Dalitz Plot Analysis of D 0 – + 0 Measurement of using B D – + 0 K Kalanand Mishra...

Dalitz Plot Analysis of D0–+0 Measurement of using BD–+0 K

Kalanand MishraKalanand MishraUniversity of CincinnatiUniversity of Cincinnati

Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 22/36/36

Left handed quarks in doubletsLeft handed quarks in doubletsRight handed quarks in singlets Right handed quarks in singlets do not couple to W do not couple to W The electroweak coupling strength of W

to left-handed quarks is described by Cabibbo-Kobayashi-Maskawa matrix

3x3 unitary matrix ==> 4 parameters

tcuui ,,=

bsdd j ,,=

relative magnitudeof the elements

Weak interaction of quarks in SMq q ii

L L == (( uuiiLL

ddiiLL))


An irremovable complex phase in VCKM is the origin of CP violation in the SM

In the Wolfenstein parameterization:

The CKM Matrix

CP the phase changes signin the CP-conjugated process


The Unitarity Triangle V is unitary: VV+=1 ===>

in the complex plane*

*arg ub ud

cb cd

V VV V

⎡ ⎤

= −⎢ ⎥⎣ ⎦

Expect to be ~ (60±10)º, if the Standard Model is consistent. But need to measure it directly, need redundant measurements ….

Several ways to measure , no single one of them is “silver bullet” !


BaBar: B and charm FactoryBaBar: B and charm Factory

Cherenkov Detector

144 quartz bars K, π, p separation

Electromagnetic Calorimeter6580 CsI crystals

e+ ID, π0 and γ reco

Drift Chamber40 layers

tracking + dE/dx

Instrumented Flux Return

12-18 layers of RPC/LST μ ID

Silicon Vertex Tracker5 layers (double-sided Si sensors)vertexing + tracking (+ dE/dx)

e+ [3.1 GeV]

e- [9 GeV]

1.5T Magnet


Kaon/Pion Discrimination: DIRCKaon/Pion Discrimination: DIRC

Cherenkov angle vs. momentum for pions and kaons

LAYOUT

>4 separationat 3 GeV/c


Extraction of with BD0K

B

b

u

u

u

cs K

D0

B bu

cu

su

D0

K

Common final state f

Magnitude ratio rB 1.034.01≈≈

−≈⋅⋅≈

colorcoloru

c

cb

ub

Ni

NVV

VV ηr

Color suppression

*

*arg ub ud

cb cd

V VV V

⎡ ⎤

= −⎢ ⎥⎣ ⎦bb

Secret to Success: interference between color-allowed D0K and color-suppressed D0K amplitudes.Decay time-independent!

The bigger the better!Larger rB larger interference term better constraints on .


A Simple Interference AlgebraA Simple Interference AlgebraAmplitude 1 = A ei

Amplitude 2 = B ei

Total amplitude = Aei + Bei

Decay Rate = A2 + B2 + 2AB cos()Decay Rate of CP-conjugate decay = A2 + B2 + 2AB cos()

If 2 parameters are known (A/B and , use the 2 equations to solve for B and .

B→DK, through a slightly more complicated analysis, allows you to measure when is not known.


Methods to Extract • D0/D0 decay to common final state• The interference depends on Vub

and therefore on • Critical parameter: ratio of

amplitudes:

• Select the D0 decays that enhance the interference:o 3-body (e.g. KS): Dalitzo CP-eigen. (e.g. KS0): GLWo DCS (e.g. D0K+-): ADS

*

*arg ub ud

cb cd

V VV V

⎡ ⎤

= −⎢ ⎥⎣ ⎦

f

fVub

color allowed

color suppressed

1.0~)()(

0

0

−−

−−

→→

≡KDBAKDBArB

measurements are overwhelmingly dominated by measurements are overwhelmingly dominated by statistical errors.statistical errors.


Evolution of Methods on Gronau, Landon, and Wyler (GLW) Phys. Lett. B 265, 172 (1991)

• This was the original B→DK paper. Reconstruct D in a CP eigenstate.• Additional measurements are needed to determine them all: rB, , .

