φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
Measurement of φ3 with
B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
BINP, Novosibirsk, Russia
Outline:
•
•
•
•
•
•
•
Introduction to the technique
D0 model determination
Signal selection
Estimation of statistical errors with toy MC
Estimation of systematic errors
Combined B+→ D0K+ and B+→ D*0K+ fit
Conclusion
March 21-28, 2004
Recontres de Moriond, EW session
1
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
CKM matrix & unitarity triangle
λ
Vus Vub   1 − λ2 / 2


1 − λ2 / 2
−λ
Vcs Vcb  ≈ 
Vts Vtb   Aλ3 (1 − ρ − iη ) − Aλ2
Vud

Vij =  Vcd
V
 td
B0 ππ
B0 ρπ
(ρ,η)
*
ub
*
cb
V V ud
V V cd
B0 D(*)π
B+ DK
March 21-28, 2004
(α)
(γ)
V t*bV t d
V c*bV c d
(β)
Recontres de Moriond, EW session
Aλ3 ( ρ − iη ) 

2
Aλ


1

= 0.2235I0.0033
A = 0.81I0.08
|-i| = 0.36I0.09
|1- -i | = 0.79I0.19
B0 J/ψ
ψKs
B0 φKs
B0 D(*)D(*)
2
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D0K+ decay
*
M 1 ~ Vcb
Vus ~ A λ3
M 2 ~Vub* Vcs ~Aλ 3(ρ + iη ) ~ e iφ3
If both D0 and D0 decay into the same final state, B+→ D0K+ and B+→ D0K+
~
amplitudes interfere. Mixed state is produced: D
0
=
D
0
+ re
iθ
D
0
Phase θ is a sum of strong and weak phases: θ = φ3 + δ
Use 3-body final state, identical for D0 and D0: Ksπ+π-.
Dalitz plot density: d σ ( m
| M ( m K2
sπ
+
, m K2
sπ
−
2
K sπ +
) | 2 =| f
,m2
) ∝| M
K sπ −
( m K2 π + , m K2 π −
s
s
|2 dm 2
)+
dm 2 −
+
K sπ
K sπ
re iθ f ( m K2 π − , m K2 π +
s
s
) |2
(assuming CP conservation in D0 decay)
March 21-28, 2004
Recontres de Moriond, EW session
3
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D0K+ decay
~
D0 = D 0 + reiθ D0
If D0 decay model is known, parameters r and θ can be
obtained by Dalitz plot analysis.
For B-→ D0K- weak phase of color-suppressed amplitude changes sign:
− iϕ 3
*
3
M 2 ∝ VubVcs ∝ A λ ( ρ − iη ) ∝ e
Strong phase is not changed. Therefore, θ − = δ − ϕ 3
(r, φ3, δ) can be obtained with simultaneous fit of B+ and B- data.
Use unbinned likelihood technique to fit Dalitz plots.
r≈
*
Vub
Vcs
*
Vcb
Vus
×
| a2 |
= 0.09 / 0.22 × 0.35 ≈ 1 / 8
| fa1 + a2 |
Factor |a2|/|fa1+a2|=0.35 related to color suppression can be estimated from
the ratio of B0→ D0K0 and B+→ D0K+ branching fractions (measured by Belle)
References:
• A. Giri, Yu. Grossman, A. Soffer, J. Zupan, hep-ph/0303187
• Belle collaboration, hep-ex/0308043 (Contributed to LP2003)
March 21-28, 2004
Recontres de Moriond, EW session
4
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
Effect of CPV and φ3 (MC)
B→ D0K decays)
s
2
MK π – (GeV 2 )
