Determination of γfrom - PPD · 19th December 2007 RAL Seminar 2 Outline Motivation for the...

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19th December 2007 19th December 2007 RAL Seminar RAL Seminar 1 1 Determination of Determination of γ γ from from B B ± ± DK DK ± ± : : LHCb and LHCb and CLEOc CLEOc Jim Libby (University of Oxford) Jim Libby (University of Oxford)

Transcript of Determination of γfrom - PPD · 19th December 2007 RAL Seminar 2 Outline Motivation for the...

Page 1: Determination of γfrom - PPD · 19th December 2007 RAL Seminar 2 Outline Motivation for the precise determination of γ LHCb –Overview –Status Measuring γwith B±→DK ± at

19th December 200719th December 2007 RAL SeminarRAL Seminar 11

Determination of Determination of γγ from from

BB±±→→DKDK±±: : LHCb and LHCb and CLEOcCLEOc

Jim Libby (University of Oxford)Jim Libby (University of Oxford)

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19th December 200719th December 2007 RAL SeminarRAL Seminar 22

OutlineOutline

�� Motivation for the precise Motivation for the precise

determination of determination of γγ

�� LHCbLHCb

–– OverviewOverview

–– StatusStatus

�� Measuring Measuring γγ withwith BB±±→→DKDK±± at LHCbat LHCb

�� Complementary measurements ofComplementary measurements of DDdecay at CLEOdecay at CLEO--cc

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19th December 200719th December 2007 RAL SeminarRAL Seminar 33

CPCP violation in weak violation in weak

decays of quarksdecays of quarks�� CPCP violation implies differences between violation implies differences between

mattermatter and and antimatterantimatter

�� In the Standard Model the weak and flavour In the Standard Model the weak and flavour

eigenstateseigenstates of the three generations of quarks of the three generations of quarks

are related by a unitary matrixare related by a unitary matrix

�� A complex phase introduces CP violating effectsA complex phase introduces CP violating effects

�� Represented in terms of the Represented in terms of the UnitarityUnitarity TriangleTriangle

∝=

tbtsi

td

cbcscd

iubusud

VVeV

VVV

eVVV

β

γ

CKMV

*cbcdVV

All sides and angles can be measured in b-hadron

decay

)(zℜ

)(zℑ

γ

γβπα −−=

β

*ubudVV *

tbtdVV

† 0ud ub cd cb td tbV V V V V V∗ ∗ ∗= ⇒ + + =CKM CKMV V Ι

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Searching for new physicsSearching for new physics

�� Non Standard Model particles Non Standard Model particles contribute within the contribute within the virtual loopsvirtual loops

�� Differences between treeDifferences between tree--level and level and looploop--level triangleslevel triangles

–– Signature of new physicsSignature of new physics

�� Complements direct searchesComplements direct searches

d

bB0 +

π

d

ue

e

ν

−W

d

b

B0 0B

d

b

−W

+Wt t

TREELOOP

d

b

B0 0B

d

b

−W~

+W~

t~ t~

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LHC StatusLHC Status

Latest official schedule (August ’07) had beam commissioning beginning inMay ’08, with then 2 months estimated before first 14 TeV collisionsSince then, there have been problems,eg. with shielding bellows in cold interconnects

Warm up of sector 7-8

Last dipole lowered April 26th this year!(First was in March 2005)

Last interconnect – Nov 2007

Quad triplet remediation – Sep 2007

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19th December 200719th December 2007 RAL SeminarRAL Seminar 66

The LHCb ExperimentThe LHCb Experiment�� Dedicated experiment for precision measurement of CP violation aDedicated experiment for precision measurement of CP violation and nd

rare decays of brare decays of b--hadrons (and charm) at the LHChadrons (and charm) at the LHC�� ColliderCollider--mode operation at same time as the generalmode operation at same time as the general--purpose detectors,purpose detectors,

with lesswith less--focused beams focused beams →→ most events have a single pp interaction most events have a single pp interaction

p

p

Interaction point

Dipole magnet

10 – 300 mrad forward acceptance

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LHCb in a slideLHCb in a slide

�� First level hardware trigger rate from 10First level hardware trigger rate from 10→→1 MHz1 MHz

–– 10 MHz the rate of bunch crossings with 1 or more interaction10 MHz the rate of bunch crossings with 1 or more interaction

