1. γ/φ3 determination with B D0(*)K(*) Dalitz analysis
ВД в эксперименте по измерению масс
25 мая 2002
φ3/γ with Dalitz analysis
γ/φ3 determination with B D0(*)K(*) Dalitz analysis
A. Poluektov
Budker Institute of Nuclear Physics
Novosibirsk, Russia
November 27, 2007
А. Полуэктов

2. φ3/γ with Dalitz analysis
B+ D0K+ decay
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:
November 27, 2007

3. Dalitz analysis method
φ3/γ with Dalitz analysis
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
November 27, 2007

4. φ3/γ with Dalitz analysis
D0  Ksπ+π– decay
Statistical sensitivity of the method depends on the properties of the 3-body decay involved.
Close relation to charm physics
Large variations of D0 decay strong phase are essential
Currently, use the model-dependent fit to
experimental data from flavor-tagged
D*± D0π± sample.
Model is described by the set of
two-body amplitudes
+ flat non-resonant term.
As a result, model uncertainty in the
γ/φ3 measurement.
November 27, 2007

5. D0  Ksπ+π– amplitude fit (Belle)
φ3/γ with Dalitz analysis
D0  Ksπ+π– amplitude fit (Belle)
Intermediate state
Amplitude
Phase, °
Fit fraction
KS σ1
KS ρ(770)
KS ω
KS f0(980)
KS σ2
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%
M (GeV 2 )
Ksπ – 2
σ1(M=520±15 MeV, Γ=466±31 MeV)
σ2(M=1059±6 MeV, Γ=59±10 MeV)
November 27, 2007

6. Dalitz model: ππ S-wave K-matrix (BaBar)
φ3/γ with Dalitz analysis
Dalitz model: ππ S-wave K-matrix (BaBar)
Goal: keep unitarity of the amplitude in the presence of overlapping resonances. Avoid σ states.
[Anisovich & Sarantev, Eur. Phys. Jour. A16, 229 (2003)]
pp S-wave
CA K*p
DCS
K*p
pp P,D-waves
m2p+p-(GeV2/c4)
c2/dof 1.2 dominated by Kp P-wave
November 27, 2007

7. Signal parameterization
Fit experimental Dalitz plot of D0 distribution from B±DK± decays
with the probability density:
No CPV or mixing effects in D decays are included.
(no problem to include them if needed)
If no CPV in D decay
Cartesian fit parameters:
Polar coordinates are bad:
rB positive-definite (biased, non-Gaussian), φ3 precision is inversely proportional to rB
November 27, 2007

8. Event selection (Belle)
φ3/γ with Dalitz analysis
Event selection (Belle)
Belle result (357 fb-1) [hep-ex/ , PRD 73, (2006)]
BD*K
BDK*
BDK
331±17 events
81±8 events
54±8 events B- B+ B- B+ B- B+
November 27, 2007

9. (x±,y±) fit results (Belle)
φ3/γ with Dalitz analysis
(x±,y±) fit results (Belle)
Fit parameters are x= rB cos(φ3+δ) and y= rB sin(φ3+δ)
Unbinned maximum likelihood fit with event-by-event background treatment
(ΔE-Mbc included into likelihood)
BD*K
BDK*
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
November 27, 2007

10. B– D(*)0K–, D0K*– signal (BaBar)
φ3/γ with Dalitz analysis
B– D(*)0K–, D0K*– signal (BaBar)
[F. Martinez-Vidal, talk at CKM2006; hep-ex/ , hep-ex/ ]
D*0K, D*0 D0p0
97±13
Signal Dp BB qq
D*0K, D*0D0g
93±12
D0K
398±23
347x106 BB
D0K*
42±8
B-DK-
B+  DK+
227x106 BB
November 27, 2007

11. (x±,y±) fit results (BaBar)
D0K
D0K*
D*0K B+ B- B+ B+ B- B-
Dalitz model systematic error
November 27, 2007