MC generated statistics (50000
M K2 π + (GeV 2 )
s
Most sensitive regions of the Dalitz plot (r = 0.125, δ=0, φ3=70°)
March 21-28, 2004
Recontres de Moriond, EW session
5
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
ER
)
Belle detector
TSUKUBA Area (Belle)
RF
WIGGLER
OHO Area
RF
(L
RF
RF
WIGGLER
Lo
fo w E
rP n
os erg
itr y R
on
in
g
NIKKO Area
)
ER
(H
KEKB Collider
g
n
Ri
gy
er
En tron
gh c
Hi r Ele
fo
HER
LER
Interaction Region
LE
c
na
Li
RF
RF FUJI Area
-
Positron
/e
Electron
+
R
e
HE
R
(TRISTAN Accumulation Ring)
3.5 GeV e+ & 8 GeV e– asymmetric Collider
3 km circumference, 11 mrad crossing angle
L= 1.2 x 1034 cm–2s–1 (world record)
∫ L dt = 219 fb–1 @ (4S)+off(~10%)
(140 fb-1: 1.52 x 108 BB pairs)
March 21-28, 2004
~350 scientists, 55 institutions
Recontres de Moriond, EW session
6
A. Poluektov
φ3 with B→D(*)0 K Dalitz analysis at Belle
Analysis overview
• Determination of D0 → Ksπ+π– decay model
• Use flavor tagged sample of D0‘s from D*–→ D0π–, D0 → Ksπ+π–
produced in continuum
• Selection of B+→ D0K+ events
• Selection of B+→ D*0K+, D*0→ D0π0 events
• Unbinned maximum likelihood fit of the D0 Dalitz plots with
free parameters (r, φ3, δ)
• Fits to control samples without opposite flavor contributions:
B+→ D0π+, B+→ D*0π+, B0→ D*+π• Evaluation of statistical errors using large number of toy MC
pseudo-experiments
• Evaluation of systematic and model errors
• Combined φ3 measurement
March 21-28, 2004
Recontres de Moriond, EW session
7
A. Poluektov
φ3 with B→D(*)0 K Dalitz analysis at Belle
D*–→ D0π–, D0 → Ksπ+π– selection
MD (GeV)
∆M (GeV)
140 fb-1 statistics
101800 events
3.1% background
• 144.6<MD*-MD<146.4 MeV
• 1.856<MD<1.874 GeV
(shape from ∆M sidebands)
March 21-28, 2004
• PD*>2.7 GeV
Recontres de Moriond, EW session
8
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
D0 → Ksπ+π– decay model
Phase, °
Fit fraction
σ1 Ks
1.66±0.11
218.0±3.8
11%
ρ(770) KS
1
0
21%
ω Ks
(3.30±1.13)·10-2
114.3±2.3
0.4%
f0(980) Ks
0.405±0.008
212.9±2.3
4.8%
σ2 Ks
0.31±0.05
236±11
0.9%
f2(1270) Ks
1.36±0.06
352±3
1.5%
f0(1370) Ks
0.82±0.10
308±8
0.9%
K* (892)-π+
1.656±0.012
137.6±0.6
60%
K*(892)+π -
0.149±0.007
325.2±2.2
0.5%
K*0(1430) -π+
1.96±0.04
357.3±1.5
5.8%
K*0(1430)+π -
0.30±0.05
128±8
0.1%
K*2(1430) -π+
1.32±0.03
313.5±1.8
2.8%
K*2(1430) +π -
0.21±0.03
281.5±9
0.07%
K*(1680) +π -
2.56±0.22
70±6
0.4%
K*(1680) -π +
1.02±0.22
102±11
0.07%
Non resonant
6.1±0.3
146±3
24%
March 21-28, 2004
Sum of two-body amplitudes:
f = aK * e
iϕ
K*
iϕ ρ
[ FD FK * M J BW (mK2 π − )] +
s
J
2
π +π −
aρ e [ FD Fρ M BW (m
)] + ...
