19th July 2007CPWG1 Model independent determination of γ from B ± →D(K 0 S π + π − )K ± Jim...

19th July 2007 CPWG 1

Model independent determination of γ from B±→D(K0

Sπ+π−)K±

Jim Libby (University of Oxford)


Outline

Current e+e− B-factory and LHCb status Explanation of the model independent

method Implementation to LHCb environment and

results Background Acceptance

Experimental systematic uncertainties Conclusions


0D

)(GeV/ 22 cm

)/GeV( 2

2

c

m

Current status of this measurement of γ

Decays of D0 or D0 to common final state gives sensitivity to γ For B+→D(K0π+π-)K+

Assume model for amplitudes

Fit D-Dalitz plots from B-decay to extract γ, rB and δB

cbV

*usV

ubV

*csV

BAKDBA )( 0 )(0)( i

BB erAKDBA

),(),(

),(),(22)(22

22)(22

mmfermmfA

mmfermmfAi

B

iB

amplitudes Dalitz ),( and massinvariant 220mmfKm S

iN

jj

ij bemmAeammf j

1

2222 ,,

)(GeV/ 22 cm


Current results Current measurements:

BABAR and Belle use large samples of flavour tagged D*+D0π+

events to find parameters of the isobar model Model uncertainties from assumptions about the resonance

structure in the model NB scaled to the BELLE value of rB BABAR model error is ~6°

Recent studies for LHCb showed that the model-dependent fit would yield an uncertainty on γ between 7-12° for an rB=0.1 Range represents differing assumptions about the background Uncertainties 1/rB

However, the best current model uncertainty is 10° with an rB=0.1 Without improvements LHCb sensitivity will be dominated by

model assumptions within 1 or 2 years of data taking

[BABAR] model))(12)syst(11)stat(4192(

[Belle] model))(9)syst(3)stat(53( 15183


Pincer movement The largest and most challenging aspects of

the model uncertainty come from Kπ and ππ S-wave Lauren Martin (CPWG 24/05/07) investigating

these issues in the model-dependent fit A model-independent method that relies on a

binned analysis of the Dalitz plot Obvious problem is that information is lost via

binning Rest of this talk will discuss this method and its

first implementation at LHCb


Binned method Proposed in the original paper by Giri, Grossman, Soffer and Zupan

and since been extended significantly by Bondar and Poluektov GGSZ, PRD 68, 054018 (2003) BP, Eur. Phys. J. C47, 347 (2006) BP, hep-ph/0703267

If one bins the Dalitz plot symmetrically about m−

2= m+2 number of entries in B decay given by:

)(),(),(2

),(),(

222222

2222222

iiDD

DBDi

sycxdDmmfdDmmf

dDmmfrdDmmfN

ii

ii

# events in bin of flavour tagged D0 decays

)sin()cos( BBBB ryrx

Average cosine and sine of strong

phase difference between D0 and

D0 decay amplitudes (ΔδD) in this bin


Binned method continued The original GGSZ paper concentrated on trying to determine si

and ci at the same time as extracting γ, rB and δB from B data 3 + 2×Nbins free parameters (ci =c-i and si =−s-i) Huge loss in γ sensitivity and not practical until you have O(106)

events (cf 2500/fb-1 @ LHCb)

However, CP-correlated e+e−→ ψ″→D0D0 data where one decay is to KSππ and the other decays to a CP eigenstate or KSππ allows si and ci to be determined KL ππ equally sensitive

CLEO-c are collecting a ~750 pb-1 sample of ψ″ data at the moment – running at ψ″ will finish later this year Analyses underway to measure ci and si

Bondar and Poluektov estimate that the uncertainties on c i and si

from this data set will lead to 3° uncertainty on γ in a model dependent fit


Implementation to LHCb Bondar and Poluektov show

that the rectangular binning is far from optimal for both CLEOc and γ analyses 8 uniform bins has only

60% of the B statistical sensitivity

c and s errors would be 3 times larger from the ψ″

Best B-data sensitivity when cos(ΔδD) and sin(ΔδD) are as uniform as possible within a bin

Absolute value of strong phase diff(BABAR model used in LHCb-48-2007)

Good approximation and the binning that yields smallest s and c errors is equalΔδD bins-80% of the unbinned precision

NimmNi D /)(2),(/)(2 2122

21


Implementation at LHCb Generate samples of

B±→D(K0Sππ)K± with a mean of

5000 events split between the charges

Bin according to strong phase difference, ΔδD

Minimise χ2

(γ=60°, rB=0.1 and δB=130°)

data] gflavour ta from [measured ),(

factorion normalizat

2),,(

bin in events )( ofnumber

)),,(()),,((

222

2

th0

8

)0(8

222

dDmmfK

h

ysxcKKKrKhhyxN

iKKDBn

n

hyxNn

n

hyxNn

iDi

iiiiiBii

Si

ii i

ii

i

ii

Bin Ki,ci and si amplitudes calculated from model

In reality from flavour tagged samples and CLEO-c No attempt to add this uncertainty yet in detail take the BP 3°


No background with predicted 2 fb-1 yield

5000 experiments

γ=60°, rB=0.1 and δB=130°

The four Cartesian coordinates and normalization are free parameters

All pulls are normal therefore calculate γ, rB and δB with propagated Cartesian uncertainties


