Bd   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
Usual Suspect 3: Penguin
Usual Suspect 4: Exchange
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
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.
A Menu of Mechanisms
_
1.  = - | s s > Is Not Exact
A] Non-magic mixing
B] Isospin violations
_
2. Assume That  = - | s s >
C] OZI-forbidden process
D] Unitarity and Final State Ints (FSI)
Intriguing possibility that Bd is
a ‘unique’ probe of FSI in B decays
-
‘Non-magic’ Mixing
1.Magic - Mixing (0)
0 = tan-1 1/ 2
_
and |> = - | s s
>
2. Physical Mixing (=0+)
_
_
_
|> = - |s s > -  | u u d d / 2
3. Amplitude, Branching Ratio
MB [non-magic] =  MB
BrB [non-magic] = 2(deg) 10-3 BrB
0-0 Isospin-violating Mixing
1. Mixing Parameter xmix:
xmix =
 φ  Hmix | ρ 
mφ2  mρ2
= 6.4 10-4
2. Amplitude Relation:
MB[iso-viol] = xmix MB
3. Branching Ratio Relation:
BrB[iso-viol] = 4 10-7
p (φ )
p( ρ )
BrB
Another Source: OZI-forbidden
The Unitarity Mechanism
 and ’
[LIPKIN NP B291 (1987) 720]
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
10 2 ( only 2η ) 
Br[φφ ]
  3

Br[ηη ]
10 ( all η  η' ) 
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. (?)
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,
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?
Recent Efforts [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 . . .
Apparent Dynamics of FSI
QCD Dynamics of FSI
`Semi-Soft QCD’ & Power Counting
Perturbative Propagator
D(t)  1
t
Effect of Soft Perturbative QCD
D(t,s)  1 [1 +  ln s/t
t
+ ( ln s/t)2/2 + . . . ]
Summing the Logs
ε
s
D(t,s)  1  
t t
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.