Atwood, Dunietz, and Soni (ADS), Phys. Rev. Lett. 78, 3257 (1997)• Noted the sizable interference between the DCS and CF decays of D, and

proposed to use them, to realize the interference.• Method can’t be used standalone either, since there is only one 2-body DCS mode,

D0→K, while at least 2 modes are needed. Need additional input of strong phase difference in D decays.

Giri, Grossman, Soffer, Zupan (GGSZ) Phys. Rev. D68, 054018 (2003)• Outlines the method for using multi-body D decays with model-

dependent and –independent analysis

BaBar, hep-ex/0507101 and Belle, hep-ex/0504013 (2005)• The experimental measurements of using B→DK, D→KS

Bondar, A. Poluektov, ph/0510246 (2005)• MC study of the model-independent (binned Dalitz plot) measurement of

BF(B DK) ~ 10 -4, BF(D fCP) ~ 10 -2

Small… strongly statistics limitedMain Drawback:Main Drawback:

Will elaborate on this Will elaborate on this laterlater

No significant signal with current No significant signal with current data data


Discrete AmbiguitiesDiscrete Ambiguities

• The observables are cos()andcos(), which are invariant under Sex : S± : S:

If f and f ’ are different enough, Sex is resolved, since you can’t simultaneously satisfy both f and f ’While measuring While measuring , one encounters two devils: statistics , one encounters two devils: statistics

and ambiguity, and they often feed each other.and ambiguity, and they often feed each other.


Dalitz Plot MethodDalitz Plot Method

We saw that at least 2 D final states are needed in order to solve for all the unknowns.

This 2-state requirement can be satisfied by a single multi-body D final states, in which each point in the final state phase space (Dalitz plot for a 3-body decay) serves effectively as a different final state.

In terms of the analysis, what differentiates 2 final states is their values of rf and/or f.. In this sense, different points in phase space can function as different D final states when they have different values of rf or f.

Broad resonances are the most obvious cause for variation of rf and f in different points of final-state phase space.


2-body vs Multi-body D2-body vs Multi-body D00 Final States Final States

Advantages of multi-body final states: Effectively, provide many final states, due to the variation of rf and f. This

helps to resolve ambiguities down to an irreducible 2-fold ambiguity :) Add statistics – access to modes for which the 2-body final-state technique

for measuring is not applicable :)

Disadvantages: More complicated analysis :( New systematic errors (how well do we understand the D final-state phase-

space distribution?) unless using model-independent analysis approach :(

Overall: A-priori, both kinds of states are approximately equally useful in measuring . Measurement is statistically limited, need all the modes we can get. In practice, some modes will turn out to be more useful than others.


Assessment of Some 3-body DAssessment of Some 3-body D00 Decays DecaysMode BR(D0→f) ln Bgd Comments

KS 2.9% n=0 l2 to 1 OK Attractive due to high stat & low background

1.5% n=1 0 Expect similar sensitivity as KS if background under control

KSK (0.34 0.26)% n=1 ~1 OK Expect similar sensitivity as

K ~0.2% n=2 l2 0 S/B probably too small for now

KK 0.3% n=1 ~1 0 bad, KK good

Low stat, but low background, so sensitivity could approach 0

KS ~1% (+?) n=0 1 0 CP eigenstate, low S/B

KS 5.5% n=0 l2 So-so High stat, but 4-body analysis is hard. Large phase space reduces D0-D0bar interference

|)(/)(| 00 DADA


Step 1: Obtain D0 → +0 Dalitz Plot parameterization using D*+→D0+ (and c.c) sample

Step 2: Fit BDK (and c.c) sample to obtain signal yield and branching-ratio asymmetry

Step 3: Fit for CP parameters using results of Steps 1 and 2 on BDK sample

Analysis Steps for BD–+0 K


3-Particle Phase Space3-Particle Phase Space

coscos22 distributiondistribution of of rr meson meson

- Dalitz plot provides info on angular distr. - Also about dynamical amplitudes involved. - Flat if no dynamics involved.