2
Amplitude
MKsπ – (GeV 2 )
Our fit
Resonance
Recontres de Moriond, EW session
M K2 π + (GeV2 )
s
9
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
s
2
MK π – (GeV 2 )
D*–→ D0π–, D0 → Ksπ+π– Dalitz plot
Doubly Cabibbo
suppressed K*
M K2 π + (GeV 2 )
s
M K2 π − (GeV 2 )
M K2 π − (GeV 2 )
s
s
ρ-ω interference
M K2 π + (GeV 2 )
s
March 21-28, 2004
M π2 +π − (GeV 2 )
Recontres de Moriond, EW session
M π2+π − (GeV 2 )
10
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B candidate selection
Pairs of B mesons are produced in Υ(4S) decays (near BB mass threshold)
⇒ E B = Ecm / 2 , low p in CM frame
CM energy difference:
∆E = ∑ Ei − ( Ecm / 2)
B meson beam-constrained mass Mbc:
M bc = ( Ecm / 2) 2 − (∑ pi ) 2
Continuum (e+e-→uu,dd,ss) background suppression:
• Angle between B candidate thrust axis and
thrust axis of the rest of the event
• Fisher discriminant based on “virtual calorimeter”
March 21-28, 2004
Recontres de Moriond, EW session
11
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D0K+ signal with 140 fb
1
D0K
D0π
misID
∆E (GeV)
Mbc (GeV)
12% reconstruction efficiency
146 events
112±12 signal
36±3 background (25%)
MD (GeV)
•|∆E|<22 MeV
•5.272<Mbc<5.288 GeV
•|MD-1.86 GeV|<11 MeV
•|cosΘthr|<0.8
•Fisher discriminant F>-0.7
•PID(K/π)>0.7
March 21-28, 2004
Recontres de Moriond, EW session
12
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D*0K+ signal with 140 fb-
1
D0K
D0π
misID
∆E (GeV)
Mbc (GeV)
MD (GeV)
MD* -MD (GeV)
6.2% reconstruction efficiency
•|∆E|<22 MeV
39 events
•5.272<Mbc<5.288 GeV
•|MD-1.86 GeV|<11 MeV
33.6±6.2 signal
4.6±1.1 background (12%)
•140<MD*-MD<145 MeV
•|cosΘthr|<0.8
•Fisher discriminant
F>-0.7
•PID(K/π)>0.7
March 21-28, 2004
Recontres de Moriond, EW session
13
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D0K+, D0→Ksπ+π- Dalitz plot
73 events
2
2
73 events
MKsπ + (GeV 2 )
MKsπ – (GeV 2 )
K*(892) bands
M K2 π + (GeV 2 )
M K2 π − (GeV 2 )
s
D0 from B+→ D0K+
March 21-28, 2004
s
D0 from B-→ D0K(π+ and π - interchanged)
Recontres de Moriond, EW session
14
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D*0K+, D0→Ksπ+π- Dalitz plot
19 events
2
2
20 events
MKsπ + (GeV 2 )
MKsπ – (GeV 2 )
K*(892) bands
M K2 π + (GeV 2 )
M K2 π − (GeV 2 )
s
D0 from B+→ D*0K+
March 21-28, 2004
s
D0 from B-→ D*0K(π+ and π - interchanged)
Recontres de Moriond, EW session
15
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
Likelihood function
Minimizing logarithmic likelihood:
N
− 2 logL = −2∑ log f (m+2,i , m−2,i ) + 2 log∫ f (m+2 , m−2 ) dm+2 dm−2
i=1
m+2,i , m−2,i
are Dalitz plot points
f (m+2 , m−2 ) =| M (m+2 , m−2 ) |2 ×ε (m+2 , m−2 ) ⊕ σ p (mπ2 +π − ) + b(m+2 , m−2 )
Matrix element
M ( m +2 , m −2 ) = f ( m +2 , m −2 ) + re iθ f ( m −2 , m +2 )
Efficiency shape
ε (m+2 , m−2 )
Momentum resolution
σ p (mπ2 +π − ) - from phase-space MC
Background
March 21-28, 2004
- from phase-space MC
b(m+2 , m−2 )
Recontres de Moriond, EW session
16
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D0K+
B+→ D*0K+
Im(reiθ)
Im(reiθ)
B+→ D(*)0K+ fit results
Re(reiθ)
Re(reiθ)
r+=0.40±0.15, θ+=256±19°
r- =0.21±0.15, θ- = 71±37°
March 21-28, 2004
r+=0.29±0.19, θ+=353±38°
r- =0.38±0.19, θ- =249±32°
Recontres de Moriond, EW session
17
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
Test sample fits
Re(reiθ)
r+=0.065±0.029, θ+=232±24°
r- =0.069±0.027, θ- =228±23°
Bias in
B0→ D*+π- (517 events)
Im(reiθ)
B+→ D*0π+ (351 events)
Im(reiθ)
Im(reiθ)
B+→ D0π+ (1850 events)
Re(reiθ)
Re(reiθ)
r+=0.041±0.069, θ+=164±100°
r- =0.057±0.054, θ- = 340±65°
r+=0.005±0.058, θ+=324±686°
r- =0.052±0.053, θ- = 201±57°
B+→ D0π+ sample (background, fluctuation?),
however, no CP violation observed
March 21-28, 2004
Recontres de Moriond, EW session
18
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D0K+ constraints
20% 97%
+
97%
74%
20%
+
+
+
(φ3, δ) and
(φ3+π, δ+π)
ambiguity
74%
r=0.28+0.09
-0.11 , φ3=86±20°, δ=168±20° — <68% CL interval from MC-based PDF
0.07<r<0.45, 37°<φ3<135°, 119°<δ<217° — <95% CL interval.
