1. Semi-inclusive hadronic B decays at the endpoint
Adam Leibovich
University of Pittsburgh
11/1/06
With J. Chay, C. Kim, J. Zupan hep-ph/

2. Outline Why semi-inclusive hadronic B decays? SCET introduction
Schematic of calculation
Charming Penguins
Phenomenology
Outlook

3. Why? Potentially large data sets SCET allows for factorization of rate
B decaying to light meson M recoiling against hadronic jet X B M X
Potentially large data sets
SCET allows for factorization of rate
The B to X part same as in
Simpler than two-body exclusive decays
Spectator interactions suppressed
Possible handle on charming penguins

4. Need for SCET Investigate in the endpoint region
B decaying to light meson M recoiling against hadronic jet X B M X
Investigate in the endpoint region
Jet X is jet of collinear particles
New small scale in the problem
SCET is effective theory coupling collinear and soft particles together

5. SCET Intro Systematic expansion in SCETI has , SCETII has
Degrees of freedom:
Collinear particles with
Soft particles with
Ultrasoft particles with
By using gauge invariance, operators constrained
Field redefinition allows leading order factorization theorems

6. } Gauge invariance restrictions Factorization
Only coupling to ultrasoft sector
Introduce usoft Wilson line:
Field redef:
Ultrasoft decouples:

7. In Pictures Heavy/soft modes do not interact with collinear modes
⇒ Rate factors!

8. Schematic of Calculation
Match QCD onto SCETI
Operators look like
Run down to SCETII scale
Factorization makes
running simple
Brodsky-Lepage kernel
for n direction
Heavy-to-light for rest

9. Schematic of Calculation, cont
For now, only look at cases where the spectator from B goes to jet
Decay amplitude looks like
Use Optical Theorem to relate decay rate to imaginary part of forward scattering
Gives lightcone
amplitude
Gives jet function
convoluted with
shape function

10. Schematic of Calculation, cont
Decay rate is
where
B shape function
Light quark jet function
Perturbative
Lightcone amplitude
Compare with
Cancel in the ratio

11. Schematic of Calculation, cont
In a picture M J X f  B J Xs
Compare to f B

12. Charming Penguin? Have been ignoring possible charm loop
For some of phase space nonperturbative size of order
Large or small? Matter for debate
Phase space factor

13. Universal up to B meson flavor
Charming Penguin?
Can include effects
Charming penguin adds new term to rate
Unknown piece
Universal up to B meson flavor

14. Strategy for Charming Penguin
Look at decays without it
Example:
Test method, within errors?
Look at decays with it
Is term from charming penguin necessary?

15. Uncertainties Lots of higher order corrections
Higher order B shape function: Mostly cancel in ratio
New subleading function enter due to correction to collinear currents: Could be large for some modes
“Chirally enhanced” terms: Unknown size
SU(3) breaking: For M of order 20% (small for B)
Also have uncertainty in parameters
(ie, lightcone amplitudes)

16. Phenomenology Put cut on invariant mass mX < 2 GeV
Normalize rate to in endpoint
Lightcone amps from QCD sum rules
Calculate CP asymmetry
Look at as many decays as possible, assuming charming penguin is small

17. Have rates for 24 different channels
Some Results
Have rates for 24 different channels
Some are listed below
Mode
Exp. (2 body)
ACP
0.16 ± 0.09 ± 0.05
> 0.078
0.30 ± 0.16 ± 0.01
0.22 ± 0.13 ± 0.03
> 0.034
0.009 ± ± 0.002
0.67 ± 0.37 ± 0.14
> 0.038
± ± 0.004
1.76 ± 0.97 ± 0.35
> 0.10
± ± 0.004
0.20 ± 0.11 ± 0.06
> 0.067
0.010 ± ± 0.001
> 0.035 -

18. Outlook With future measurements, could constrain charming penguin
Error estimates could be done better
All modes so far have spectator going to jet
Do not need to do this restriction
Will have new results without this assumption soon
Allows for many more modes
New data from BaBar