1. The CKM Angles a and b a/f2 g/f3 b/f1 Introduction Measuring b/f1
Theory overview
Experiments at B-factories
Measuring b/f1
Measuring a/f2
Summary
a/f2
g/f3
b/f1

2. The Cabibbo-Kobayashi-Maskawa Matrix
The weak interaction can change the favor of quarks and lepton
Quarks couple across generation boundaries
Mass eigenstates are not the weak eigenstates
The CKM Matrix rotates the quarks from one basis to the other
Vcb
Vub u d t c b s l l3 l2
l=sin(qc)=0.22 d’
Vud
Vus
Vub d s’ =
Vcd
Vcs
Vcb s b’
Vtd
Vtb b

3. Visualizing CKM information from Bd decays The Unitarity Triangle
The CKM matrix Vij is unitary with 4
independent fundamental parameters
Unitarity constraint from 1st and 3rd columns:
i V*i3Vi1=0
Testing the Standard Model
Measure angles, sides in as many ways possible
Area of triangle proportional to amount of CP violation u
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb c t
CKM phases
(in Wolfenstein convention)
unitarity
4 parameters (3 real, 1 complex phase)
many representations. Wolfenstein – matches hierarchy shown on previous slide
In this representation the Vtd and Vub – the small elements in the corner carry a complex phase. UT
will be our guide for the remainder of the talk.

4. Three Types of CP Violation
I) Indirect CP violation/CP violation in mixing
K®pp, K®pln, expected to be small (SM: 10-3) for B0’s
II) Direct CP violation: Prob(B®f) ¹ Prob(B®f)
e¢/e in K®pp
Br(B0®K-p+) ¹ Br(B0®K+p-)
III) Interference of mixing & decay: Prob(B(t)®fCP) ¹ Prob(B(t)®fCP)
B0®yKs (CKM angle b)
B0®p+p- (CKM angle a)
Due to quantum numbers of
Y(4S) and B meson we must
measure time dependant
quantities to see this CP violation
Only CP violation possible for
charged B’s
In this talk we will be discussing type III) CP violation

5. CP Violation at the Y(4S)
CP violation from the interference between two paths, decay with and without mixing
mixing
q/p
|BL>=p|B0>+q|B0>
|BH>=p|B0>- q|B0>
Measure time dependent decay rates
&
Dm from B0B0 mixing
Direct CP Violation: C¹ 0
|Af/Af|≠1→ direct CP violation
|q/p|≠1→ CP violation in mixing
Sf and Cf depend on CKM angles

6. Getting the Data Sample
Use e+e- annihilations at Y(4S) to get a clean sample of B mesons
At Y(4S) produce B-/B+ (bu/bu) and B0B0 (bd/bd) mesons
mB0 ~ mB- ~ 5.28 GeV
BB Threshold
motivation for asymmetric B factory
The Y(4S) - a copious, clean source of B meson pairs
1 of every 4 hadronic events is a BB pair
No other particles produced in Y(4S) decay
Equal amounts of matter and anti-matter

7. Note: 1fb-1 ~ 1.1 million BB pairs
B Factories
To get the large data set necessary to measure CP-violation with B’s use B-factories
SLAC and KEK
Both factories have attained unprecedented high luminosities: >1034/cm/s2
BaBar has 352 fb-1 and Belle has 610fb-1 of data
Note: 1fb-1 ~ 1.1 million BB pairs

8. Asymmetric e+e- Colliders
KEKII
PEPII
KEK/SLAC are asymmetric e+e− colliders
KEK: 8 GeV (e-)/3.5 GeV (e+)
SLAC: 9 GeV (e-)/3.1 GeV (e+)
B travels a measurable distance before decay:
SLAC: bg=0.56 → bgct~260mm
KEK: bg=0.42 → bgct~193mm

9. Detectors at Asymmetric e+e- Colliders
Both detectors feature:
Charged particle tracking (silicon+drift chambers + 1.5T B-field)
Electromagnetic calorimetry (CsI) ® g and electron ID
p/K/p separation up to the kinematic limit
BABAR: dE/dx+DIRC
Belle: dE/dx+aerogel+ToF
Muon/KL identification

10. Key Analysis Techniques
Threshold kinematics: we know the initial energy of the Y(4S) system
Therefore we know the energy and magnitude of momentum of each B
Event topology
Signal
Signal
(spherical)
explain that the initial state is known
Delta E
the beam energy is better known (2-3 MeV) than the reconstructed energy (20 MeV) -> mes
Background
Background
(jet-structure)
Most analyses use an unbinned maximum likelihood fit to extract parameters of interest

