1. f3 measurements by Belle
Pavel Krokovny
KEK
Introduction
Apparatus
Method
Results
Summary

2. Unitarity Triangle Using unitarity requirement:
φ1 is measured with a high accuracy (~1º) at B-factories.
φ3 is the most challenging angle to measure.
Measurement of all the angles needed to test SM.

3. Constraints of the Unitarity Triangle
World average as of summer 2005
from GLW, ADS, Dalitz and sin(2φ1+φ3):
γ/φ3=70 -14°
+12

4. KEKB and Belle KEKB Collider L= 1.65 x 1034 cm–2s–1 (world record)
3.5 GeV e+ & 8 GeV e– beams
3 km circumference, 11 mrad crossing angle
L= 1.65 x 1034 cm–2s–1 (world record)
L dt = 630 Υ(4S)+off(~10%)

5. B+ D0K+ decay B– D0K–: B– D0K– :
Need to use the decay where Vub contribution
interferes with another weak vertex.
B– D0K–: B– D0K– :
If D0 and D0 decay into the same final state,
Relative phase: (B– DK–), (B+ DK+)
includes weak (γ/φ3) and strong (δ) phase.
Amplitude ratio:

6. GLW method  A1,2 of different signs
M. Gronau and D. London, PLB 253, 483 (1991);
M. Gronau and D. Wyler, PLB 265, 172 (1991)
СР eigenstate of D-meson is used (DCP).
CP-even : D1 K+K–, π+ π –
CP-odd : D2  KS π0, KS ω, KS φ, KSη…
СР-asymmetry:
for D1
 A1,2 of different signs
for D2
Additional constraint:
4 equations (3 independent: ), 3 unknowns

7. GLW method B D1K B D2K B D*1K B D*2K Belle results (253 fb-1)
Phys. Rev. D 73, (R) (2006)
B± DK±
B D1K
1.13 ±0.16±0.05
0.06±0.14±0.05
B D2K
1.17±0.14±0.14
-0.12±0.14±0.05
B+ D1K+
B- D1K-
B± D*K±
B D*1K
1.41±0.25±0.06
-0.20±0.22±0.04
B D*2K
1.15±0.31±0.12
0.13±0.30±0.08
B+ D2K+
B- D2K-
GLW analyses alone do not constrain γ/φ3 significantly yet, but can be combined with other measurements and provide information on rB

8. ADS method  B–D0K– - color allowed B–D0K– - color suppressed
D. Atwood, I. Dunietz and A. Soni, PRL 78, 3357 (1997);
PRD 63, (2001)
Enhancement of СР-violation due to use of Cabibbo-suppressed D decays
B–D0K– - color allowed
D0K+π– - doubly Cabibbo-suppressed
B–D0K– - color suppressed
D0K+π– - Cabibbo-allowed 
Interfering amplitudes
are comparable

9. ADS method rB<0.18 (90% CL) Belle results (357 fb-1) hep-ex/0508048
Suppressed channel not visible yet:
Using rD=0.060±0.003,
for maximum mixing (φ3=0, δ=180°):
rB<0.18 (90% CL)

10. Dalitz analysis method
A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, (2003)
A. Bondar, Proc. of Belle Dalitz analysis meeting, Sep 2002.
Using 3-body final state, identical for D0 and D0: Ksπ+π-.
Dalitz distribution density:
(assuming СР-conservation in D0 decays)
If is known, parameters are obtained from the fit to Dalitz distributions of D Ksπ+π– from B±DK± decays

11. Dalitz analysis: D0  Ksπ+π–
Statistical sensitivity of the method depends on the properties
of the 3-body decay involved.
(For |M|2=Const there is no sensitivity to the phase θ)
Large variations of D0 decay strong phase are essential
Use the model-dependent fit to
experimental data from flavor-tagged
D* D0π sample.
Model is described by the set of
two-body amplitudes
+ nonresonant term.
As a result, model uncertainty in the
γ/φ3 measurement.

12. D0  Ksπ+π– Decay Model D*->D0π->[KSπ+π-]π Doubly Cabibbo
M (GeV 2 )
Ksπ – 2
Doubly Cabibbo
Suppressed K*
ρ-ω interference

13. Dalitz analysis: sensitivity to f3

14. Dalitz analysis
Phys. Rev. D 73, (2006)
Fit parameters are x= r cos(φ3+δ) and y= r sin(φ3+δ)
(better behaved statistically than )
are obtained from frequentist statistical
treatment based on PDFs from toy MC simulation.
BDK
BD*K
BDK*
x–=
y–=
x+= –
y+= –
+0.072
x-= –
y-= –
x+=
y+=
x–= –
y–= –
x+= –
y+= –
+0.167
+0.249
+0.093
+0.172
+0.440
+0.069
+0.120
+0.177
+0.090
+0.137
+0.164

15. Dalitz analysis Belle result (357 fb-1) 331±17 events 81±8 events
Phys. Rev. D 73, (2006)
BD*K
BDK*
BDK
331±17 events
81±8 events
54±8 events B- B+ B- B+ B- B+

