Moduli stabilization and flavor structure in 5D SUGRA with multi moduli Yutaka Sakamura (RIKEN) in collaboration with Hiroyuki Abe (Yukawa Inst.) June 17,

Introduction Problems in Standard Model gauge hierarchy problem Yukawa hierarchy Charge quantization Anomaly cancellation GUT? SUSY? … flavor sym., extra dim., …

0 RR y f (0) i Yukawa hierarchy from extra dimension e.g.) zero-mode: 5D mass (Arkani-Hamed & Schmaltz, PRD61(2000)033005;…) (4D Yukawa) = (overlap integral)

In 5D SUGRA, : Radion (chiral) multiplet Flavor-dependent SUSY breaking (e.g. Scherk-Schwarz SUSY breaking) Yukawa hierarchy SUSY flavor problem

5D SUGRA with Multi moduli Yukawa hierarchy SUSY breaking cf.) In string context, “Mirror mediation”, Conlon, JHEP0803 (2008) 025

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, ) where Norm function

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

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

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

4D effective theory Soft SUSY parameters physical Yukawa coupling (cf. H.Abe & Y.S., PRD75 (2007) )

Single modulus case tachyonic soft masses from F X (cf. H.Abe’s talk)

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

e.g.) All moduli are stabilized. Vacuum

In this case, When the second term dominates. Positive soft squared masses No SUSY flavor problem from KK vector multiplets

Integration out for 5D gauge coupling

When, RR y Integration out for

When, RR y Integration out for

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

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

Summary 5D SUGRA with multi moduli Yukawa hierarchy SUSY breaking Radius: Additional contribution to the Kahler potential can save Tachyonic sfermion masses at tree level SUSY flavor problem