–– Bunch crossing rate 30 MHz (offset interaction point)Bunch crossing rate 30 MHz (offset interaction point)

�� Software Higher Level Trigger (HLT): Software Higher Level Trigger (HLT):

–– inclusive and exclusive selections to reduce storage rate to 2 kinclusive and exclusive selections to reduce storage rate to 2 kHzHz

Muon DetectorTracking stations

TriggerTracking

interactionregion

�� pppp collisions at a collisions at a centre of mass centre of mass energy of 14 energy of 14 TeVTeV–– 101012 12 bbbb/year/year

�� Ring Imaging Ring Imaging CherenkovCherenkovdetectorsdetectors–– hadronhadron ID for ID for

momentum from momentum from 2 to 100 2 to 100 GeV/cGeV/c

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SiSi Vertex Locator (VELO)Vertex Locator (VELO)�� 21 stations of Si wafer pairs21 stations of Si wafer pairs

with with r r andand φφ strip readoutstrip readout

�� Split in two halves to allow Split in two halves to allow

retraction from beam lineretraction from beam line

–– When closed 8 mm from beamWhen closed 8 mm from beam

�� Both detector halves now Both detector halves now

completed, installed in the pit completed, installed in the pit

r-measuringφ-measuring

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19th December 200719th December 2007 RAL SeminarRAL Seminar 99

RICHRICH

Readout: Hybrid PhotoDiodes HPD– 1024 pixels – LHCb development

80mm

120m

m

RICH2

RICH1

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Status: RICH2 ready: full DAQ exercisedStatus: RICH2 ready: full DAQ exercised

RICH1: full commissioning early 2008RICH1: full commissioning early 2008

RICH DetectorsRICH Detectors3 radiators: RICH1 3 radiators: RICH1 AerogelAerogel (2(2--10 10 GeVGeV), C), C44FF1010 (10(10--60 60 GeVGeV))

RICH2 CFRICH2 CF44 (16(16--100 100 GeVGeV))

2GeV/c5.1 5.15 5.2 5.25 5.3 5.35 5.4 5.45 5.5

Cou

nts

0

50

100

150

200

250

300 -π +π → dB-π + K→ dB- K+ K→ sB- K+π → sB

- p K→ bΛ-π p → bΛ

ππ invariant mass

With PID

2MeV/c5100 5150 5200 5250 5300 5350 5400 5450 5500

Cou

nts

0

200

400

600

800

1000

1200 -π +π → dB-π + K→ dB- K+ K→ sB- K+π → sB

- p K→ bΛ-π p → bΛ

ππ invariant mass

No PID

K± identificationefficiency ~ 97%

π± misid rate ~ 5%

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Software trigger (HLT)

� Full detector info available, only limit is CPU time

� Use more tracking info to re-confirm L0+high IP

� Full event reconstruction: exclusive and inclusive

streams tuned for specific final states

Hardware trigger (L0)

� Fully synchronized (40 MHz), 4 µs fixed latency� High pT particles: µ, µµ, e, γ and hadron

� (typically pT ~1-4 GeV/c)

1 MHz (readout of all detector components)

≤ 2 kHz (storage: event size ~35kB)PC farm of ~1000 nodes

(multicore)

L0, HLT and L0×HLT efficiency

TriggerTriggerFull bandwidth for flavour unlike GPDs

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View of the cavernView of the cavern

It’s full!Installation of major structures is essentially complete

Will be ready for collision mid-2008

Muon detector

Calorimeters

RICH-2

Magnet

OT

VELO

RICH-1

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�� BB→→DKDK decays involve decays involve bb→→cc and and bb→→uu transitionstransitions

�� Access Access γγ via interference if Dvia interference if D00 and Dand D0 0 decay to the same final statedecay to the same final state

�� These measurements are theoretically cleanThese measurements are theoretically clean

–– No penguin No penguin ⇒⇒CKM standard candle CKM standard candle

–– largest correction is sublargest correction is sub--degree from Ddegree from D--mixingmixing

�� LHCb looking at a number of strategies to study such decaysLHCb looking at a number of strategies to study such decays

–– BB++: : AtwoodAtwood--DunietzDunietz--SoniSoni ('ADS'),('ADS'), 3 and 4 body 3 and 4 body DalitzDalitz Plot Anal.Plot Anal.