11. How to Measure Time Dependent Decay Rates
We need to know the flavour of the B at a reference t=0.
Dz = Dt gbc
At t=0 we know this meson is B0
B 0
rec
B 0
(4S)
bg =0.56
l - (e-, m -)
B 0
tag
The two mesons oscillate coherently : at any given time, if one is a B0 the other is necessarily a B0
In this example, the tag-side meson decays first.
It decays semi-leptonically and the charge of the lepton gives the flavour of the tag-side meson :
l - = B l + = B 0.
Kaon tags also used.
Dt picoseconds later, the B 0 (or perhaps it is now a B 0) decays.
There is an additional slight complication as our B0B0bar pair is in a coherent state
Tagging
explain lepton tag. We also use a kaon tag from a subsequent D decay. Combined the tagging efficiency is roughly 30%

12. The Many Ways to Measure sin2b
Can use 3 different categories of B0 decays to measure b:
With this device and the rest of the BaBar detector we then collected almost 230 million BB events and analyzed the data
looking for psiKs final states plus, of course, a tag for the other B in the event.
We ended up with 7730 events and shown here is the decay time difference for B0 tags and B0bar tags
clear difference. no asymmetry in the background.
The second plot shows the raw asymmetry and the fit result is
golden mode

13. Precise Measurement of sin2b from B0®charmonium K0
Theoretically very clean:
ACP(t)=Sfsin(DmDt)-Cfcos(DmDt)
The dominant penguin amplitude (suppressed by l2Cab) has same phase as tree
SM prediction: Cf=0 Þ ACP(t)=Sfsin(DmDt)
confirmed by recent model-independent analyses [e.g. PRL (2005)] DS=0.000±0.012
Experimentally very clean:
Many accessible decay modes
with (relatively) large BFs
B→ψK0~8.5x10-4
B→ψ(2S)K0~6.2x10-4
B→χc1K0~4x10-4
B→ηcK0~1.2x10-3
CP odd
CP even

14. Precise Measurement of sin2b from B0®charmonium K0
hep-ex/
386x106 BB
sin2b=0.652±0.039±0.020
(was 0.728±0.056±0.023, Nov. 2004
PR D71, , 152x106 BB)
(cc) KS (CP odd) modes
J/y KL (CP even) mode
PRL94, (2005)
227x106 BB
sin2b=0.722±0.040±0.023

15. Brief history of sin2b from B0charmonium K0
1s CKM fit 2s
World Average sin2b[WA]=0.687±0.032
From external constraints
sin2bUTFit= 0.793±0.033 (sides) sin2bUTFit=0.734±0.024 (all)
Great success for Standard Model
Great success for all of us
theorists, experimentalists, accelerator physicists

16. Resolving the sin(2b) Ambiguity
sin(2b) is the same for b, p/2-b, p+b, 3p/2-b
Belle: Use bcud [B 0DCP(Ksp+p-) h0] decays
[A.Bondar, T.Gershon, P.Krokovny, PL B624 1 (2005)]
Theoretically clean (no penguins), Neglect DCS B0DCPh0 decay
Interference of Dalitz amplitudes sensitive to cos2b
Dalitz model fitted in D*-tagged D0 decays
f1=(16±21±12)o rules out 97% CL
[Belle. hep-ex/ ]
BABAR: B0J/yK*0(K*0Ksp0)
Extract cos2b from interference of CP-even and CP-odd
states (L=0,1,2) in time-dependent transversity analysis
cos2b<0 excluded at 86% C.L.
[BABAR, PRD 71, (2005)]
h0=p0,h,w

17. These decays suffer from potential penguin-pollution:
b®d penguin amplitude
has different weak & strong
phases with respect to tree.
BABAR: B0® J/yp0 updated measurements [hep-ex/ , submitted PRD-RC]:
Br(B0® J/yp0)=(1.94±0.22±0.17)x10-5
SJ/yp0=-0.68±0.30±0.04
CJ/yp0=-0.21±0.26±0.09
Consistent with previous Belle results:
PRL93, (2004)
SJ/yp0=-0.72±0.42±0.09
CJ/yp0=-0.01±0.29±0.03

