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Insights into Large Rescatterings in Rare B Decays

Delve into the study of large rescatterings in rare B decays through detailed analysis and factorization works, exploring different scenarios and their implications on CP patterns. Understand the formalism, fit parameters, and heuristic pictures to uncover the complexities of rescattering phenomena.

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Insights into Large Rescatterings in Rare B Decays

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

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

  3. I. Motivation • History • Kp/ppLarge: Need for Large g[He-WSH-Yang ’99] and Factorization Works! George W.S. Hou

  4. I. Motivation • History • Kp/ppLarge: Need for Large g[He-WSH-Yang ’99] George W.S. Hou

  5. I. Motivation • History • Kp/ppLarge: Need for Large g[He-WSH-Yang ’99] • Speculation: Rate/aCP Pattern(late ’99 Data) •  Rescattering ? [WSH-Yang ’00] Final State Isospin Decomposition In Principle Present George W.S. Hou

  6. Can Shift Rate/CP Pattern —— esp. CPV George W.S. Hou

  7. I. Motivation • History • Kp/ppLarge: Need for Large g[He-WSH-Yang ’99] • Speculation: Rate/DCP Pattern(late ’99) •  Rescattering? [WSH-Yang ’00] • Present(Impact of B Factories!) • 2001:D⁰h⁰Discovery ― Large(Rescatt.?) • [Chua-WSH-Yang ’02] • K¯p⁺/K¯p⁰DCPV: Sign • p⁰p⁰Hint • Enigma Revisit Rescattering Belle/CLEO; BaBar 2003 George W.S. Hou

  8. II. Ansatz: Multimode Fit⊕FSI Phases Naïve Factorization ⊗ Final StateRescattering OtherwiseDouble Counting Special Quasi-Elastic Inelastic Phases “Cancel” Gerard-WSH; Suzuki-Wolfenstein George W.S. Hou

  9. 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 • TWOPhysical Phase Difference: • [Extend fromD⁰h⁰3 ⊗8→3 ⊗8Formalism] Unable to Treat 1, i.e. 1 ⊗ 8 ~ηʹK etc. (η₁), Will take η ≃ η₈ George W.S. Hou

  10. Heuristic Picture SU(3) Correspondence Π≡P George W.S. Hou

  11. δ George W.S. Hou

  12. δ,σ N.B. 1. 2. σArise from  Combo Only George W.S. Hou

  13. Heuristic Picture SU(3) Correspondence Π≡P George W.S. Hou

  14. Fit: à laWSH-Smith-Würthwein hep-ex/9910014 • Inputs: • Fit Parameters Output:Fitted Rates Crosscheck Reasonableness George W.S. Hou

  15. “World Average” > > > > > > > > > > Not Good Less Good Large FSI Phases ! What Drives Them? George W.S. Hou

  16. Correct Sign w/ Rescattering Settleδbetween themselves N.B. Disfavors sinδ<0 George W.S. Hou

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

  18. δ= δ(Fit) Determine σ between each other (& KK) George W.S. Hou

  19. George W.S. Hou

  20. Not Used in Fit δ= δ(Fit) δ= δ(Fit) Fit 1 ~ 96˚ Weak σ dep. Strong g/ϕ₃ dep. Fit 2 = 60˚ George W.S. Hou

  21. Varied Landscape ! Flat forδ-σin First Quadrant George W.S. Hou

  22. III.Two Scenarios― Driven by Otherwise, Difference is marginal except, Scenario 1 Better Fit  Scenario 2 gives - Too Small p¯p⁰ ! (3σ) - Utilize Smaller F.F. … But Maybe Belle’s Right ? George W.S. Hou

  23. “World Average” > > > > > > > > > > Not Good Less Good Large FSI Phases ! What Drives Them? George W.S. Hou

  24. Discussion • In Past Two Years • K¯p⁺/K¯p⁰aCP: Sign • p⁰p⁰Hint • App, SppEnigma • Large Color Suppressed D⁰h⁰ Rescattering? Two (Sizable) FSI Phases Improve Understanding it feels real … Should be Clarified Soon by Data George W.S. Hou

  25. Conclusion N.B. Treatment of FSI SU(3) Phases as “Parameters”. George W.S. Hou

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