b d and fsi gene golowich physics dept umass (amherst) super b factory workshop in hawaii january...
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Bd and FSI
Gene GolowichPhysics Dept
UMass (Amherst)
Super B Factory Workshop in HawaiiJanuary 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 IDCharged 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 backgroundsBeware: 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. = - | > 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
_
ss
_
ss
- ‘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
21/
2
_
ss
_
ss __
ddu u|
0-0 Isospin-violating Mixing
1. 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)(p)(p
ρφ
22mix
mm|H
ρφ
ρφ
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
)' all(10
)2 only(10
]Br[]Br[
3
2
ηη
η
ηηφφ
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)
Effect of Soft Perturbative QCD
D(t,s) [1 + ln s/t + ( ln s/t)2/2 + . . . ]
Summing the Logs
D(t,s)
t1
t1
t1
ε
ts
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 meaningfulinsight of whether (and how) soft physics affects power counting.
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