f3 measurements at
superKEKB
Pavel Krokovny
KEK
Introduction
Methods
Summary
World average (UTfit)
UTfit averages
including all results
γ/φ3=88±16°
available today
The total Belle+Babar luminosity used in this average is about 1ab-1.
Naively we can expect f3 error of 70(20) for 5ab-1 (50ab-1)
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Unitarity Triangle Fit (50/ab)
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Atwood-Dunietz-Soni method
D. Atwood, I. Dunietz and A. Soni, PRL 78, 3357 (1997);
PRD 63, 036005 (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

f3 at superKEKB
P. Krokovny
Interfering amplitudes
are comparable
CKM 2008, Rome
Gronau-London-Wyler method
[Phys. Lett. B 253 (1991) 483]
[Phys. Lett. B 265 (1991) 172]
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:
Α1,2 
Br ( B   D1, 2 K  )  Br ( B   D1, 2 K  )
Br ( B   D1, 2 K  )  Br ( B   D1, 2 K  )
 
 
  
for D1
for D2

2rB sin   sin 
1  rB2  2rB cos   cos 
 A1,2 have opposite signs
Additional constraint:
R 1, 2 
Br ( B  D1, 2 K ) / Br ( B  D1, 2 )
Br ( B  D 0 K ) / Br ( B  D 0 )
4 equations (3 independent:
f3 at superKEKB
 1  rB2  2rB cos   cos 
A1R 1   A2R 2 ), 3 unknowns (rB ,  ,  )
P. Krokovny
CKM 2008, Rome
ADS method (Belle)
Belle collaboration, 657M BB pairs [arXiv: 0804:2063, submitted to PRD(RC)]
B−→[K+π−]D K− (suppressed) and B−→[K–π+]D K− (favored) modes are
selected.
B→D K
B→D K


supp
6.3+2.0
3
RADS = 8.0+5.7

10
 2.8
fav
CP asymmetry:
AADS = 0.13+0.98
0.88 ± 0.26
rB<0.19 at 90%
CL
(with the conservative
assumption cos φ3 cos δ = –1)
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
GLW method (BaBar)
BaBar collaboration, 382M BB pairs [arXiv: 0802:4052]
CP-even modes: DCP+→K+K–, π+ π –
CP-odd modes : DCP−→KS π0, KS ω
ACP+
+ 0.27 ± 0.09 ± 0.04
ACP-
− 0.09 ± 0.09 ± 0.02
RCP+
1.06 ± 0.10 ± 0.05
RCP-
1.03 ± 0.10 ± 0.05
The same result expressed in Cartesian variables:
x + − 0.09 ± 0.05± 0.02
x − + 0.10 ± 0.05 ± 0.03
r2
0.05 ± 0.07 ± 0.03
x± precision comparable to Dalitz analysis
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
ADS+GLW
• Both methods are theoretical clean and have no
model uncertainty. The f3 precision is limited by
statistics only.
• Current f3 error is in order of 300
• The expected f3 accuracy is 150 with 5ab-1 and
50 with 50 ab-1
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Dalitz analysis method
• Measure B+/B- asymmetry across Dalitz plot


B   K s    D K 



A  f m2 , m2  rBeif3 ei f m2 , m2

m2  m 2 K s 


Mirror symmetry
between D0 and D0
Dalitz plots
Sensitivity to φ3 in interference term
Determine f in flavor-tagged D*+D0π+ decays
Current statistical accuracy is about 150
The model uncertainty is in order of 5-100
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Belle/Babar model-dependent results
•
•
HFAG averages for x± = rB cos( δ ± f3 ) , y± = rB sin( δ ± f3 )
Belle/Babar measurements in good agreement
•
Note: σ(f3) depends significantly on the value of rB
Contours do not include
Dalitz model errors
Contours do not include
Dalitz model errors
2f3
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Binned analysis: DCP
[A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003)]
Number of events in
Number of events in
-i
D0-plot: K i
B-plot
 N  i  hB [ Ki  rB2 Ki  2 Ki Ki ( xci  ysi )]
i
where
x  rB cos(  3 )
y  rB sin(  3 )
Free parameters
C (m2 , m2 )  cos( D (m2 , m2 )   D (m2 , m2 ))
S (m2 , m2 )  sin(  D (m2 , m2 )   D (m2 , m2 ))
DCPKSπ+π–:
PCP  (m2 , m2 ) | f D  f D |2  PD  PD  2 PD PD C
2 2 2 2
2