16. Dalitz analysis φ3=66-20 °(stat) φ3=86-93°(stat) φ3=11-57°(stat) +19
Phys. Rev. D 73, (2006)
BDK
BDK*
BD*K
φ3=66-20 °(stat)
φ3=86-93°(stat)
φ3=11-57°(stat)
+19
+37
+23
Combined for 3 modes: φ3=53°+15 3° (syst)9° (model)
8°<φ3<111° (2σ interval)
rDK = 0.012(syst)0.049(model)
CPV significance: 74% rD*K= 0.013(syst)0.049(model)
rDK*= 0.041(syst)0.084(model)
-18
-0.050
-0.099
-0.155

17. sin(2φ1+φ3) from B0 D*π decay
Use B flavor tag, measure time-dependent decay rates:
Btag  B0
B  D-+
Btag  B0
where
CP violation

18. sin(2φ1+φ3) - full reconstruction with - partial reconstruction
Belle result (357 fb-1)
Phys. Rev. D 73, (2006)
- full reconstruction
with partial reconstruction
(reconstruct only pions)
D*π partial rec
D*π full rec

19. sin(2φ1+φ3) S +(D*π)=0.049±0.020±0.011 S –(D*π)=0.031±0.019±0.011
Phys. Rev. D 73, (2006)
S +(D*π)=0.049±0.020±0.011
S –(D*π)=0.031±0.019±0.011
S +(Dπ)=0.031±0.030±0.012
S –(Dπ)=0.068±0.029±0.012
Full-rec +
partial-rec
Full-rec
CP violation significance: 2.5σ
If R~0.02:
|sin(2φ1+φ3)|>0.46 (0.13)
|sin(2φ1+φ3)|>0.48 (0.07)
at 68% (95%) CL

20. Summary
The angle φ3/g remains the most difficult angle of the Unitarity
Triangle to measure, although there is a tremendous progress
from B-factories.
O(20º) Precision in direct measurements of φ3 is achieved using new
GGSZ method (B->D0[KSππ]K)
Other methods do not constrain γ/φ3 significantly yet, but can be used in combined fit and provide information on rB
The precision is statistically limited  good perspectives for
improving the result with larger data set

21. Backup

22. B± DK±, DKSπ+π– Dalitz plots
K*(892) bands
D0 from B- D0K-
(π+ and π - interchanged)
D0 from B+ D0K+

23. Control sample
Same fit procedure was applied for the control sample: B  D(*) p
The results are consistent with r=0.01 for D(*)0 and with 0 for D*- p+

24. Systematic errors
Background shape: baseline – BB MC + continuum data sample, variations – continuum only, MBC sidebands.
Efficiency over Dalitz plot: main fit – MC, variation – use high momentum D*[D p]
DE – MBC shape: vary shape parameters by 1 s
DE – MBC for BB and qq: use different shape for qq and BB

25. D0  Ksπ+π– decay model Intermediate state Amplitude Phase, °
Fit fraction
KS σ (M=520±15 MeV, Γ=466±31 MeV)
KS ρ(770)
KS ω
KS f0(980)
KS σ (M=1059±6 MeV, Γ=59±10 MeV)
KS f2(1270)
KS f0(1370)
KS ρ(1450)
K* (892)+π–
K*(892)–π+
K*(1410)+π–
K*(1410)–π+
K*0(1430)+π–
K*0(1430)–π+
K*2(1430)+π–
K*2(1430)–π+
K*(1680)+π–
K*(1680)–π+
Nonresonant
1.43±0.07
1 (fixed)
0.0314±0.0008
0.365±0.006
0.23±0.02
1.32±0.04
1.44±0.10
0.66±0.07
1.644±0.010
0.144±0.004
0.61±0.06
0.45±0.04
2.15±0.04
0.47±0.04
0.88±0.03
0.25±0.02
1.39±0.27
1.2±0.2
3.0±0.3
212±4
0 (fixed)
110.8±1.6
201.9±1.9
237±11
348±2
82±6
9±8
132.1±0.5
320.3±1.5
113±4
254±5
353.6±1.2
88±4
318.7±1.9
265±6
103±12
118±11
164±5
9.8%
21.6%
0.4%
4.9%
0.6%
1.5%
1.1%
61.2%
0.55%
0.05%
0.14%
7.4%
0.43%
2.2%
0.09%
0.36%
0.11%
9.7%

26. Model-independent approach
D0 decay amplitude:
D0-D0 interference from B+ D0K+:
is measured directly,
is model-dependent
If CP-tagged D0 are available (e.g. from ψ’’ D0 D0 , where tag-side
D0 decays into CP-eigenstate) phase difference can be measured:

27. Model-independent Approach
A.Giri, Yu. Grossman,
A. Soffer, J. Zupan, PRD 68, (2003)
A.Bondar, A.Poluektov hep-ph/
50 ab-1 at SuperB factory
should be enough for
model-independent γ/φ3
Measurement with
accuracy below 2°
~10 fb-1 at ψ(3770) needed to
accompany this measurement.

28. Dalitz analysis: sensitivity to f3

29. Constraints to rB