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Changing the mirage messenger scale in mixed modulus-anomaly mediation

August 2, 2006 @ PPP 2006. Changing the mirage messenger scale in mixed modulus-anomaly mediation. Tetsutaro Higaki (Tohoku Univ.). Based on articles. PRD 73 : 046005, 2006. with Hiroyuki Abe (YITP) and Tatsuo Kobayashi (Kyoto Univ.). 1. Introduction. Superstring theory :

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Changing the mirage messenger scale in mixed modulus-anomaly mediation

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  1. August 2, 2006 @ PPP 2006. Changing the mirage messenger scale in mixed modulus-anomaly mediation Tetsutaro Higaki (Tohoku Univ.) Based on articles • PRD 73 : 046005, 2006 with Hiroyuki Abe (YITP) and Tatsuo Kobayashi (Kyoto Univ.)

  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 coupling constants and others. : gauge couplings, : Yukawa couplings, etc. : gaugino mass, : squark, slepton mass, : A-terms, etc. gravity mediation ( moduli mediation )

  3. 6D 10D 4D Examples of moduli fields (Ex) volume of cycle and ratio of volume between two cycles. 6D Volume modulus Shape modulus ⇒ 4D effective theory can have many moduli fields.

  4. 2. KKLT model S.Kachru, R.Kallosh, A.Linde and S.P.Trivedi, PRD 68 (2003) 046005 Type IIB O3/O7 system on warped Calabi-Yau (CY) threefold with Metric : : CY volume : string coupling : warp factor

  5. ② CY 3 ① b.g. 3-form flux Warped (KS) throat ③ 1. The minimum of warp factor 2. Potentials for dialton and shape moduli and the positions of D7/ 3-branes ① ② ・ Non-pertuebative potential for volume modulus ・ Explicit SUSY breaking and uplifting ③

  6. Moduli fields : Complex dilaton : Volume modulus : shape moduli

  7. ③ ①-1 We will consider… Effective N=1 SUGRA + explicit SUSY breaking. ①-2 ②

  8. ①-1 : The minimum of warp factor 3-form fluxon the warped throat can determine the minimum of warp factor. S.B. Giddings, S.Kachru and J.Polchinski, PRD 66 (2002) 106006

  9. ①-2 : 3-form flux can generate Superpotential of moduli can be stabilized by flux. The minimum of potential (SUSY point) : become heavy. Fine tuning for low energy SUSY

  10. ② : SU(N) gluino condensationon the D7-brane can generate the potential for volume modulus Now, relevant potentials are

  11. ・“Gravitino mass” ・Negativecosmological constant: Now, SUSY point is the minimum of this potential AdS vacuum. ・ V.e.v.s of moduli ~ 1-loop factor

  12. vacuum energy (explicit SUSY breaking) ③ dS minimum with anti-D3( ) uplifting potential Fine tuning of the cosmological constant : Here, Position moduli (singlet scalar) are stabilized due to ISD flux.

  13. By solving the stationary condition, we can estimate the difference of properties between and .

  14. At linear order ( = 4D cut off scale ) SUSY breaking order parameters The tree level modulus mediation is comparable to the loop-induced anomaly mediation.

  15. Anomaly / modulus ratio : Mixed modulus / anomaly 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)

  16. Mirage scale : Gaugino mass are unified at the mirage scale. We can have similar results for A-terms and scalar masses. ● scalar mass at ● A-term at We will find distinctive pattern of sparticle spectrum at TeV scale !

  17. When α=2 , ・ We can easily control SUSY flavor problem at TeV scale as mSUGRA in this model. ・ 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

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

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

  20. 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 %)

  21. Anomaly mediation is dominant.

  22. Moduli-mixing gauge coupling Heterotic (M-)theory: Type IIB O3/O7, magnetized D-branes:

  23. SU(N) gaugino condensation (GC): Moduli-mixing superpotential Moduli-mixing racetrack model : ② + uplifting potential. In the following section, we will take ①-2

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

  25. Single light modulus : Assuming that and are stabilized by flux, such that D3-branes sit on singularity.

  26. Results :

  27. No fine-tuning

  28. ● Remark : GC on D3 (or flux) and mD9 Naturally , This gauge coupling contribution would be needed to avoid hierarchy problem for α=2 when we have anomalous U(1). K.Choi and K.Jeong, hep-th/0605108

  29. 4. Summary • Modulus/anomaly ratio of SUSY breaking mediation α can take various values (α=1 in KKLT model). • rich sparticle spectrum • Destabilization due tohightemperature/overshooting problem may be avoided. ・Modulus decay → gravitino problem? ・Stabilization of exotic matter on (magnetized) brane?

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