Anomalous U(1) GUT

1. Anomalous U(1) GUT • Introduction • Anomalous U(1) GUT • Horizontal symmetry • Summary and Discussion Toshifumi YAMASHITA (Kyoto University) 2004/12/7 @UC Irvine

2. SUSY? Introduction Higgs? hierarchal Yukawa? • SUSY-GUT • fascinating extension of SM • gauge coupling unification (GCU) • unifications of forces and of matter • charge quantization • stabilization of the weak scale Proton decay?

3. Introduction • SUSY-GUT • The Hierarchy problem is solved. • Gauge Coupling Unification But ・・・ • DT Splitting problem • Proton decay (vs GCU) • Fermion Yukawa • SUSY flavor problem U(1)A Flavor Symm. Almost all the problem can be solved!!

4. Anomalous U(1) GUT • Assumptions • “generic interaction” • all the possible interactions • order 1 coefficients • no fine-tuning • number of parameters order of magnitude : order of magnitude a few ( # of fields) : precise analysis ( # in SM)

5. Anomalous U(1) GUT • Assumptions <Z> may break GUT symmetry • vacuum structure • : GUT singlet operator, : charge • : VEV of the Froggatte-Nielsen field • in a mass unit, the cutoff scale mass term for and : factorization

6. Anomalous U(1) GUT M.Bando N.Maekawa and T.Y. • Overview • “Generic interaction” • FN mechanism • SUSY-zero mechanism • “Natural Gauge Coupling Unification hierarchal Fermion Yukawa DW VEV DT Splitting proton decay

7. Anomalous U(1) GUT PTP 107, 1201 (2002) N.Maekawa and T.Y. • Example of E6 model • Gauge Coupling Unification • Doublet-Triplet Splitting

8. Anomalous U(1) GUT PTP 107, 1201 (2002) N.Maekawa and T.Y. • Example of E6 model

9. Horizontal Symmetry • How to break SUSY? S.Martin Hep-ph/9709356 (1,2)-components of sfermion mass, , should be suppressed. PL B561, 273(2003) N.Maekawa “SUSY flavor problem”

10. Horizontal Symmetry • Solutions to SUSY flavor problem is in mass basis given from in flavor basis by • degenerate • alignment • decoupling degenerate If 1st and 2nd generations belong to a single multiplet, they can be degenerate. non-Abelian horizontal symmetry

11. Large mixing Large (1,2) element Horizontal Symmetry • horizontal symmetry breaking Because fermion Yukawa is not symmetric. The degeneracy is lifted by Even if , becomes large. 3rd should also be degenerate. E-twisting SU(2)E

12. SU(2)H : SU(2)E : Horizontal Symmetry PLB561, 273(2003) N.Maekawa • model

13. Horizontal Symmetry • model • constraints RG factor : (in MSSM)

14. Horizontal Symmetry JHEP 0407 (2004) 009N.Maekawa and T.Y. • Horizontal symmetry in Higgs sector Inspired by the decomposition :

15. Summary and Discussion • “Anomalous U(1) GUT” • DT Splitting through DW VEV • Realistic Fermion Yukawa • “Natural Gauge Coupling Unification” • Non-abelian horizontal symmetry • SUSY flavor problem can be solved. • Horizontal symmetry in Higgs sector. A road toward realistic E8 Unification (?)

16. Introduction • Anomalous U(1) Symmetry • Low energy theory of string theory • Anomaly Green-Schwartz mechanism • Froggatte-Nielsen mechanism

17. Introduction • Anomalous U(1) Symmetry • Low energy theory of string theory • Anomaly Green-Schwartz mechanism • Froggatte-Nielsen mechanism Ex)

18. Anomalous U(1) GUT • sector in E6 model • E-twisting M.Bando and T.Kugo mass massless : • mildhierarchy in sector !! • all come from and . large mixing

19. In the effective theory below , Anomalous U(1) GUT • SUSY-zero mechanism Only positively chargedoperators can appear. : analytic does not appear in .

20. In the effective theory below , Anomalous U(1) GUT • SUSY-zero mechanism Only positively chargedoperators can appear. Ex) Adjoints of SO(10) : Dimopoulos-Wilczek VEV DTS

21. Anomalous U(1) GUT PRL 90, 121801 (2003) N.Maekawa and T.Y. • Gauge Coupling Unification • We can calculate the Flows. • When we recalculate the Flows by MSSM • from the low energy values, • three couplings meet at the cut-off scale • if . • When , Proton Decay via Dim.5 operators • are suppressed. GCU in the minimal SU(5) SUSY-GUT!!

22. Anomalous U(1) GUT PRL 90, 121801 (2003) N.Maekawa and T.Y. • Gauge Coupling Unification