=0=0 ==rr++

Dalitz applied this method first to KL-decays- To resolve τ/θ puzzle with only few events- goal was to determine spin and parity

And he never called them Dalitz plots !

DD00--++00 Dalitz plot

Step 1

2 ObservablesFrom four vectors 12Conservation laws -4Final state particle masses -3Free rotation in decay plane -3Σ

2 Usual choice

Invariant mass squared m212

Invariant mass squared m213

π2

D0

π1

{ π1 , , π2, , π3 } } == { { ++, , 00, , - }- }

π3


⎪⎪⎩

⎪⎪⎨

⎧

−−

Γ−−=

)(1

)(1

)(

222

211

2

2

ggiMsM

siMsMsBW

rr

rrrJr

ρρ

Isobar Model FormalismIsobar Model Formalism three-body decay Dthree-body decay DABC decaying through an r=[AB] ABC decaying through an r=[AB] resonanceresonance

D decay three-body amplitudeD decay three-body amplitude ),(),( 1312013120 sseaeass r

ri

rr

iD AA ∑=

Jr

Jr

Jr

JDr BWMFFss ××=( 3A Relativistic Breit-WignerRelativistic Breit-Wigner

Angular distributionAngular distributionD D and and r r Blatt-WeisskopfBlatt-Weisskopf form form factorsfactors

NR termNR term(direct 3 body (direct 3 body decay)decay)aa00, , δδ00, a, arr, , δδrr : Free parameters of fit : Free parameters of fit

ff00(980)(980)

1 1

12

2

3 3 3

{12} {13} {23}12

32

NRNR

(( aa00(980)(980)

Step 1


DD00––++0 0 Dalitz Plot AmplitudesDalitz Plot AmplitudesInterference between three types of singly Cabibbo-suppressed amplitudes

(I)(I) (II)(II)

(III)(III)

Color-suppressedColor-suppressed

PDF for signal events = | f |PDF for signal events = | f |22

Step 1

Assumes no D-mixing, no CP violation in D decays!

mm22++00 + m + m22

--00 + m + m22++-- = =

mm22++ + m + m22

-- + m + m220 0 + +

mm22DD00


DD00--++00 Event Event ReconstructionReconstructionDD00--++00 Reconstruction Reconstruction

– and + tracks are fit to a vertex Mass of 0 candidate is constrained to m0 at –+ vertex PCM ( D0 ) > 2.77 GeV/c

D* Reconstruction D*+ candidate is made by fitting the D0 and s

+ to a vertex constrained in x and y to the measured beam-spot. |mD* - m D0 - 145.5| < 0.6 MeV/c2

Vertex c2 probability > 0.01 Choose the best candidate per event with the smallest c2 for the decay chain (multiplicity = 1.03).

Background Sources Charged track combinatoric Mis-reconstructed 0

Real D0, fake s

K0 reflection in sideband

Step 1

Phys. Rev. D74, 091102 (2006)Phys. Rev. D74, 091102 (2006)

Event SelectionEvent Selection

PCM ( D0) > 2.77 GeV/c|mD* - m D0 - 145.5| < 0.6 MeV/c2

D0+

soft

0

–

+

XDee → − *


Dalitz Plot Analysis of Dalitz Plot Analysis of DD00→→ππ––ππ++ππ00Step 1

• Three I =1 particles in the final state• Gives rise to a rich interference structure• The three r regions are clearly enhanced in the DP, and r-r destructive interference is evident

rr destructive interference

KS veto

Events used for bkg shape

±1 region: ≈ 45000 events

rr++

rr00

Motivation: CKM angle γ using B±D[D[ππ––ππ++ππ00] ] KK±

232 fb-1

The 3 destructively The 3 destructively interfering interfering rr amplitudes amplitudes suggest an suggest an II = 0, = 0, DDI = 1/2 I = 1/2 dominated final state. dominated final state. C. Zemach, Phys. Rev. 133, B1201 C. Zemach, Phys. Rev. 133, B1201 (1964). (1964).

