?/f3 model-independent Dalitz analysis (Dalitz CP tagged Dalitz plots and ?/f3 extraction)

1
?/f3 model-independentDalitz analysis(DalitzCP
tagged Dalitz plots and ?/f3 extraction)

• Alex Bondar, Anton Poluektov
• Budker Institute of Nuclear Physics
• Novosibirsk, Russia

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The relative phase ? (f3)

• Interference between tree-level decays
  theoretically clean

Favored Vcb Vus
Vcs Vub suppressed
u
s
Common final state
K()-
K()-
s
u
u
b
B-
B-
b
c
c
u
f
D()0
D()0
u
u
Parameters f3, (rB, d) per mode

• Three methods for exploiting interference (choice
  of D0 decay modes)
• Gronau, London, Wyler (GLW) Use CP eigenstates
  of D()0 decay, e.g. D0 ? Ksp0, D0 ? p p -
• Atwood, Dunietz, Soni (ADS) Use doubly
  Cabibbo-suppressed decays, e.g. D0 ? Kp -
• Giri, Grossman, Soffer, Zupan (GGSZ) / Belle Use
  Dalitz plot analysis of 3-body D0 decays, e.g. Ks
  p p-

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Dalitz analysis method

• Measure B/B- asymmetry across Dalitz plot
• Includes GLW (D0 ? Ks ?0, CP eigenstate) and ADS
  (D0 ? Kp-, DCS 2-body decay)
• regions

amplitude
decay
Mirror symmetry between D0 and D0 Dalitz plots
Sensitivity to f3 in interference term
Determine f in flavor-tagged D?D0p decays
2-fold ambiguity on f3 (f3, d) ? (f3p, dp)
Model uncertainty 100
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D0 ? Kspp decay model
Doubly Cabibbo suppressed K
?-? interference
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Belle/Babar model-dependent results

• HFAG averages for x rB cos( d f3 ) , y rB
  sin( d f3 )
• Belle/Babar measurements in good agreement
• Note s(f3) depends significantly on the value of
  rB

Contours do not include Dalitz model errors
Contours do not include Dalitz model errors
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Model-independent analysis
Model-independent way obtain D0 decay strong
phase from ?(3770)?DD data
(1)
where
Free parameters
Unknown, can be obtainedfrom charm data
DCP?KSpp
(2)
(3)
?(3770)?(KSpp)D (KSpp)D
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Model-independent analysis

• CLEO-c with 750 pb-1 (estimated numbers) 1000
  DCP?KSpp decays with CP-eigenstate tag.
• 2000 correlated D0 decays ?(3770)?(KSpp)D
  (KSpp)D
• 
  ?(3770)?(KLpp)D (KSpp)D
• We need to find a way
• how to use this data most efficiently
• how to combine the results of two experiments
• Binned approach
• Divide Dalitz plots into bins
• Solve the system of equations with constraints

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Binned analysis DCP
A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD
68, 054018 (2003)
Number of events in D0-plot
Number of events in B-plot
-i
(4)
i
Number of events in DCP-plot
(5)
( 1 if bin size is small enough)

• ci , si can be obtained from B data only
• ci from DCP, si from B data
• si constrained as

? Very poor sensitivity
? Poor sensitivity for y
? Bias if bin size is large
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Binned analysis DCP
A. Bondar, A.Poluektov, Eur. Phys. J. C47
347-353 (2006), hep-ph/0510246
50 ab-1 (50000 ev.) at SuperB should be enough
for model-indep. f3 measurement with accuracy
2-3 10 fb-1 (10000 ev.) at ?(3770) needed to
accompany this measurement. Nearest future
1000 DCP events at CLEO. Bin size should be
large ? bias due to
rB0.2
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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

Satisfy simultaneously for binning with Good
approximation uniform binning in ?dD But the
optimal binning depends onD0 model. ? bias if it
differs from the actual one (10 by toy MC).
causes unavoidablemodel
sensitivity. Reduces as data increases (by
applying finer binning).
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Binned analysis (KSpp)2
2 correlated Dalitz plots, 4 dimensions
(6)
Can use maximum likelihood technique
(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, its OK to have Nijlt1. Can
obtain both ci and si.
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Binned analysis (KSpp)2
A. Bondar, A.Poluektov, hep-ph/0703267

• Can use the same binning as in DCP
• ci ,si measured independently ? no model
  uncertainty due to
  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 ?dD-binning
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MC simulation of the bias in f3 measurement
Model dependence for 2x8 bins in Dcp
case Model dependence for 2x8 bins in
(Kspp-)2 case
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Summary of stat. sensitivity
Errors corresponding to 1000 events in B, DCP and
(Kpp)2 samples
Binning B-stat. error B-stat. error DCP-stat. error DCP-stat. error (Kpp)2-stat. error (Kpp)2-stat. error
Binning sx sy sx sy sx sy
Uniform, N8 0.033 0.060 0.0053 0.0097 0.0145 0.0322
?dD, N8 0.027 0.037 0.0042 0.0072 0.0050 0.0095
Optimal, N8 0.023 0.032 0.0058 0.0114 0.0082 0.0114
Uniform, N20 0.027 0.055 0.0042 0.0112 - -
?dD, N20 0.027 0.035 0.0048 0.0074 - -
Optimal, N20 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 (Kpp)2) sx0.003,
sy0.007 ? s(f3)3 with rB0.1
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Conclusion

• Several approaches are proposed for
  model-independent analysis
• Binned with DCP (original GGSZ) implemented,
  studied. Bias with limited statistics.
• Binned with (KSpp)2 Twice as much data,
  similar to DCP sensitivity. No bias, less
  ambiguity.
• Getting ready for model-independent measurement
  together with CLEO. Analysis strategy
  needs to be discussed

C/t factory
BaBar
Super HFAG
Super B factory
Belle
HFAG
CLEO
Super Babar/Belle
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Backup slides
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Dalitz analysis method
A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD
68, 054018 (2003) A. Bondar, Proc. of Belle
Dalitz analysis meeting, 24-26 Sep 2002.
Using 3-body final state, identical for D0 and
D0 Kspp-. Dalitz distribution density
(assuming ??-conservation in D0 decays)
If is known,
parameters are obtained from the
fit to Dalitz distributions of D? Kspp from
B?DK decays
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D0 ? Kspp decay
Statistical sensitivity of the method depends on
the properties of the 3-body decay involved.
(For M2Const there is no sensitivity to the
phase ?) Large variations of D0 decay strong
phase are essential
Use the model-dependent fit to experimental data
from flavor-tagged D ?D0p sample. Model is
described by the set of two-body amplitudes
flat non-resonant term. As a result, model
uncertainty in the ?/f3 measurement (10
currently).
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Binning optimization
?
Maximizing binning quality function
allows to find a binning
with the B-stat. sensitivity close to unbinned
approach.