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.