12. φ3/γ with Dalitz analysis
Statistical issues
Measure Cartesian parameters x= rB cos(φ3+δ) and y= rB sin(φ3+δ)
4 parameters z=(x , y)  3 parameters μ=(φ3, rB, δ) for one mode
12 parameters z=(x , y)DK, D*K, DK*  7 parameters μ=(φ3, (rB, δ)DK, D*K, DK*) for 3 modes
Use frequentist treatment to obtain μ CL for measurement result z0.
Use toy MC to obtain p(z|μ)
Not Gaussian (tails), systematic bias
Number of “true” parameters < number of fit parameters.
Classical Neyman ordering is not correct, especially far from physical region rB+=rB [B. Yabsley, hep-ex/ ]
Use Feldman-Cousins:
November 27, 2007

13. φ3/γ with Dalitz analysis
Model uncertainty
Variation of fit model give an estimate of model uncertainty: ~10°
Fit model
(Δr)max
(Δφ3)max
(Δδ)max
Formfactors = 1
0.01
3.1
3.3
Γ(q2)=Const
0.02
4.7
9.0
Reduced num. of resonances
0.05
8.5
22.9
No σ scalar
2.6
4.3
CLEO set of resonances
5.7
8.7
At the statistics of >1 ab-1, this uncertainty starts to affect the precision.
Use charm data.
[See next talk by A. Bondar.]
Validate the model
Model-independent measurement
November 27, 2007

14. φ3/γ with Dalitz analysis
φ3 constraints
BDK only:
φ3= °(stat)
+19
BDK , BD*K , BDK* combined:
φ3=53°+15 3° (syst)9° (model)
rDK = 0.012(syst)0.049(model)
rD*K= 0.013(syst)0.049(model)
rDK*= 0.041(syst)0.084(model)
-18
-0.050
-0.099
-0.155 2s 1s
BDK and BD*K combined:
γ=92°±41°±11°(syst)±12°(model)
rDK<0.142 (<0.198)
0.016<rD*K <0.206 (<0.282)
November 27, 2007

15. BaBar and Belle: HFAG comparison
φ3/γ with Dalitz analysis
BaBar and Belle: HFAG comparison
BaBar has better precision on (x±,y±)
Belle has better separation between B+ and B– regions  better φ3 precision.
As statistics increases (σ(rB)<< rB) distributions become more Gaussian but hard to extrapolate the sensitivity since rB is unknown.
November 27, 2007

16. Other possibilities: D0π+π–π0 (BaBar)
φ3/γ with Dalitz analysis
Other possibilities: D0π+π–π0 (BaBar)
[BaBar collaboration, hep-ex/ ]
Modified likelihood to account for Br difference of B+ and B–:
No significant constraint on γ yet. D KsK+K–: more promising?
November 27, 2007

17. Other possibilities: B0D0K*0 (BaBar)
φ3/γ with Dalitz analysis
Other possibilities: B0D0K*0 (BaBar)
[V. Sordini, talk at CKM2006; hep-ph/ ]
Both amplitudes are color-suppressed, rB larger:
Self-tagging decay: K*0K+π–
Estimated signal yield with 350 fb-1:
45 events.
With that low statistics, toy MC shows significant bias in (x,y).
November 27, 2007

18. φ3/γ with Dalitz analysis
Summary
Dalitz analysis of Ksπ+π- final state allowed to obtain first constraints on γ/φ3, but the significance is still low.
When γ/φ3 will actually be measured, depends not only on statistics, but also on rB value. If rB~0.1, the evidence for CPV can be obtained in the nearest time.
So far, only B  D(*)K, D  Ksπ+π–, provided significant constraint. However, many other possibilities exist:
Other B meson decays: (B0D0K*0, larger rB~0.4)
Other 3-body D decays: D  KsK+K–, D  π0π+π–, D  K–π+π0.
4-body D decays: DK+K–π+π– [Rademacker, Wilkinson, hep-ph/ ]
In all cases, the input from charm data is essential. For precision γ/φ3 measurement, charm factory is necessary.
November 27, 2007