CP violation significance: 94% (φ3≠0).
r > 0 with 97% CL.
March 21-28, 2004
Recontres de Moriond, EW session
19
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D*0K+ constraints
20%
97%
74%
+
74%
20%
+
+
+
(φ3, δ) and
(φ3+π, δ+π)
ambiguity
r<0.25, φ3=51±47°, δ=302±47° — <68% CL interval from MC-based PDF
r<0.44, -31°<φ3<133°, 220°<δ<384° — <95% CL interval.
CP violation significance: 38% (φ3≠0).
March 21-28, 2004
Recontres de Moriond, EW session
20
A. Poluektov
φ3 with B→D(*)0 K Dalitz analysis at Belle
Estimation of systematic errors
B+→ D0K+ B+→ D*0K+
Background shape
Background fraction
Efficiency shape
Momentum resolution
B+→ D0π+ test sample bias:
Total
March 21-28, 2004
4.6°
0.1°
3.5°
2.5°
11°
13°
1.3°
0.6°
0.8°
2.5°
11°
11°
Recontres de Moriond, EW session
21
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
Model uncertainty
D0
decay amplitude f = | f
(m+2 , m−2 ) |
| f (m+2 , m−2 ) |2
directly measured
φ (m+2 , m−2 )
model-dependent
e
iφ ( m+2 ,m−2 )
Fit model
K*, ρ, ω, f0 + non-resonant
Meson formfactors Fr=FD=1
Constant BW width Γ(q2)=Const
Non-resonant amplitude aNR=0
No σ(500)
(∆φ3)max,°
Total
11
March 21-28, 2004
9.9
3.1
4.7
0.4
0.7
Recontres de Moriond, EW session
22
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D0K+ and B+→ D*0K+ combined
Multiply φ3 PDF’s for
Combined fit
B+→ D0K+
B+→ D0K+ and B+→ D*0K+
samples
(r and δ left independent)
B+→ D*0K+
Stat. confidence intervals:
φ3=81±19° (68% CL)
φ3=81±46° (95% CL)
68%
March 21-28, 2004
95%
Combined result:
φ3=81 ±19°±13°(syst)±11°(model)
Recontres de Moriond, EW session
23
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
Constraints on unitarity triangle
η
D0K Dalitz
B→J/ψKs
<95% CL
regions
B→ππ
Indirect
measurements
ρ
March 21-28, 2004
Recontres de Moriond, EW session
24
A. Poluektov
φ3 with B→D(*)0 K Dalitz analysis at Belle
Conclusion
• B+→ D0K+ and B+→ D*0K+, D0 → Ksπ+π- samples analyzed with 140 fb-1
φ3=81°±19°±13°(syst)±11°(model) for combined fit
95% CL interval from combined fit: 35°<φ3<127°
• Direct CP violation effect significance is 94%.
• A new promising method to measure φ3 using Dalitz plot analysis of
D0 from B→D(*)0K decay is applied to the data collected by Belle.
• Advantages:
• Higher statistical power than methods based on branching
fractions
• No absolute branching fractions involved ⇒ lower detector
systematics
• Model-independent approach exists based on the
cτ-factory data.
