1. Measurement of f3 using Dalitz plot analysis of B+ D(*)K(*)+ 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 L dt = 655 fb–1
3.5 GeV e+ & 8 GeV e– beams
3 km circumference,
11 mrad crossing angle
L= 1.65 x 1034 cm–2s–1
L dt = 655 fb–1

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. 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

7. 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.

8. 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%

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

10. Dalitz analysis: sensitivity to f3

11. 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+

12. 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

13. 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 p+ and with 0 for D*- p+

14. 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

15. 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

16. 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:

17. Model-independent Approach
A.Bondar, A.Poluektov hep-ph/
A.Giri, Yu. Grossman,
A. Soffer, J. Zupan, PRD 68, (2003)
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.

18. Summary
The angle φ3/g remains the most difficult angle of the Unitarity Triangle to measure, although there is a big progress from B-factories.
O(20º) Precision in direct measurements of φ3 is achieved using Dalitz analysis method (B->D0[KSππ]K)
The precision is statistically limited  good perspectives for
improving the result with larger data set

19. Backup

20. Constraints to rB