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

Usual Suspect 1: External Tree

Usual Suspect 2: Internal Tree

Usual Suspect 3: Penguin

Usual Suspect 4: Exchange

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

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

A Menu of Mechanisms 1.  = - | > 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 B d  is a ‘unique’ probe of FSI in B decays

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

 0 -  0 Isospin-violating Mixing 1.Mixing Parameter x mix : x mix = = Amplitude Relation: M B  [iso-viol] = x mix M B  3. Branching Ratio Relation: Br B  [iso-viol] = Br B 

Another Source: OZI-forbidden

The Unitarity Mechanism

 and  ’ [LIPKIN NP B291 (1987) 720]

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

B d   Summary Flavor Disadvantaged (`FD’) Decay Hadron final state, yet highly suppressed Challenge to SuperB to detect FD decays B d   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. (?)

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

Cross Sections at High Energy

DGPS Analysis [PRL 77 (1996)] Basic Premises Hadronic degrees of freedom, Unitarity, m B   limit. Insights: Soft Rescattering (S-R) S-R suffers m B -2 suppress. in phase spce But Optical Theorem: M soft  s 1.08 (!) Conclusion Can soft physics upset power counting?

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

Apparent Dynamics of FSI

QCD Dynamics of FSI

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

Final Thoughts on Soft FSI 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.