hep-ex / 0703037hep-ex / 0703037

purity ≈ 98 %


Systematic errors:• and r(1700) parameters• reconstruction & PID eff• Form factor variation• Flavor mistags

hep-ex/0703037hep-ex/0703037

Fit ResultsFit Resultsrr++ : 68 % : 68 %rr–– : 35 %: 35 %rr0 0 : 26 % : 26 %

Small contributions Small contributions from higher from higher rr, f, f00, f, f22 and and states states

The distribution is The distribution is marked by 3 marked by 3 destructively destructively interfering interfering rr amplitudes, suggesting amplitudes, suggesting an an II = 0, = 0, DDI = 1/2 I = 1/2 dominated final state. dominated final state. C. Zemach, Phys. Rev. C. Zemach, Phys. Rev. 133, B1201 (1964). 133, B1201 (1964). (400, (400,

600)600)

Step 1


Strong-phase Diff. & Amplitude Ratio Strong-phase Diff. & Amplitude Ratio The strong phase difference D and relative amplitude rD between the

decays of D0 and D0 to r(770)+ – state are defined, neglecting direct CP violation in D decays, by the equation:

We find

These measurements are consistent with each These measurements are consistent with each other.other.

Hep-ex / 0306048 (2003)Hep-ex / 0306048 (2003)Hep-ex / 0703037 (2007)Hep-ex / 0703037 (2007)

__

rD = 0.714 0.008 (stat) 0.003 (syst)δD = -2.0° (stat) ± 0.6° ± 0.6° (syst)

rD = 0.65 0.03 (stat) 0.04 (syst)δD = -4° ± 3° (stat) ± 4°(syst)

CleoCleoBaBarBaBar

Step 1


Introducing Angular MomentsIntroducing Angular Moments

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

=

=

=

202

01

2200

524

cos24

4

PY

PSY

PSY

SP

π

φπ

π For S- and P- waves only, in the absence of cross-feeds from other channels, the amplitudes and the relative phase are given by:

We cannot solve these Eqs for the We cannot solve these Eqs for the system (due to system (due to crossfeeds) to extract |S|, |P|, and cos crossfeeds) to extract |S|, |P|, and cos SPSP in a model in a model independent way.independent way.

Schrödinger‘s Equation

Angular Amplitude

Dynamic Amplitude (BW, Flatte, S-wave)

In case only l = 0 (S-wave) and 1 (P-wave) amplitudes are present :In case only l = 0 (S-wave) and 1 (P-wave) amplitudes are present :

Step 1


Large interference between S and P Large interference between S and P waves.waves.

Each event is weighted by the spherical Each event is weighted by the spherical harmonicharmonic functions (functions (ll=0,1,2,…..).=0,1,2,…..).

Excellent agreement between data & fit.

Mass-projections & Angular MomentsMass-projections & Angular Moments

r(770)+ r(770)– r(770)0

mm22((++00) (GeV) (GeV22/c/c44)) mm22((––00) (GeV) (GeV22/c/c44)) mm22((––++) (GeV) (GeV22/c/c44))

KKSS veto veto

Step 1


Event Selection for BD–+0 K Based on BR and asymmetry analysis

• 5.272 < mES < 5.3 GeV (Avoids DP-mES correlations in bkg)

• 1.83 < mD < 1.895 GeV (Avoids DP-mD correlations in bkg)

• Kaon, pion identification• KS→ veto (D0KS0 is a CF decay unrelated to GGSZ method)

• q > 0.1 (continuum NN) • d > 0.25 (fake D0 NN)• = 11.4%

Phys. Rev. D72, 071102 (2005)Phys. Rev. D72, 071102 (2005)

Step 2


1. DKD: Correctly reconstructed signal (“signal”)

2. DKbgd: Mis-reconstructed signal events

3. DD: Correctly-reconstructed D with misidentified as K

4. DbadD: D events with a fake D candidate. K candidate is usually a true kaon picked at random from the event

5. DKX: B→DK with D →non-0. The K is good6. DX: B→D/r with D →non-0. K candidate is usually a true kaon

picked at random from the event7. BBCD: Combinatoric BB events with a good D candidate