cbV

*usV

ubV

*csV

BAKDBA =→ −− )( 0 )(0)( γδ −−− =→ i

BB erAKDBA

Introduction Introduction BB±±→→DKDK±±

Ratio of absoluteamplitudes of

colour/CKM suppressed to favoured (~0.1)

Strong phasedifference

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�� For For BB++→→D(KD(K00ππ++ππ−− )K)K+ +

�� Assume isobar model (sum of Assume isobar model (sum of BreitBreit--WignersWigners))

�� Fit Fit DD--DalitzDalitz plots from plots from BB--decay to extractdecay to extract γγ, , rrBB and and δδBB

0D)/GeV(

2

2

c

m−

BB±±→→D(KD(K00SSππ

++ππ−−)K)K±±

),(),(

),(),(22)(22

22)(22

+−+

−++

−++−

+−−

+=

+=

mmfermmfA

mmfermmfAi

B

iB

δγ

δγ

amplitudes Dalitz ),( and massinvariant 220m

mmfKm S ±±=

±π

( ) ( ) βα iN

jj

ij bemmAeammf j +

= ∑

=−+−+

1

2222 ,,)(GeV/ 22 cm+

K*(892)

ρ(770)

Number of resonances

Amplitude and phase extracted from D*+→D0π+ sample at B-factories

Rel. BW

Non-resonant

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Current eCurrent e++ee−− resultsresults

�� Current best direct constraints on Current best direct constraints on γγ::

�� Based on ~300 events each (1/3 of final data set)Based on ~300 events each (1/3 of final data set)

�� However, large error from isobar model assumptionsHowever, large error from isobar model assumptions

�� BABAR and Belle use large samples of flavour tagged BABAR and Belle use large samples of flavour tagged D*D* ++→→DD00ππ++

events to find parameters of the isobar modelevents to find parameters of the isobar model–– Excellent knowledge of Excellent knowledge of ||ff||22 but phases less well knownbut phases less well known

�� Model uncertainties from assumptions about the resonance Model uncertainties from assumptions about the resonance structures in the modelstructures in the model

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

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

o

o

±±±=

±±= +−

γφ

PRD 73, 112009 (2006)hep-ex/0607104

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K*0(1430)

Isobar model uncertaintyIsobar model uncertainty

�� Most challenging aspects Most challenging aspects

of the model uncertainty of the model uncertainty

come from Kcome from Kππ and and ππππ SS--

wavewave

BABAR (PRL 95 121802,2005)

Fit to flavour tag sample

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BB±±→→D(KD(K00SSππ

++ππ−−)K)K±± at LHCbat LHCb

�� Simulation studies performed to determine the Simulation studies performed to determine the expected yields and backgrounds at LHCbexpected yields and backgrounds at LHCb–– One One ‘‘nominalnominal’’ year of datayear of data--taking 2 fbtaking 2 fb--1 1

–– Total luminosity goal 10 fbTotal luminosity goal 10 fb--11

�� Selection studies performed on Selection studies performed on PYTHIA/EVTGEN/GEANT4 simulated samples of PYTHIA/EVTGEN/GEANT4 simulated samples of signal and background eventssignal and background events

�� Limited statistics available for background estimates Limited statistics available for background estimates

–– 34 million 34 million bb--inclusive events corresponds to ~15 inclusive events corresponds to ~15 minutes of data taking at nominal luminosityminutes of data taking at nominal luminosity

�� Trigger simulation is applied for LevelTrigger simulation is applied for Level--0 and large 0 and large impact parameter with impact parameter with ppt t HLTHLT

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19th December 200719th December 2007 RAL SeminarRAL Seminar 1818

BB±±→→D(KD(K00SSππ

++ππ−−)K)K±± at LHCbat LHCb

�� Selection based on Selection based on

large impact parameter, large impact parameter,

RICH particle ID and RICH particle ID and

good p resolutiongood p resolution

�� Efficiency =Efficiency = 0.70.7××1010--33

�� Backgrounds:Backgrounds:

–– BB±±→→D(KD(K00SSππ

++ππ−− ))ππ±±

B/S=0.24B/S=0.24

–– CombinatoricCombinatoric

B/S<0.7 at 90% B/S<0.7 at 90% c.lc.l..

