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))
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 33/36/36
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
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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” !
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 55/36/36
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
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Kaon/Pion Discrimination: DIRCKaon/Pion Discrimination: DIRC
Cherenkov angle vs. momentum for pions and kaons
LAYOUT
>4 separationat 3 GeV/c
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 77/36/36
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 .
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 88/36/36
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.
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 99/36/36
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.
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 1010/36/36
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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 1111/36/36
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.
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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.
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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.
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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
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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
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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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 1717/36/36
⎪⎪⎩
⎪⎪⎨
⎧
−−
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
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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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 1919/36/36
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 → − *
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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 %
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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( 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
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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
––
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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.
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• 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
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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.
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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
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BR of BD–+0 K : PDF Shapes“Normalize” neural net variables q dq q’ = tanh(q – ½ (qmax+qmin) / ½(qmax – qmin)]
Signal
DE PDFs are Gaussians and 2nd-order polynomial:
Sig
Step 2
Fit BDKsample with DE, q, d
Obtain signal yield and asymmetry.
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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
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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 4242/36/36
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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 4343/36/36
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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 4444/36/36
Dalitz Model:
BR:
CP systematics
Systematics detailsStep 3
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 4545/36/36
: 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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 4646/36/36
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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 4747/36/36
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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 4848/36/36
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 =
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 4949/36/36
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
Kalanand MishraKalanand MishraPerugia, October 12, 2007Perugia, October 12, 2007 5050/36/36
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 −
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