18. CP-odd fraction extracted with transversity analysis:
D*+D*-: [PRL 95, (2005)]
VV decay: both CP-odd and CP-even components.
CP-odd fraction extracted with transversity analysis:
fodd=0.125±0.044±0.070
S+=-0.75±0.25±0.03
C+=+0.06±0.17±0.03
D(*)+D- [PRL 95, (2005)]:
SDD =-0.29±0.63±0.06
CDD =+0.11±0.35±0.06
SD*+D-=-0.54±0.35±0.07
CD*+D-=+0.09±0.25±0.06
SD*-D+=-0.29±0.33±0.07
CD*-D+=+0.17±0.24±0.04
D*+D-
D*-D+
D+D-

19. All results consistent with SM expectation of tree dominance
DSDD≡SDD-sin2b~ [Z-Z. Xing, PR D (2000)]
Still below current experimental sensitivity

20. Sin2beff in b → s Penguins
Decays dominated by gluonic penguin diagrams
Golden example: B0→fKS
No tree level contributions: theoretically clean
SM predicts: ACP(t) = sin2bsin(Dmt) NP SM
Impact of New Physics could be significant
New particles could participate in the loop → new CPV phases
Measure ACP in as many b→sqq penguins as possible!
φK0, K+ K− KS, η′ KS, KS π0, KS KS KS, ω KS, f0(980) KS
BUT there are complications:
Low branching fractions (10-5)
non-penguin processes can pollute u s d b B

21. All “sin2b” Results Compared
Will be discussed in O. Long’s talk “Rare decays and new physics studies”

22. b g a The Unitarity Triangle (0,0) (0,1) (r,h) Vub Vud Vcd Vcb *
Vtd Vtb g a b
Successfully reached the main goal of the B factory program
now let’s go for more
[21.7 ± 1.3]o

23. The CKM angle a
In an ideal world we could access a from the interference of
a b→u decay (g) with B0B0 mixing (b):
B0B0 mixing
Tree decay g
a = p - b - g
harder because of the lower BR
B0→K+p- large
Br~2x10-5
~Pure Penguin
But we do not live in the ideal world.
There are penguins...

24. sin(2a): Overcoming Penguin Pollution
Access to a from the interference of a b→u decay (g) with B0B0 mixing (b) complicated by Penguin diagram
B0B0 mixing
Tree decay
Penguin decay  g
Inc. penguin contribution
now the formalism gets slightly more complicated
the “C” term direct CP violation due to the interference of the T and P decays but our sin(2a) term gets also modified
and the question is how can we obtain a from aeff?
How can we obtain α from αeff ?
T = "tree" amplitude P = "penguin" amplitude d=strong phase
Time-dep. asymmetry :

25. How to estimate |a-aeff|: Isospin analysis
Use SU(2) to relate decay rates of different pp final states
p+p-, p+p0, p0p0
Important point is that pp can have I=0 or 2 but gluonic penguins only contribute to I=0 (by DI=1/2 rule) &EW penguins are negligible
Need to measure several B.F.s:
Da=2|aeff -a| f
A(B->p p )
=A(B->p p ) 1 2 ~
Gronau-London: PRL65, 3381 (1990)
BF(B+®p+p0)=BF(B-®p-p0) since p+p0 is pure I=2, only tree amplitude
not enough data but maybe we can limit a-aeff
if A00 is very small…
look for this decay
However, for this technique to work
p0p0 amplitudes must be very small
or very large!

26. B0→p+p- 227×106 B pairs 275×106 B pairs 467±33 signal events
Phys.Rev.Lett. 95 (2005)
Phys.Rev.Lett. 95 (2005)

27. B0→p+p- S = −0.67±0.16±0.06 C = −0.56±0.12±0.06 S = −0.30±0.17±0.03
So two comparable measurements of S = sin(2aeff) Measurements of direct CP asymmetry less compatible

28. B0→p0p0 275 x 106 BB pairs 227 x 106 BB pairs PRL 94, 181803(2005)

29. Using isospin in pp system
PRL 94, 181802 (2005)
Precision measurement of a not possible with current stats using pp

30. B → rr to the Rescue Pseudoscalar→ Vector Vector Nature is KIND!
3 possible ang. mom. states:
S wave (L=0, CP even)
P wave (L=1, CP odd)
D wave (L=2, CP even)
Nature is KIND!
B0®r+r-~100% longitudinally polarized!
Transverse component taken as 0 in analysis,
essentially all CP even
Large Branching Fraction!
Br(B0®r+r-)=(30±4±5)x10-6
Br(B0®r+r-)~6xBr(B0®p+p-)
PRL 93 (2004)
r helicity angle
signal
bkg