P
(
m
,
m
,
m
,
m
)

|
f
f

f
f
|

Corr




D
D
D
D
ψ(3770)(KSπ+π–)D (KSπ+π–)D :
 PD PD  PD PD  2 PD PD PD PD (CC   SS )
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Binned analysis: DCP
[A. Bondar, A.Poluektov, Eur. Phys. J. C47 347-353 (2006), hep-ph/0510246]
• ci , si can be obtained from B data only
 Very poor sensitivity
• ci from DCP, si from B data
 Poor sensitivity for
• si constrained as
si   1  ci 2
50 ab-1 (50000 ev.) at SuperB
should be enough for model-indep.
φ3 measurement with accuracy 2-3°
~10 fb-1 (10000 ev.) at
y
 Bias if bin size is large
rB=0.2
ψ(3770) needed
to accompany this measurement.
Nearest future: ~1000 DCP events at
CLEO.
Bin size should be large 
bias due to si   1  ci 2
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Binned analysis: (KSπ+π–)2
2 correlated Dalitz plots, 4 dimensions:
 M  ij  h [ K i K  j  K j K i  2 K i K i K j K  j (ci c j  si s j )]
(6)
Can use maximum likelihood technique:
 2 log
L  2 log p
( M ij ,  M  ij )  min
Poisson
(7)
with ci and si as free parameters.
For the same binning as in DCP, number of bins is
N2 (instead of N),
but the number of unknowns is the same.
With Poisson PDF, it’s OK to have Nij<1.
Can obtain both ci and si.
It’s convenient to use combined likelihood of (Ks+-)2 and B data
to account for errors in ci and si.
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Binned analysis: (KSπ+π–)2
[A. Bondar, A.Poluektov, hep-ph/0703267, arXiv:0711.1509]
• Can use the same binning as in DCP
• ci ,si measured independently 
no model uncertainty due to
si   1  ci 2 constraint
• Only 4-fold ambiguity: ci -c-i or si -s-i.
reduces to 2-fold if DCP data are used
with the same binning.
• Stat. sensitivity comparable to DCP
ci ,si measured in toy MC (points) and
calculated (crosses) for ΔδD-binning
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Model-independent Dalitz analysis
• The binned Dalitz analysis has almost the same
statistical power that the unbind. But the model
uncertainty can by eliminated by using the CP tagged
DCP events form charm factories.
• The expected f3 accuracy is 70 with 5ab-1 and 2.50
degrees with 50 ab-1. This measurement will require 103
(104) CP tagged DCP from charm factory, CLEOc/BES
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Conclusion
•
Several methods can be used to measure f3 with superKEKB.
• GLW+ADS are theoretical clean. Accuracy depends on
statistics only. The expected error is 150 (50) with 5ab-1 (50ab-1)
• The Dalitz analysis method will be limited by model
uncertainty.
• The model independent Dalitz method can be used. The
information form charm factories are required. The expected f3
error is 70 (2.50) with 5ab-1 (50ab-1)
• Combining together ADS, GLW and Dalitz methods, we can
reach accuracy of 60 (20) with 5ab-1 (50ab-1)
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Other possibilities: D0π+π–π0 (BaBar)
[BaBar collaboration, hep-ex/0703037]
Modified likelihood to account for Br difference of B+ and B–:
No significant constraint on γ yet.
f3 at superKEKB
D KsK+K–: more promising?
P. Krokovny
CKM 2008, Rome
Other possibilities: B0D0K*0 (BaBar)
[V. Sordini, talk at CKM2006; hep-ph/0703292]
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).
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Binned analysis: DCP
[A. Bondar, A.Poluektov, hep-ph/0703267]
To use the limited CLEO-c data:
• Find binning with optimal sensitivity
• Get rid of bias due to si   1  ci 2
Satisfy simultaneously for
ci2  si2  1 binning with
Good approximation: uniform binning in ΔδD:
But the optimal binning depends on D0 model. 
bias if it differs from actual one (same ~10°).
si   1  ci 2 causes unavoidable model
sensitivity. Reduces as data increases (by
applying finer binning).
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
MC simulation of the bias in f3 measurement
Model dependence for 2x8 bins
in (Ks+-)2 case:
No bias when changing
the model, but stat. error
degrades.
Model dependence for 2x8 bins
in Dcp case:
f3 at superKEKB
P. Krokovny
CKM 2008, Rome
Summary of stat. sensitivity
Errors corresponding to 1000 events in B, DCP and (Kππ)2 samples
B-stat. error
Binning
DCP-stat. error
(Kππ)2-stat. error
σx
σy
σx
σy
σx
σy
Uniform, N=8
0.033
0.060
0.0053
0.0097
0.0145
0.0322
ΔδD,
N=8
0.027
0.037
0.0042
0.0072
0.0050
0.0095
Optimal, N=8
0.023
0.032
0.0058
0.0114
0.0082
0.0114
Uniform, N=20
0.027
0.055
0.0042
0.0112
-
-
ΔδD,
N=20
0.027
0.035
0.0048
0.0074
-
-
Optimal, N=20
0.022
0.029
0.0078
0.0110
-
-
Unbinned
0.021
0.028
-
-
-
-
Expected charm data contribution for 750 fb-1 at CLEO-c:
(1000 DCP and 2000 (Kππ)2)
σx=0.003, σy=0.007  σ(φ3)~5° with rB=0.1
f3 at superKEKB
P. Krokovny
CKM 2008, Rome