1. July 19, 2003George W.S. Hou July 19, 2003 HEP2003, Aachen Indications for Large Rescatterings in Rare B Decays

2. July 19, 2003George W.S. Hou ٭ Motivation ٭Ansatz: (PP)Multimode Fit ٭Ansatz: (PP) Multimode Fit ( Generalized ) Factorization ( Generalized ) Factorization Rescattering Phases ⊕ Rescattering Phases ٭ Two Scenarios ― Driven by & ٭ Conclusion/Discussion Outline SU(3) Formalism: SU(3) Formalism: 8 ⊗ 8 → 8 ⊗ 8 Rescattering

3. July 19, 2003George W.S. Hou I. Motivation History K  Large: Need for Large   [He-WSH-Yang ’  ] Factorization Works! and Factorization Works!

4. July 19, 2003George W.S. Hou I. Motivation History K  Large: Need for Large   [He-WSH-Yang ’  ]

5. July 19, 2003George W.S. Hou I. Motivation Final State Isospin Decomposition History K  Large: Need for Large   [He-WSH-Yang ’  ] Speculation: Rate/a CP Pattern (late ’  Data)  Rescattering ? [WSH-Yang ’00] In Principle Present

6. July 19, 2003George W.S. Hou Can Shift Rate/CP Pattern —— esp. CPV

7. July 19, 2003George W.S. Hou D : Dispersive A : Absorptive CP asymmetry needs ➀ ∃ A ⇒ CP-Inv. Phase [Strong Int.] ➁ ∃ Phase Difference btwn D & A ⇒ CP- Viol. Phase [Weak Int.] Mechanism for CP Violating Rate Asymmetries e.g. for b → s Complex CKM Matrix Elements

8. July 19, 2003George W.S. Hou I. Motivation History K  Large: Need for Large   [He-WSH-Yang ’  ] Speculation: Rate/DCP Pattern (late ’  )  Rescattering? [WSH-Yang ’00] Present (Impact of B Factories!) 2001: D ⁰ h ⁰  Discovery ― Large (Rescatt.?) [Chua-WSH-Yang ’02] K ¯  ⁺  K ¯  ⁰ DCPV: Sign  ⁰  ⁰  Hint Enigma Belle/CLEO; BaBar 2003 Revisit Rescattering

9. July 19, 2003George W.S. Hou II. Ansatz: Multimode Fit ⊕ FSI Phases Naïve Factorization ⊗ Final State Rescattering Quasi-Elastic Inelastic Phases “Cancel” Gerard-WSH; Suzuki-Wolfenstein Otherwise Double Counting Special

10. July 19, 2003George W.S. Hou B → PP Only: VP Unsettled (VV More So) P : 8 of SU(3), ∴ PP → PP FSI Rescattering i.e., 8 ⊗ 8 = 1 ⊕ 8 ⊕ 8 ⊕ 10 ⊕ 27 Symmetric  TWO Physical Phase Difference: [Extend from D ⁰ h ⁰  3 ⊗ 8 → 3 ⊗ 8 Formalism] Unable to Treat 1, i.e. 1 ⊗ 8 ~ ηʹK etc. (η ₁ ), Will take η ≃ η ₈

11. July 19, 2003George W.S. Hou Heuristic Picture SU(3) Correspondence Π ≡ PΠ ≡ P

12. July 19, 2003George W.S. Hou δ

13. July 19, 2003George W.S. Hou δ,σδ,σ N.B. 1. 2. σ Arise from Combo Only 

14. July 19, 2003George W.S. Hou Heuristic Picture SU(3) Correspondence Π ≡ PΠ ≡ P

15. July 19, 2003George W.S. Hou Fit : à la WSH-Smith-Würthwein Inputs: Fit Parameters Output: Fitted Rates Crosscheck Reasonableness hep-ex/9910014

16. July 19, 2003George W.S. Hou Large FSI Phases ! What Drives Them? “World Average” Not Good Less Good > > > > > > > > > >

17. July 19, 2003George W.S. Hou Settle δ between themselves N.B. Disfavors sinδ<0 Correct Sign w/ Rescattering

18. July 19, 2003George W.S. Hou Settle δ between themselves N.B. Disfavors sinδ<0 Correct Sign w/ Rescattering

19. July 19, 2003George W.S. Hou N.B. Treating limits as Gaussian is Wrong. K-K+ Mode Can Be Small

20. July 19, 2003George W.S. Hou Determine σ between each other (& KK) δ= δ (Fit)

21. July 19, 2003George W.S. Hou

22. July 19, 2003George W.S. Hou δ= δ(Fit) Not Used in Fit Weak σ dep. Fit 1 ~ 99 ˚ Fit 2 = 60 ˚ Strong ϕ ₃ dep.

23. July 19, 2003George W.S. Hou Not Used in Fit Fit 2 = 60 ˚ Fit 1 ~ 96 ˚ δ= δ(Fit) Weak σ dep. δ= δ(Fit) Strong  / ϕ₃ dep.

24. July 19, 2003George W.S. Hou Varied Landscape ! Flat for δ-σ in First Quadrant

25. July 19, 2003George W.S. Hou III. Two Scenarios ― Driven by Otherwise, Difference is marginal except, Scenario 1 Better Fit  Scenario 2 gives - Too Small  ¯  ⁰ ! (3σ) - Utilize Smaller F.F. … But Maybe Belle’s Right ?

26. July 19, 2003George W.S. Hou Large FSI Phases ! What Drives Them? “World Average” Not Good Less Good > > > > > > > > > >

27. July 19, 2003George W.S. Hou Discussion In Past Two Years K ¯  ⁺  K ¯  ⁰ a CP : Sign  ⁰  ⁰  Hint A , S  Enigma Large Color Suppressed D ⁰ h ⁰ Rescattering? Two (Sizable) FSI Phases Improve Understanding it feels real … Should be Clarified Soon by Data

28. July 19, 2003George W.S. Hou Conclusion N.B. Treatment of FSI SU(3) Phases as “ Parameters ”.