σ=15 MeV

5000 events/2fb-1

(LHCb(LHCb--048048--2007)2007)

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19th December 200719th December 2007 RAL SeminarRAL Seminar 1919

Model uncertainty impact on LHCbModel uncertainty impact on LHCb

�� The modelThe model--dependent likelihood fit yields an dependent likelihood fit yields an uncertainty onuncertainty on γγ between between 77--1212°° for anfor an rrBB=0.1=0.1–– Range represents differing assumptions about the backgroundRange represents differing assumptions about the background

�� However, the current model uncertainty is 10However, the current model uncertainty is 10--1515°° with an with an rrBB=0.1=0.1–– Uncertainties Uncertainties ∝∝1/1/rrBB

�� Without improvements LHCb sensitivity Without improvements LHCb sensitivity will be dominatedwill be dominated by model assumptions by model assumptions within 1 year of data takingwithin 1 year of data taking

�� Motivates a modelMotivates a model--independent method that independent method that relies on a binned analysis of the relies on a binned analysis of the DalitzDalitz plotplot–– Disadvantage is that information is lost via Disadvantage is that information is lost via binningbinning

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19th December 200719th December 2007 RAL SeminarRAL Seminar 2020

)(),(),(2

),(),(

222222

2222222

iiDD

DBDi

sycxdDmmfdDmmf

dDmmfrdDmmfN

ii

ii

−−−++−

−++−−

++

+∝

∫∫

∫∫Average cosine and

sine of strong phase difference between D 0 and

D0 decay amplitudes (∆δD) in this bin

Binned methodBinned method

�� Proposed in the original paper by Proposed in the original paper by GiriGiri, Grossman, , Grossman, SofferSoffer and and ZupanZupan

and since been extended significantly by and since been extended significantly by BondarBondar and and PoluektovPoluektov–– GGSZ, PRD GGSZ, PRD 6868, 054018 (2003), 054018 (2003)

–– BP, most recently arXiv:0711.1509v1 [hepBP, most recently arXiv:0711.1509v1 [hep--ph]ph]

�� Bin the Bin the DalitzDalitz plot symmetrically plot symmetrically

about mabout m−−22= m= m++

2 2 then number of entries in Bthen number of entries in B−−

decay given by:decay given by:

∝ # events in bin of flavour tagged D0 decays

s'coordinateCartesian '

)sin()cos( γδγδ ±=±= ±± BBBB ryrx

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19th December 200719th December 2007 RAL SeminarRAL Seminar 2121

Binned method continuedBinned method continued

�� Can determine Can determine ssii and and cci i at at the same time as extracting the same time as extracting γγ, , rrB B and and δδB B from from B B datadata–– 3 + 3 + NNbinsbinsfreefree parameters (parameters (ccii ==cc--ii

and and ssii ==−−ss--ii))–– Huge loss in Huge loss in γγ sensitivity not sensitivity not

practical until you have O(10practical until you have O(1066) ) events (2500/fbevents (2500/fb--11 @ LHCb)@ LHCb)

�� However, However, CPCP--correlated correlated ee++ee−−→→ ψ″→ψ″→DD00DD00 datadata where where oneone decay is todecay is to KKSSππππ and the and the other decays to a CP other decays to a CP eigenstateeigenstate andand KKSSππππ allowsallows cciiand and ssii to be determined, to be determined, respectivelyrespectively

0D 0D

0even-CPD 0

odd-CPD

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19th December 200719th December 2007 RAL SeminarRAL Seminar 2222

Enter CLEOEnter CLEO--cc

CLEO is the grand-daddy of flavourphysics, with history of achievementdating back over 25 years

Cornell University, Ithaca NY, USA

CLEO-c is latest incarnation.Dedicated programme of data-takingat and above the cc threshold Important studies for LQCD and B physics

Oxford LHCb physicists (with Bristol) have joined CLEO-c in order to measure quantities essential for the γ studies

CESR

CLEO-c

Friedmanwrestling

centre

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19th December 200719th December 2007 RAL SeminarRAL Seminar 2323

CLEOCLEO--c detectorc detector

ZD drift chamber

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CLEOCLEO--c data samplesc data samplesCLEOCLEO--c: Oct. 2003 c: Oct. 2003 –– April FoolApril Fool’’s Day 2008s Day 2008

3686MeV3686MeV, 54 , 54 pbpb--11, N(, N(ψψ(2S)(2S)))≈≈27M 27M ee++ee−−→→ ψψ(2S) (2S) →→ ππππ J/J/ψψ, , γγγγγγγγχχχχχχχχc c etc.etc.

