03Hou

Slide1: 

July 19, 2003 HEP2003, Aachen Indications for Large Rescatterings in Rare B Decays

Outline: 

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

I. Motivation: 

I. Motivation History Kp/pp Large: Need for Large g [He-WSH-Yang ’99] and Factorization Works!

I. Motivation: 

I. Motivation History Kp/pp Large: Need for Large g [He-WSH-Yang ’99]

I. Motivation: 

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

Slide6: 

Can Shift Rate/CP Pattern —— esp. CPV

Slide7: 

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

I. Motivation: 

I. Motivation History Kp/pp Large: Need for Large g [He-WSH-Yang ’99] Speculation: Rate/DCP Pattern (late ’99)  Rescattering? [WSH-Yang ’00] Present (Impact of B Factories!) 2001: D⁰h⁰ Discovery ― Large (Rescatt.?) [Chua-WSH-Yang ’02] K¯p⁺/K¯p⁰ DCPV: Sign p⁰p⁰ Hint Enigma Belle/CLEO; BaBar 2003 Revisit Rescattering

Slide9: 

II. Ansatz: Multimode Fit ⊕ FSI Phases Naïve Factorization ⊗ Final State Rescattering Quasi-Elastic Inelastic Phases “Cancel” Gerard-WSH; Suzuki-Wolfenstein Otherwise Double Counting Special

Slide10: 

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 D⁰h⁰ 3 ⊗ 8 → 3 ⊗ 8 Formalism] Unable to Treat 1, i.e. 1 ⊗ 8 ~ ηʹK etc. (η₁), Will take η ≃ η₈

Slide11: 

Heuristic Picture SU(3) Correspondence Π ≡ P

Slide12: 

δ

Slide13: 

δ,σ N.B. 1. 2. σ Arise from Combo Only 

Slide14: 

Heuristic Picture SU(3) Correspondence Π ≡ P

Fit: à la WSH-Smith-Würthwein: 

Fit: à la WSH-Smith-Würthwein Inputs: Fit Parameters Output: Fitted Rates Crosscheck Reasonableness hep-ex/9910014

Slide16: 

Large FSI Phases ! What Drives Them? “World Average” Not Good Less Good > > > > > > > > > >

Slide17: 

Settle δ between themselves N.B. Disfavors sinδ<0 Correct Sign w/ Rescattering

Slide18: 

Settle δ between themselves N.B. Disfavors sinδ<0 Correct Sign w/ Rescattering

Slide19: 

N.B. Treating limits as Gaussian is Wrong. K-K+ Mode Can Be Small

Slide20: 

Determine σ between each other (& KK) δ= δ(Fit)

Slide22: 

δ= δ(Fit) Not Used in Fit Weak σ dep. Fit 1 ~ 99˚ Fit 2 = 60˚ Strong ϕ₃ dep.

Slide23: 

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

Slide24: 

Varied Landscape ! Flat forδ-σin First Quadrant

III. Two Scenarios ― Driven by : 

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 ?

Discussion: 

Discussion In Past Two Years K¯p⁺/K¯p⁰ aCP: Sign p⁰p⁰ Hint App, Spp Enigma Large Color Suppressed D⁰h⁰ Rescattering? Two (Sizable) FSI Phases Improve Understanding it feels real … Should be Clarified Soon by Data

Conclusion: 

Conclusion N.B. Treatment of FSI SU(3) Phases as “Parameters”.