8. BBCbadD: Combinatoric BB events with a fake D candidate

9. qqD: Continuum with a good D candidate

10. qqbadD: continuum with a fake D candidate

Event Types in BD–+0 K Step 2


BR Asymmetry for BD–+0 K Step 2

qq Signal

DE PDFs are Gaussian and 2nd-order polynomial:

qqSig

Fit BDKsample with DE, q, d

Obtain signal yield asymmetry

Nsig 170 ± 29

Asym -0.02 ± 0.15

BR(BDK) = (4.6 ± 0.8 ± 0.7) 10

A(BDK) = 0.02 ± 0.15 ± 0.03


B+

b

u

u

u

cs K+

D0

B+ bu

cu

su

D0

K+

bu

bc

• Based on GGSZ method of PRD68, 054018, so far used only with D→KS

• Goal: add modes for maximum precision

A±(s+,s) = fD(s+,s) + rBei(±) fD(s,s+)

Dalitz plot variables

B±DK± amplitude D00 amplitude D00 amplitude

Extraction of Extraction of : Basic Idea : Basic IdeaAtwood et al., PRL78, 3257 (1997)Giri et al., PRD68,054018 (2003)

B is strong phase diff. of A(B-

D0K-) and A(B- D0K-) Unknowns: rB, B and

Step 3


The Dalitz plot shape |A±(s+,s)|2 depends on the CP parameters rBei(±)

• Previous Dalitz analyses, with KS, used only this signature

But the branching fractions = |A±(s+,s)|2 are also sensitive to the CP parameters• Using both the shape and the absolute rates gives higher sensitivity

It turns out that in this mode , the BRs give a much higher sensitivity• Don’t know how it is in KSneed to check. If the same is true

there, expect significant improvement in KS sensitivity to

Add more Information to the LikelihoodStep 3


To make use of both the shape and the absolute decay rates, we minimize the function

⎟⎟⎠⎞

⎜⎜⎝⎛

−−

=expectedmeas

expectedmeas

AsymAsymNN

Y

LDP = log ∏PDP LBA = ½ Yi Vij1 Yj

L = LDP + LBA

V = error matrix from N and Asym fit

N±expected=η|A±(s,s)|2 (s,s) / |fD(s,s)|2 (s, s)

NBB BR(D00) BR(BD0K)

CP Parameters: Max Likelihood FitStep 3


rBei(±) = x± + y±

LDP

LBA

N+expected

1- contour lines

• LDP (LBA) has Cartesian (polar) symmetry• LBA is more sensitive (denser contour lines) in radial direction (r), not sensitive at all in

Min.

Min.

Toy exp., S+B

Behavior of LDP & LBA for xtrue = ytrue = 0Step 3


LDP LBA

+

=

L

• Highest sensitivity• But correlated contours due to polar symmetry of LBA

• Can’t quote sensible errors• Switch to polar coordinates

r

Combined behavior L = LDP + LBAStep 3


( 220±±± +−≡ yxxρ ⎟⎟⎠

⎞⎜⎜⎝⎛

−≡

− 0

1tanxx

yθ

x0 = fD(s+,s)* fD(s,s+) dsds+ = 0.85

r± = x0 and = 180 for rB = 0 (no CP violation)

LBA L

+ =

LDP

Polar coordinatesStep 3


X marks point of no bu ampr = 0.85, = 180

rBei(±) = x± + y±

( 220±±± +−≡ yxxρ

⎟⎟⎠⎞

⎜⎜⎝⎛

−≡

− 0

1tanxx

yθ

x0 = 0.85

r = 0.72 ± 0.11 ± 0.06 ; = (173 ± 42 ± 16)r = 0.75 ± 0.11 ± 0.06 ; = (147 ± 23 ± 11)

First measurement of CP-violating quantities in BDK

First combined use of DP distribution and absolute BR to extract CP parameters.

is too large for a meaningful extraction of from this analysis alone

r is small enough to contribute to overall CKMFitter/UTFit fits of

Result with 344 M e+e-BB Events

However, not trivial to directly determine work in progress

––


from BDKs0–+ K , role of rB

better precision of BaBar (x,y) does NOT translate to a smaller error on . Why?