31. B0 → r+r- BaBar (227 x 106 BB) Belle (275 x 106 BB)
PRL 96, (2006)
PRL 95, 041805 (2005)

32. But How large is B0→r0r0 ?
Phys.Rev.Lett. 94 (2005)
In rr system the amount of neutral decays is small
Measure: B0→r0r0 events in 227 x 106 BB events
Br < 1.1 x 10-6 at 90% CL.
Isospin triangle for rr is flattened compared to pp
k=2|aeff -a|
A(B->r r ) 1 2 ~
=A(B->r r )
Penguin Pollution Defeated!

33. B±→r±r0 New result with 231 x 106 BB events
Previous BaBar/Belle HFAG average
hep−ex/
New result is better match to isospin model
Moriond QCD 2006
Smaller uncertainty on |aeff−a| compared to pp mode

34. B0 → (rp)0 Analysis B0 → (rp)0 →p+p−p0 is not a CP eigenstate
6 decays to disentangle:
Tried by BaBar and Belle for just r± phase space
Did not set limits on a
Can use a Dalitz plot analysis to get a from decays
Snyder & Quinn: Phys. Rev. D48, 2139 (1993)
r0p0
r+p-
r-p+
Convert to a square Dalitz plot
Mostly resonant decays Move signal away from edges Simplifies analysis MC
q0=r helicty angle
m0=invariant mass of charged tracks

35. B0 → (rp)0 Dalitz plot analysis
Dalitz plot analysis yields CP asymmetries and strong phases of decays
Using 213 x 106 BB events hep-ex/
1184±58 B→p+p-p0 Signal events
Blue histos are different types of backgrounds
m’ and q’ are variables for a square Daltiz plot
Analysis provides a weak
determination of a:
However, useful for
resolving ambiguities…..

36. Combined constraints on a
rr gives single best measurement
rp resolves 2-fold ambiguity from rr
World Average:
Global CKM Fit (w/o a):
Dms

37. a g b The Unitarity Triangle (0,0) (0,1) (r,h) Vub Vud Vcd Vcb *
Vtd Vtb g b
[99 ± 11]o a
being able to measure 2 angles is already a surprise but let’s go for 3
[21.7 ± 1.3]o

38. Summary and Outlook
BABAR & Belle measure sin2b in ccK0 modes to 5% precision
sin2bcharmonium=0.687±0.032
Comparison with sin2beff in b s penguin modes could reveal new physics effects
BUT need to carefully evaluate SM contributions
sin2beff measurements are statistically limited, can add new modes, beat 1/√L scaling
Extraction of a depends crucially on penguin contributions
B→r0r0/r+r0
Theory Û experimental feedback is helpful
Expected precision Vs time
reference +1s
sin2b in penguins
reference (current r0r0 Br)
reference -1s
from rr
Luminosity (ab-1)

39. Putting it all together
As of today the complex phase in the CKM matrix correctly
describes CP Violation in the B meson system! h
this is a confusing plot because it combines 30 years worth of information.
Consistent
But not enough r
More to come from BABAR/Belle, CDF/D0, and LHCb
Will they find CKM violation????

40. Extra Slides

41. Adding Theoretical Uncertainties
size of possible discrepancies Δsin2β have been evaluated for some modes:
estimates of deviations based on QCD-motivated specific models; some have difficulties to reconcile with measured B.R.
Beneke at al, NPB675
Ciuchini at al, hep-ph/
Cheng et al, hep-ph/
Buras et al, NPB697
Charles et al, hep-ph/
model independent upper limits based on SU(3) flavor symmetry and measured b d,sqq B.R.
[Grossman et al, PRD58; Grossman et al, PRD68; Gronau, Rosner, PLB564; Gronau et al, PLB579; Gronau et al, PLB596; Chiang et al, PRD70]
2xΔsin2β
‘naive’ upper limit based on final state quark content,
CKM (λ2) and loop/tree (= ) suppression factors
[Kirkby,Nir, PLB592; Hoecker, hep-ex/ ]

42. There is a problem B0  p+p- B0  K+p- B0p+p- 157  19q pp Kp
B0  p+p-
B0  K+p-
B0p+p-
157  19
(4.7  0.6  0.2) x 10-6
B0K+p-
589  30
(17.90.9 0.7) x 10-6
Penguin/Tree ~ 30%