1. Selected topics in B physics
Lecture IV
Selected topics in B physics

2. Outlines B! VV polarizations B! K direct CP asymmetries
Mixing-induced CP in b! s
(Student’s interest gets stronger from bottom to top)
(New physics signal gets stronger from top to bottom)

3. B! VV polarizations

4. Counting Rules
The fractions follow the counting rules, RL~O(1), Rk~R?~O(mV2/mB2) from naïve factorization and kinematics.
The measured longitudinal fractions RL for B !   are close to 1.
RL~ 0.5 in  K* dramatically differs from the counting rules.
Are the  K* polarizations understandable?

5. Helicity Amplitudes transverse V1 rest V2 V1 S-wave  longitudinal
D-wave  parallel
transverse
P-wave  perpendicular

6. S,P,D-waves
L must balance

7. The longitudinal component dominates
left-handed (-)
Transverse
right-handed (+)
Longitudinal
H--
mq/mb
costs
+ ! Ak , - ! A?
ALÀ Ak¼ A? AL
(mq/mb)(mq’/mb)
costs q’
H++
The longitudinal component dominates

8. RL=|AL|2, Rk=|Ak|2, R?=|A?|2 Pure-penguin 0.52+-0.08+-0.03
Pure-penguin

9. Pure penguin in PQCD (02) Too large
(I) FA, (II) add nonfactorizable only, (III) add annihilation only, (IV) Add both nonfactorizable and annihilation
Prediction 0.75 > data 0.5. Though we could not explain  K*….

10. Penguin annihilation
Naïve counting rules for pure-penguin modes are modified by annihilation from (S-P)(S+P)
Annihilation contributes to all helicity amplitudes equally => Sizable deviation from RL~1
RL~0.8 (Lu et al.)
T+C~ P
RL~0.9
 K* seems to be the only puzzle
Consistent with PQCD

11. Plausible resolutions
New physics (Grossman 03; Yang et al. 04; Giri, Mohanta 04; Das et al.)
Annihilation effect in QCDF (Kagan 04)
Charming penguin in SCET (Bauer et al, 04)
Rescattering effect (Colangelo et al. 04; Ladisa et al. 04; Cheng, Chua, Soni 04)
Exotic b! sg (Hou,Nagashima 04)

12. Parameters in QCDF; Data fitting
No definite predictions for others
Parameters in SCET; should be
factorizable at leading power
No definite predictions for others
RL~0.5 for Ds*D* propagates
Into  K* final state
Also contribute to  K*
Transversely polarized gluon
Fragments into the  meson
=> Enhance Rk, R?
Also contribute to  K*, =(uu+dd)/2

13. PQCD predictions correspond to A0=0.40, A1=0.26, V=0.35
Data:
 T1~T2~0.30
Large energy symmetry relations among
A1, V, T1, T2
 PQCD predictions for transverse Brs are reasonable.

14. Too large total Brs imply too large longitudinal Brs
Data:
Too large total Brs imply too large longitudinal Brs
So far, no data, except  K*, control A0
B! () K* are governed by B! () form factors
=> A0 for B! K* could be smaller?
Model-dependent estimations A0=0.3~0.5.
Choose the asymptotic models for the corresponding
K* meson distribution amplitudes  A0=0.28

15. Experimental discrimination
If our explanation is valid, RL~0.6 for K*0K*
 K*: b! s(s s) K*K*: b! d(s s)
K*,  K* polarizations should be updated or
measured by Babar and Belle

16. Conclusion
Very small  K* polarization. New physics? It might be just due to QCD uncertainty (smaller A0 for B! K*).

17. B! K direct CP

18. Power counting
Estimate order of magnitude of a decay amplitude in power of » 0.22
It is not power counting from some rigorous theory
Amplitude» (CKM) (Wilson coefficient)
CKM matrix elements
|-i|¼ 0.4

19. Wilson coefficients

20. s s u u u s

21. Amplitude parametrization
(C2/C4)(VusVub/VtsVtb)» (1/2)(5/2)» 

22. Direct CP If T=0 If T=0 T exp(i3) T exp(i3) Br P P Br = Br
Recall

23. B! K puzzle
K+- and K+0 differ by subleading amplitudes Pew and C. Their CP are expected to be similar.
Their data differ by 3.6! A puzzle!

24. Explanation 1
Large K+- CP implies large T (predicted by PQCD in 2000)
Large PEW to cancel its effect (Buras et al.; Yoshikawa) in K+0 ) new physics?
T exp(i3) P
T exp(-i3)
Br¼ Br
PEW

25. Explanation 2
Or large C to cancel its effect (Charng and Li; He and McKellar) in K+0 ) mechanism missed in SM calculation?
T exp(i3)
(T+C) exp(i3) P
(T+C) exp(-i3)
Br¼ Br

26. Explanation 3 Explanation 3 = Explanation 1 + Explanation 2
Both pew and C are large (Wu and Zhou, Kim et al.)

27. Hint from B!

28. Large C! P, C, and Pew in 00 are all subleading.
We should have Br(00)¼ O(2)Br(+-)
Data show Br(00)¼ O()Br(+-)
This is the B!  puzzle.
C > Pew.It is easier to resolve both the puzzles by enhancing C.
How large could C be?

29. PQCD predictions (NLO)

30. Vertex correction
Vertex correction enhances C/ a2, and makes it complex.
Without vertex correction
Re, with vertex correction
Im, with vertex correction
Is negative. It rotates T!

31. QCDF
Vertex correction has been considered in QCDF, but the B! K puzzle can not be resolved.
T has a wrong sign in QCDF. C just makes the situation worse.
T exp(i3) P
(T+C) exp(i3)
Br = Br
(T+C) exp(-i3)

32. Vertex correction enhances |Acp(K+0)| in QCDF.

33. Conclusion
ACP(K+0) much differs from ACP(K+-). new physics in PEW? Simply a larger C?
It is not sure. Look at
Can not rule out a new physics phase for Pew (Buras et al.)
PQCD

34. b! s mixing-induced CP

35. sin 21 or sin 2 fCP=(q/p) (AfCP/AfCP) (see Jeff’s lectures)
If AfCP=AfCP, fCP=exp(-2i1)
Measure mixing-induced CP SfCP/ ImfCP
) measure sin(21)
Either pure-tree or pure-penguin modes serve the purpose
Pure-tree B! J/ KS are golden modes
Penguin pollution:
P/T» (C4/C2)(VtsVtb/VcsVcb)» 2» 5%

37. C

38. MS is also small from SU(3) symmetry analysis
.06(.02,-.03)
MS is also small from SU(3) symmetry analysis
(Chiang, Gronau, Rosner,Suprun 04)
MS( KS) / (C/P) cos(C-P )
C increases by a factor 3, but C-P ¼ 90o

39. Conclusion
If data of MS remain large, they will be a promising new physics signal.