• The precision can be increased by adding other suitable modes
(neutral B decays, other three- and four-body D0 decays)
March 21-28, 2004
Recontres de Moriond, EW session
25
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
D0 → Ksπ+π- fit result (discussion)
• Needed to introduce two scalars in π+π- channel:
• σ1 with mass M=538±9 MeV, BW width Γ=452±15 MeV
• σ2 with mass M=1048±8 MeV, BW width Γ=109±11 MeV
• Large non-resonant amplitude observed.
• Correlated with σ1 amplitude:
• aNR=4.66±0.15 for aσ =0 (compared to 6.1±0.3)
• aσ =0.78±0.05 for aNR=0 (compared to 1.65±0.10)
• Probably indicates poor description of σ1. Consider as a
systematic effect.
• Use symmetric set of resonances, i.e. take doubly Cabibbo
suppressed partners for all flavor-specific modes (K*(892)+π -,
K*0(1430)+π-, K*0(1430)+π-, K*(1680) +π-). Otherwise systematic
bias of opposite flavor admixture r.
March 21-28, 2004
Recontres de Moriond, EW session
26
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D0K+ fit result
Error estimation from the fit likelihood
CL vs. (δ, φ3)
CL vs. (r, φ3)
-2 log L vs. φ3
r=0.31±0.11, φ3=86±17°, δ=168±17° or (φ3+π, δ+ π)
March 21-28, 2004
Recontres de Moriond, EW session
27
φ3 with B→D(*)0 K Dalitz analysis at Belle
A. Poluektov
B+→ D*0K+ fit result
Error estimation from the fit likelihood
CL vs. (δ, φ3)
CL vs. (r, φ3)
-2 log L vs. φ3
r=0.34±0.14, φ3=51±25°, δ=302±25° or (φ3+π, δ+ π)
March 21-28, 2004
Recontres de Moriond, EW session
28
A. Poluektov
φ3 with B→D(*)0 K Dalitz analysis at Belle
Parameterization of fit PDF
PDF for the single Dalitz plot fit:
2
2
r
r
r
r
θ
θ
θ
θ
(
cos
−
cos
)
+
(
sin
−
sin
)
d 2 P (r ,θ ) ∝ exp[−
]rdrdθ
2
2σ
r ,θ - true values, r ,θ - reconstructed values
PDF of reconstructed values
values
r , ϕ3 , δ
r , ϕ3 , δ
for a given set of true
for combined fit of two Dalitz plots (B+ and B-):
d 2P
d 3P
d 2P
(r , ϕ 3 , δ ) ∝
(r , δ + ϕ 3 ) ⋅
(r , δ − ϕ 3 )
drdϕ 3dδ
drdθ +
drdθ −
Can also obtain PDF of true values r , ϕ 3 , δ for a given set
of reconstructed values r , ϕ 3 , δ with this parameterization.
This PDF is used to obtain confidence intervals and significance.
March 21-28, 2004
Recontres de Moriond, EW session
29
A. Poluektov
φ3 with B→D(*)0 K Dalitz analysis at Belle
Backgrounds
•
qq combinatorial (including real D0)
B →D0 K
B→D*0K
22.1%
9.0%
2.2%
2.1%
1.0%
0.6%
0.4%
0.4%
<0.4%
<0.4%
– Fraction: from ∆E distribution
– Dalitz plot: from continuum data
• Other B decays
– Fraction and Dalitz plot: from
generic MC
• “Wrong” particles in D0 decay
– Fraction and Dalitz plot: from
B→D0K MC
•
B→D0π with K/π misID
– Fraction: from ∆E distribution
– Dalitz plot: D0
• Flavor tagging K from combinatorics
– Fraction from MC
March 21-28, 2004
Recontres de Moriond, EW session
30
A. Poluektov
φ3 with B→D(*)0 K Dalitz analysis at Belle
Illustration of CP asymmetry
Select regions on Dalitz plot with σ(B+)>σ(B-) or σ(B-)>σ(B+) by >20%
Calculate the number of B+ and B- decays in each of the regions.
CP asymmetry ⇒ difference in number of B+ and B- events
March 21-28, 2004
Recontres de Moriond, EW session
31