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B d   and FSI

B d   and FSI. Gene Golowich Physics Dept UMass (Amherst) Super B Factory Workshop in Hawaii January 19-24, 2004 East West Center at UH. From Out of the Past. Adventurers Again. Adventurers Again. Adventurers Again. Usual Suspect 1: External Tree. Usual Suspect 2: Internal Tree.

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B d   and FSI

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  1. Bd   and FSI Gene Golowich Physics Dept UMass (Amherst) Super B Factory Workshop in Hawaii January 19-24, 2004 East West Center at UH

  2. From Out of the Past

  3. Adventurers Again

  4. Adventurers Again

  5. Adventurers Again

  6. Usual Suspect 1: External Tree

  7. Usual Suspect 2: Internal Tree

  8. Usual Suspect 3: Penguin

  9. Usual Suspect 4: Exchange

  10. On Detecting the Bd  Mode Good for Vertex ID Charged particles only (each  K+K-) -peak is narrow -peak is near threshold in M2[K+K-] Comb. Bckgd limited near M2[K+K-] thrhld 2-body decay (momentum of  is fixed) Four kaons good for particle ID (discriminate against comb. bckgds) Angular distribution for 0- 1-1- decay. However Bd  is very rare Essential to understand backgrounds Beware: Can get ’s from Ds’s, etc

  11. Bd  Strategy Experimental Keep lowering bound on branching ratio (Current PDG bound is <1.2 10-5) Eternal hope: Rare mode New Physics Theoretical Which SM amplitudes contribute? (Donoghue, Golowich, Petrov, Soares) Help clarify interpretation of signal.

  12. A Menu of Mechanisms •  = - | > Is Not Exact A] Non-magic mixing B] Isospin violations 2. Assume That  = - | > C] OZI-forbidden process D] Unitarity and Final State Ints (FSI) Intriguing possibility that Bd is a ‘unique’ probe of FSI in B decays

  13. - ‘Non-magic’ Mixing 1.Magic - Mixing (0) 0 = tan-1 and |> = - | > 2. Physical Mixing (=0+) |> = - | > -  / 3. Amplitude, Branching Ratio MB[non-magic] =  MB BrB[non-magic] = 2(deg) 10-3 BrB

  14. 0-0 Isospin-violating Mixing • Mixing Parameter xmix: xmix = = 6.4 10-4 2. Amplitude Relation: MB[iso-viol] = xmix MB 3. Branching Ratio Relation: BrB[iso-viol] = 4 10-7 BrB

  15. Another Source: OZI-forbidden

  16. The Unitarity Mechanism

  17.  and ’ [LIPKIN NP B291 (1987) 720]

  18. Unitarity Estimate 1. Disclaimer: Many intermediate states at E = mB. Cancellations make it more uncertain! Br’s unknown for Bd  2,2’,’. 2. Numerics: Consider two cases: a]  Intermediate State Only b] All 2-body ,’ Int. States Find that

  19. Bd   Summary Flavor Disadvantaged (`FD’) Decay Hadron final state, yet highly suppressed Challenge to SuperB to detect FD decays Bd  IS There! Variety of secondary SM mechanisms. Potential for `unique’ test of FSI. But cancellations reduce unitarity signal. Testing New Physics (N.P.)? BR Detection at O(10-7)  N.P. (?)

  20. FSI in B Decays `Hard’ Physics (pQCD): HQET: Beneke, Buchalla, Neubert, Sachrajda [PRL 83 (1999)], Keum,Li,Sanda [PRD 63 (2001)] Etc SCET: Bauer, Fleming, Luke [PRD 63 (2001)], Bauer, Fleming, Pirjol, Stewart [ “ ], Etc `Soft’ Physics (non-pQCD): Unitarity: JD, EG, AP, JS [PRL 77 (1996)]. QCD: Donoghue, Golowich, Mojzis (recent) Etc

  21. Cross Sections at High Energy

  22. DGPS Analysis [PRL 77 (1996)] Basic Premises Hadronic degrees of freedom, Unitarity, mB   limit. Insights: Soft Rescattering (S-R) S-R suffers mB-2 suppress. in phase spce But Optical Theorem: Msoft s1.08 (!) Conclusion Can soft physics upset power counting?

  23. RecentEfforts [JD,EG,MM] Modified Premises Still `FSI & soft physics’ issue, Still mB   limit, . . but . . Now work directly with QCD. Aim of Study Can power counting be upset? Seek dynamical insights . . .

  24. Apparent Dynamics of FSI

  25. QCD Dynamics of FSI

  26. `Semi-SoftQCD’& Power Counting Perturbative Propagator D(t)  Effect of Soft Perturbative QCD D(t,s)  [1 +  ln s/t + ( ln s/t)2/2 + . . . ] Summing the Logs D(t,s) 

  27. FinalThoughts on SoftFSI The Unlikely To get a quantitatively accurate measure of `soft’ FSI in B decay which is a rigorous consequence of QCD. The Possible To obtain, as a matter of principle in quantum field theory, a meaningful insight of whether (and how) soft physics affects power counting.

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