BaBar: o)9353( 15

18 = −Belle:

[D*K included]

o)13104192( =

Dx ≈ Dy ≈ rBD D~ 1/rB

the error of is ~ proportional to the uncertainty in (x,y) and inversely proportianal to the distance from (0,0).

Belle measurement is consistent with larger rB.


• Direct measurement ofDirect measurement of is crucial to constrain new physics is crucial to constrain new physics contributions in quark sector of the Standard Model.contributions in quark sector of the Standard Model.• Many different approaches to measure Many different approaches to measure . Information from . Information from GLW, ADS, GGSZ, and other methods are all useful.GLW, ADS, GGSZ, and other methods are all useful.• The The GGSZ/DalitzGGSZ/Dalitz method has emerged as the most powerful method has emerged as the most powerful technique. technique. • Precise parameterizations of the amplitudes and phases and Precise parameterizations of the amplitudes and phases and the inclusion of information on branching ratio and decay-rate the inclusion of information on branching ratio and decay-rate asymmetry improve sensitivity in asymmetry improve sensitivity in . A lot of progress made in . A lot of progress made in the analysis and technique development. the analysis and technique development. • Statistics are the only thing holding us back ! Adding Statistics are the only thing holding us back ! Adding additional D decay modes to additional D decay modes to BBDKDK and combining results from and combining results from them will definitely help in the future analysis.them will definitely help in the future analysis.

SummarySummary

End of Talk ! Thank You !End of Talk ! Thank You !

Back up slides


Analysis with Multi-body DAnalysis with Multi-body D00 Final States Final States1. The simplest extension of the 2-body analysis.

2. Divide phase space into small bins, so that variations of rf and f within each bin can be ignored. Distant bins will have values of rf and f that are different enough so as to constitute different final states, and the analysis can be carried out, in principle, with as few as 2 bins.

3. A more accurate solution is not to ignore the variations of rf and f over the bin. But this introduces a new unknown for each bin. We now have 3 unknowns - rf, sin f, and cos f. The analysis then requires a minimum of 4 bins.

4. The only approach carried out so far is to parameterize the continuous variation of rf and f over phase space by using a sum of interfering Breit-Wigner resonances.


Signal Dalitz PDFs

r r( r(

f0(1500) f2’(1525) f0(1710)

f0(980) f2(1270) f0(1370

NR

NRPW NRPW NRPW

r r( r(

r r( r(

Step 1


BR of BD–+0 K : PDF Shapes“Normalize” neural net variables q dq q’ = tanh(q – ½ (qmax+qmin) / ½(qmax – qmin)]

qq

Signal

DE PDFs are Gaussians and 2nd-order polynomial:

qq

Sig

Step 2


Obtain signal yield and asymmetry.


BR Asymmetry for BD–+0 K Step 2

“Normalize” neural net variables q dq q’ = tanh(q – ½ (qmax+qmin) / ½(qmax – qmin)] qq

Signal

DE PDFs are Gaussian and 2nd-order polynomial:

qqSig


Obtain signal yield asymmetry

Nsig 170 ± 29

Asym -0.02 ± 0.15

BR(BDK) = (4.6 ± 0.8 ± 0.7) 10

A(BDK) = 0.02 ± 0.15 ± 0.03


Step 2 BR of BD–+0 K : Fit Projections

Nsig 170 ± 29

Asym -0.02 ± 0.15

NBB fake D 1138 ± 76

Nqq fake D 2383 ± 71

ND 57 ± 20

NDX/NBB 0.53 ± 0.15

BR(BDK) = (4.6 ± 0.8 ± 0.7) 10


BD–+0 K : Bkg Dalitz ShapesStep 3

Fake-D background Dalitz shapes are NR + 3 incoherent, unpolarized r’s:

Shape for 2 event types can’t be fit to this way. We use an empirical shape from simulation:

- Fit D0 → +0 Dalitz plot from BDK sample with DE, q, s+, s

- NN variable d not used – highly correlated with s+, s

- mES and MD not used – correlated with other variables for the backgroundFor CP FitFor CP Fit


Dalitz Model:

BR:

CP systematics

Systematics detailsStep 3


: Key Analysis Technique: Key Analysis Technique

2*2*BbeamES pEm −= **

beamB EEE −=D

Background Background

(spherical)

(jet-structure)

Event topology

Signal Signal

Exploit kinematics of e+e (4S) BB for signal selection


DD00 KKSS00ππ++ππ–– Dalitz Plot Dalitz Plot

analysisanalysis 270 fb-1Motivation: CKM angle γ using BD[KS0+–]K– decay

390K K*(892)-

ρ(770)

mm22(K(Kss00--))

mm22(K(Kss00++)) mm22((++--))

K*(892)+

DCSDCS


DD00→K→Kss00ππ++ππ-- (Isobar Model) (Isobar Model)

DCSDCS

DCSDCS

DCSDCS

(490, 406)(490, 406)(1024, 89)(1024, 89)

Important for Important for and D- and D-mixing mixing measurementmeasurements s

K*(892)K*(892)–– : 58 % : 58 %rr(770)(770)0 0 : 22 %: 22 %Non-Res.: 8 %Non-Res.: 8 % (500): 8 %(500): 8 %K*(1430)K*(1430)–– : 7 % : 7 %ff00(980): 6 %(980): 6 %

hep-ex/0607104hep-ex/0607104


The ‘Cartesian coordinates’ Goal: Fit the Dalitz plot distributions of D0KS from B-

and B+ decays to extract rB, B and Complication: The Maximum Likelihood fit overestimates

rB and underestimates the error of Solution: Write the Likelihood as a function of the

cartesian coordinates x±, y±:

( ( **2222 Im2Re2)()( −++−++−++++ ++++∝Γ ffyffxfyxfB

( ( **2222 Im2Re2)()( +−−+−−+−−−− ++++∝Γ ffyffxfyxfB

Likelihood is Gaussian and unbiased in x±, y±),( 22≡ mmA D mm

Strategy: Extract x±, y± from ML fit to the D0KS Dalitz plot and derive rB, B and from x±, y± with stat. procedure

)cos( mm BBrx =)sin( mm BBry =


DKS Dalitz plot distribution in signal region

B-D0K- B+D0K+

(x±,y±) are extractedfrom the D0KS Dalitz plot

B

B+ B-

B+

BD0K

CPVdirect 0sin2 ⇒≠= Br

2 1

D0

K

rb

(

deg)

347 106 BB

(5dim confidence intervals projections)

1 (2)

= (92 ± 41± 10± 13)= (92 ± 41± 10± 13)oo

(stat) (syst) (Dalitz)

hep-ex/0607104hep-ex/0507101

Used frequentist method to extract , rB,B from (x±,y±)

From x,y to


Sensitivity to over Dalitz plot Sensitivity varies strongly over Dalitz plane 2nd derivative of the log(L) event-by-event weighs the

event

*DCS (892)K −

0 *

0 *

Interference of [ ]

(suppressed) witA

h [ ]DS like

B D K K

B D K K

− − −

− − −

≡

→ →

→ →

2m−

2m

2

2

ln( )d Ld

weight =

22

2

1( ) ~ln( )d L

d

*0DCS (1430)K −

0 0 0SD K r→

events: points (weight = 1)

rB=0.12

=70°

B=180°

0 0 0

0 0 0

Interference of [ ]

with [GLW ke

]li

S

S

B D K K

B D K K

r

r

− −

− −

≡

→ →

→ →

*DCS (892)K −

Dalitz Plot Analysis of D 0 – + 0 Measurement of using B D – + 0 K Kalanand Mishra...

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Transcript of Dalitz Plot Analysis of D 0 – + 0 Measurement of using B D – + 0 K Kalanand Mishra...