3773MeV3773MeV, , 800pb800pb--1 1 delivered, ~3delivered, ~3 milionmilion ψψ(3770)(3770) →→DD00DD00

4170MeV4170MeV, 195 , 195 pbpb--1 1 →→ ~ 300pb~ 300pb--1 1 →→moremore→→ ~720pb~720pb--11, , DD(s(s))((**))DD((ss))

((**))

39703970––4260MeV4260MeV energy scan, energy scan, 60pb60pb--11 in 12 pointsin 12 points

PDG-2006

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CLEOCLEO--c: double tagged c: double tagged ψψ(3770) events(3770) events

[ ]0000

21 DDDDee −→′′→−+ ψ

CLEO-c has collected ~ 800 fb-1 at the ψ (3770)

DDbar produced in quantum entangled state:

Reconstruct one D in decay of interest for γanalysis (eg. Kππ), & other in CP eigenstate(eg. KK, Ksπ

0 …) then CP of other is fixed.

⇐⇐⇐⇐Almost background free

Can use KL⇒⇒⇒⇒

From talk by E. Whiteat Charm 07

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CLEOCLEO--c measurement statusc measurement status

Studies not complete but projected uncertainties

on c and s will lead to 3-5 degree uncertainty on γ

1/3 of total data(<1/2 the CP tags)

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Inkblot testInkblot test

�� BondarBondar and and PoluektovPoluektov show show that the rectangular binning that the rectangular binning is far from optimal for both is far from optimal for both CLEOcCLEOc and and γγ analysesanalyses

–– 16 uniform bins has only 16 uniform bins has only 60% of the B statistical 60% of the B statistical sensitivitysensitivity

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

�� Best BBest B--data sensitivity data sensitivity when when coscos((∆δ∆δDD)) and sin(and sin(∆δ∆δDD)) are are as uniform as possibleas uniform as possiblewithin a binwithin 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 equal∆δD bins-80% of the unbinned precision

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

21 +<∆<− −+ πδπ

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Implementation at LHCbImplementation at LHCb

�� Generate samples of Generate samples of

BB±±→→D(KD(K00SSππππ)K)K

±± with a mean of with a mean of

5000 events split between the 5000 events split between the

chargescharges

�� Bin according to strong phase Bin according to strong phase

difference, difference, ∆δ∆δDD⇒⇒

�� Minimise Minimise χχ22

(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

−+±

±±−±±±±

±−+±±

≠−=−

−−−−

+++

++

=

=±++=

→=

−+−=

m

ππ

χ

� Ki, ci and si amplitudes calculated from model

� In reality from flavour tagged samples and CLEO-c

(rad)Dδ∆-6 -4 -2 0 2 4 6

/4πE

ntrie

s/

0

100

200

300

400

500

(rad)Dδ∆-

-B+B

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No background with No background with

predicted 2 fbpredicted 2 fb--1 1 yieldyield

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

)° (γ20 30 40 50 60 70 80 90 100

°E

ntrie

s/2

0

100

200

300

400

500Mean 60.49

RMS 7.854

)° (γσ0 2 4 6 8 10 12 14 16 18 20

°E

ntrie

s/0.

5

0

100

200

300

400

500

600

700

800

900Mean 7.771

RMS 1.268

Pullγ-4 -3 -2 -1 0 1 2 3 4 5 6

Ent

ries/

0.2

0

50

100

150

200

250

300

350

400 Mean 0.04484

RMS 1.048

Br0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

-310×

Ent

ries/

4

0

100

200

300

400

500

600

Mean 0.1017

RMS 0.0131

Brσ

0 0.005 0.01 0.015 0.02

-410×

Ent

ries/

40

200

400

600

800

1000

1200

1400

1600

1800

2000Mean 0.01272

RMS 0.001684

PullBr-4 -3 -2 -1 0 1 2 3 4 5 6

Ent

ries/

0.2

0

50

100

150

200

250

300

350

400 Mean 0.1431

RMS 1.023

5000 experiments

Input parametersγ=60°, rB=0.1 and δB=130°

γ σ(γ) Pull

rB σ(rB) Pull

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19th December 200719th December 2007 RAL SeminarRAL Seminar 3030

γγ uncertainties with 5000 uncertainties with 5000

toy experimentstoy experiments

11.711.7°°5.75.7°°12.812.8°°DKDKcombcomb(B/S=0.7)(B/S=0.7)

