1. Moduli stabilization and flavor structure in 5D SUGRA with multi moduli Yutaka Sakamura (RIKEN) with Hiroyuki Abe (Yukawa Inst.) Aug. 1, 2008@YITP arXiv:0807.3725

2. Problems in Standard Model gauge hierarchy problem Yukawa hierarchy Introduction SUSY? … flavor sym., extra dim., … We consider effective theories of SUSY extra -dimensional models, focusing the flavor structure.

3. 0 RR y f (0) i Yukawa hierarchy from extra dimension e.g.) zero-mode: 5D mass (Arkani-Hamed & Schmaltz, 2000 ;…) (4D Yukawa) = (overlap integral)

4. In effective theories of 5D SUGRA, : Radion (chiral) multiplet (Luty & Sundrum, 2000) Purpose Study the flavor structure of the effective theory for more general 5D SUGRA. In general, the radius is given by chiral multiplets

5. 5D (off-shell) SUGRA on S /Z Field content Weyl multiplet: Vector multiplet: (One of them is the graviphoton multiplet.) Hypermultiplet: 1 2 compensator physical (Kugo & Ohashi, 2000-2002) where Norm function

6. 5D Lagrangian bulk part (bulk mass) (gauge coupling) =

7. T = zero-mode of  Single modulus case: I I T is the radion multiplet. Moduli

8. 5D SUGRA with multi moduli Field content Vector multiplet: Hypermultiplet: Orbifold parity Yukawa hierarchy SUSY matter gauging

9. 4D effective theory Yukawa couplings and Soft SUSY parameters (cf. H.Abe & Y.S., 2007) (physical Yukawa coupling)

10. where If, the soft scalar masses are

11. Single modulus case tachyonic soft masses from F X

12. Multi moduli case If the second term of dominates, No SUSY flavor problem

13. e.g.) All moduli are stabilized. Vacuum

14. In this case, When the second term dominates. non-tachyonic flavor universal Soft masses are

15. RR 0y Single modulus case: sequestered Multi moduli case: not sequestered When

16. Integration out for 5D gauge coupling

17. RR y Integration out for When,

18. RR y Integration out for

20. Physical vector multiplets Vecter multiplets (I=1,2,…,n) : parity-odd : parity-even Superconformal gauge-fixing … (# of physical vector multiplets) = n-1 Single modulus case: no KK vector multiplets

21. Summary 5D SUGRA with multi moduli Radius: Additional contribution to the Kahler potential exist, and it can save Tachyonic sfermion masses at tree level SUSY flavor problem