z boson and the axino The lifetime of the higgsino is for Higgsino decay into Higgs provides an interesting signal of displaced vertex emitting hard jets

20. Jun. 19, 2008SUSY 08 Axino with mass can explain the present DM abundance 5. Summary We have introduced the axion superfield in the mirage mediation to solve two crucial problems moduli problem We showed that PQ scale is obtained in the axion window by stabilizing the axion superfield problem