A. BondarModel-independent φ 3 measurement August 6, 2007Charm 2007, Cornell University1/15 γ/φ 3...

August 6, 2007 Charm 2007, Cornell University 1/15

A. Bondar Model-independent φ3 measurement

γ/φ3 model-independentDalitz analysis

(Dalitz+CP tagged Dalitz plots and γ/φ3 extraction)

Alex Bondar, Anton Poluektov

Budker Institute of Nuclear PhysicsNovosibirsk, Russia



The relative phase γ (φ3)

Interference between tree-level decays; theoretically clean

Parameters: , (rB, δ) 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 Ksπ0, D0 π+ π -

• Atwood, Dunietz, Soni (ADS): Use doubly Cabibbo-suppressed decays, e.g. D0 K+π -

• Giri, Grossman, Soffer, Zupan (GGSZ) / Belle: Use Dalitz plot analysis of 3-body D0 decays, e.g. Ks π+ π-

Vcs* Vub: suppressedFavored: Vcb Vus

*

b

u

s

u u

b

u

cD(*)0

K(*)-

B- B-

u

s

u

c

D(*)0f

Common

final state

K(*)-

30

0 iiBKDBA

KDBA eer



Dalitz analysis method

• Measure B+/B- asymmetry across Dalitz plot

• Includes GLW (D0 Ks ρ0, CP eigenstate) and ADS (D0 K*+π-, DCS 2-body decay)

regions

2222 ,, 3

mmfeermmfA ii

B KKB Ds

Sensitivity to in interference term

2-fold ambiguity on 3 : (3, δ)→ (3+π,

δ+π) Model uncertainty ~ 100

decay amplitude

Determine f in flavor-tagged D*+D0π+ decays

sKmm 22 Mirror symmetry between D0 and D0 Dalitz plots



ρ-ω interference

Doubly Cabibbosuppressed K*

)(GeV22sK

M

)(GeV22sK

M

)(GeV22sK

M )(GeV22sK

M

)(GeV 22

M )(GeV 22

M

M

(

GeV

2 )

Ksπ

–

2

D0 Ksπ+π– decay model



Belle/Babar model-dependent results • HFAG averages for x± = rB cos( δ ± ) , y± = rB sin( δ ± )

• Belle/Babar measurements in good agreement

• Note: σ(3) depends significantly on the value of rB

Contours do not include Dalitz model errors

Contours do not include Dalitz model errors

rB

23



Model-independent analysisModel-independent way: obtain D0 decay strong phase from ψ(3770)DD data

22222 |),(|),( mmfmmP DD

CPPPPffmmP DDDDDDCP 2||),( 222

][2|)(|),( 2222 SyCxPPPrPfiyxfmmP DDDBDDDB

)),(),(cos(),( 222222 mmmmmmC DD

)),(),(sin(),( 222222 mmmmmmS DD

22222 |),(|),( mmfmmP DD

)(2

||),,,( 22222

SSCCPPPPPPPP

ffffmmmmP

DDDDDDDD

DDDDCorr

DCPKSπ+π–:

ψ(3770)(KSπ+π–)D (KSπ+π–)D :

where )cos( 3 Brx

)sin( 3 BryFree parameters

Unknown, can be obtained

from charm data:

(1)

(2)

(3)



Model-independent analysis

CLEO-c with 750 pb-1 (estimated numbers) ~ 1000 DCPKSπ+π– decays with CP-eigenstate tag.

~ 2000 correlated D0 decays: ψ(3770)(KSπ+π–)D (KSπ+π–)D

ψ(3770)(KLπ+π–)D (KSπ+π–)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



Binned analysis: DCP

[A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003)]

)](2[ 2iiiiiBiBi ysxcKKKrKhN

]2[ iiiiiCPi cKKKKhN

Number of events in B-plot

Number of events in DCP-plot

122 ii sc ( =1 if bin size is small enough)

i

-i

• ci , si can be obtained from B data only

• ci from DCP, si from B data

• si constrained as

21 ii cs

Very poor sensitivity

Poor sensitivity for y

Bias if bin size is large

Number of events in D0-plot: iK

iic DD )(cos iis DD )(sin

(4)

(5)




[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.

φ3 measurement with accuracy 2-3°

~10 fb-1 (10000 ev.) at ψ(3770) needed

to accompany this measurement.

Nearest future: ~1000 DCP events at

CLEO.

Bin size should be large

bias due to

rB=0.2

21 ii cs




[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 21 ii cs Satisfy simultaneously for

binning with

Good approximation:

uniform binning in ΔδD

But the optimal binning depends on

D0 model. bias if it differs from

the actual one (~10° by toy MC).

causes unavoidable

model sensitivity.

Reduces as data increases

(by applying finer binning).

122 ii sc

21 ii cs



Binned analysis: (KSπ+π–)2

)](2[ jijijjiiijjiij ssccKKKKKKKKhN

2 correlated Dalitz plots, 4 dimensions:

Can use maximum likelihood technique:

min),(log2log2 ijijPoisson NNpLwith 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.

(6)

(7)



Binned analysis: (KSπ+π–)2

ci ,si measured in toy MC (points) and

calculated (crosses) for ΔδD-binning

• 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

21 ii cs

[A. Bondar, A.Poluektov, hep-ph/0703267]



MC simulation of the bias in 3 measurement

Model dependence for 2x8 bins in Dcp case:

Model dependence for 2x8 bins in (Ks+-)2 case:



Summary of stat. sensitivity

BinningB-stat. error 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 - - - -

Errors corresponding to 1000 events in B, DCP and (Kππ)2 samples

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)~3° with rB=0.1



Conclusion

• Several approaches are proposed for model-independent analysis:

• Binned with DCP (original GGSZ): implemented, studied.

Bias with limited statistics.

• Binned with (KSπ+π–)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

Belle

CLEO

HFAG

BaBar

Super B factory

Super Babar/Belle

C/ factory

Super HFAG



Backup slides



If is known, parameters are obtained from

the fit to Dalitz distributions of D Ksπ+π– from B±DK± decays

Dalitz analysis method

Using 3-body final state, identical for D0 and D0: Ksπ+π-.

Dalitz distribution density:22222 ||),(

ssss KKKK

dmdmmmd A

222 |),(| ss KKmmA

(assuming СР-conservation in D0 decays)

000~DerDD i

B

A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, 054018 (2003)A. Bondar, Proc. of Belle Dalitz analysis meeting, 24-26 Sep 2002.

),( 22 ss KK

mmf ),,( Br



Statistical sensitivity of the method depends on the propertiesof 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 + flat non-resonant term.

As a result, model uncertainty in the

γ/φ3 measurement (~10° currently).

D0 Ksπ+π– decay



Binning optimization

Maximizing “binning quality” function allows to

find a binning with the B-stat. sensitivity close to unbinned approach.

i i

iii

N

scNQ

)( 222

A. BondarModel-independent φ 3 measurement August 6, 2007Charm 2007, Cornell University1/15 γ/φ 3...

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