No background with predicted 2 fb-1 yield

Model independent average uncertainty 7.7° (c.f. Model dependent 5.9°)


Acceptance Acceptance in each bin calculated as a weighted average of the acceptance

function used for model dependent studies I will come back to the use of D amplitudes rather than B amplitudes for this relative differences in weighted efficiency below 3×10-3 in every bin

Modifies the fit function:

Average γ uncertainty increases to 8.1°

))(08.01(1028.0),( where),(),(

2),,(

22322

22222

2

mmmm

K

dDmmmmfa

ysxcKKKrKhahyxN

i

Di

iiiiiBiii

i


Background 3 types of background to consider

B→D(KSππ)π (DC04 B/S = 0.24) rB O(10-3) so Dalitz plots are like D0 and D0 for B− and B+, respectively

Combinatoric (DC04 B/S<0.7) Admixtures of two types considered

1. DKcomb: real D→ D(KSππ) combined with a bachelor K Dalitz plot a even sum of D0 and D0 decays

2. PScomb: combinatoric D with a bachelor K Follows phase space

Integrate background PDFs used in model-dependent analysis over each bin, then scaled to background level assumed:

iicomb

iiiiicomb

iii

PPSN

KaKaDKN

KaDN

)(

)()(

)(

21

fractional area of Dalitz space covered by bin


γ uncertainties with 5000 toy experimentsScenario 2 fb-1 Mod. Indep. 10 fb-1 Mod. Indep. 2 fb-1 Mod. Dep.

(LHCb-048-2007)

No background 7.9° 3.5° 5.9°

Acceptance 8.1° 3.5° 5.5°

Dπ (B/S = 0.24) 8.8° 4.0° 7.3°

DKcomb (B/S=0.7) 12.8° 5.7° 11.7°

PScomb (B/S=0.7) 12.8° 5.5° 9.1°

DKcomb (B/S=0.35)

+PScomb (B/S=0.35)

12.7° 5.4° 9.8°


Systematic related to acceptance The acceptance varies over the Dalitz plane The relative acceptance in each bin can be measured using the B→Dπ

control sample with DK selection applied without bachelor K PID

With the DC04 selection expect 60k events/2 fb-1

Relative relative-efficiency uncertainty 1-3%/ΔδD bin with 2 fb-1

Increased statistics reduces error Toy MC study smearing bin efficiencies in event generation by this amount

leads to an additional 1° uncertainty without background and 2.5° uncertainty with DKcomb B/S=0.7 Small effect compared to statistical uncertainty

NB: the efficiency related to the PID of the bachelor π/K can be factored out and will be determined from the D*→D(Kπ)π data to better than one percent-ignore at present

))D(KN(B),(),( 0

S

22222

i

i

i

Di KK

dDmmmmfa i


Asymmetry in efficiency in Dalitz space Concern was raised a while ago about

asymmetries in the efficiency across the Dalitz plane i.e. ε(m2

+, m2 −)≠ε(m2

−, m2 +)

Generated with the efficiency biased relative to one another by up to 10% depending on whether the event had m2

+>m2 − or m2

+<m2 −

Significant biases on x± and y± but they effectively cancel in determination of γ

Maximum bias on γ induced was 0.5° for 10% relative effect and full background


Resolution ΔδD binning has some narrow regions in

Dalitz space Preliminary investigation of how

resolution on the Dalitz variables might affected the extraction of γ

Assumed a 10 MeV2/c4 resolution on Dalitz variables and generated toy experiments with this smearing

Found that this led to a few bins with largest (red) and smallest (dark blue) phase difference having a 2-3% relative changes in expected yields due to resolution induced migration

Fit results on toy experiments where resolution included in generation but ignored in fit found no significant bias (<0.5°) on γ Cartesian coordinates exhibit bias but

cancels in extraction of γ


Background fractions Combinatoric background rate will be determined

from B and D mass sidebands which will cover at least 2-3 times the area of the signal region Use 10× in DC04 background studies but this will probably

be unrealistic with data If background distributions relatively flat in masses

one can estimate that this leads to B/S will be determined absolutely to around 0.01 or better

Toy studies suggest that there is no impact on γ precision with this kind of uncertainty

Maybe complications depending on Dalitz space distribution of the PS background but can only speculate until we have the data in hand


Conclusion Implemented model independent fit

with binning that yields smallest error from exploiting CLEO-c data Binning depends on model - only consequence

of incorrect model is non-optimal binning

Such a measurement will be better than model dependent method after one year of data taking if we can not improve the model error 10 fb-1 statistical uncertainty 4-6° depending on background assumptions

Experimental systematic uncertainties considered can be controlled from data Acceptance determined from B→Dπ sample will contribute ~2.5° with

2 fb-1

Liaison required with CLEO-c to get common binning and to best understand all uncertainties related to the ψ″ data Some further scope to optimise binning for combined statistical

sensitivity

Model independentModel dependent

σ(model)=10°

σ(model)=5°

19th July 2007CPWG1 Model independent determination of γ from B ± →D(K 0 S π + π − )K ± Jim...

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