(Worst case scenario)(Worst case scenario)

7.37.3°°4.04.0°°8.88.8°°DDππ (B/S = 0.24)(B/S = 0.24)

(Best case scenario)(Best case scenario)

5.55.5°°3.53.5°°8.18.1°°AcceptanceAcceptance

5.95.9°°3.53.5°°7.97.9°°No backgroundNo background

2 fb2 fb--1 1 Mod. Dep. Mod. Dep. (LHCb(LHCb--048048--2007)2007)

10 fb10 fb--1 1 Mod. Mod. IndepIndep..2 fb2 fb--1 1 Mod. Mod. IndepIndep..ScenarioScenario

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19th December 200719th December 2007 RAL SeminarRAL Seminar 3131

)-1Int. luminosity (fb1 2 3 4 5 6 7 8 9 10

)° (

mod

el(C

P)

σ⊕

stat

σ

0

2

4

6

8

10

12

14

16

18

20

BB±±→→D(KD(K00SSππ

++ππ−−)K)K±± at LHCbat LHCb

�� Model independent fit with binning Model independent fit with binning that yields smallest error that yields smallest error from exploiting CLEOfrom exploiting CLEO--c datac data–– Binning depends on model Binning depends on model -- only only consequence of incorrect model consequence of incorrect model is nonis non--optimal binning and a loss optimal binning and a loss of sensitivityof sensitivity

�� Measurement has no troublesome and hardMeasurement has no troublesome and hard--toto--quantify systematic quantify systematic and outperforms modeland outperforms model--dependent approach with full LHCb dataset dependent approach with full LHCb dataset with currently assigned model errorwith currently assigned model error–– 10 fb10 fb--1 1 statistical uncertainty 4statistical uncertainty 4--66°° depending on backgrounddepending on background

�� CLEOCLEO--c measurements essential to validation of c measurements essential to validation of assumptions in model dependent measurementassumptions in model dependent measurement

�� LHCbLHCb--20072007--141 141 –– Available via CERN document server Available via CERN document server

Model independentModel dependent

σ(model)=10°

σ(model)=5°

Page 32: Determination of γfrom - PPD · 19th December 2007 RAL Seminar 2 Outline Motivation for the precise determination of γ LHCb –Overview –Status Measuring γwith B±→DK ± at

19th December 200719th December 2007 RAL SeminarRAL Seminar 3232

ADSADS

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19th December 200719th December 2007 RAL SeminarRAL Seminar 3333

�� Look at DCS and CF decays of D to Look at DCS and CF decays of D to obtain obtain rates that have enhanced rates that have enhanced interference termsinterference terms

�� Unknowns : Unknowns : rrBB~0.1, ~0.1, δδBB, , δδDDKKππ, , γγ, , NNKKππ, , NNhhhh ((rrDD=0.06=0.06 well measured)well measured)

�� With knowledge of the relevant efficiencies and With knowledge of the relevant efficiencies and BRsBRs, the normalisation , the normalisation constants constants ((NNKKππ, , NNhhhh) can be related to one another) can be related to one another

�� Important constraint from Important constraint from CLEOcCLEOc σσ((coscosδδDDKKππ)=0.1)=0.1−−0.20.2�� OverconstrainedOverconstrained: 6 observables and 5 unknowns: 6 observables and 5 unknowns

)cos(21))((

)cos(21))((

)cos(2)())((

),cos(2)(1))((

),cos(2)())((

),cos(2)(1))((

2

2

22

2

22

2

γδγδ

γδδπγδδπγδδπγδδπ

πππ

πππ

πππ

πππ

+++∝→Γ

−++∝→Γ

++++∝→Γ

+−++∝→Γ

−+++∝→Γ

−−++∝→Γ

+−++

−−+−

++−+

+−++

−−+−

−+−−

BBBD

BBBD

KDB

KDB

KDBD

KDB

KDB

KDBD

KDB

KDB

KDBD

KDB

KDB

KDBD

rrKhhB

rrKhhB

rrrrKKB

rrrrKKB

rrrrKKB

rrrrKKB

ADS methodADS method

h=π or K

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19th December 200719th December 2007 RAL SeminarRAL Seminar 3434

Expected yieldsExpected yields

�� ADS measurement is a counting experiment ADS measurement is a counting experiment -- but but suppressed modes have ~10suppressed modes have ~10--77 BRsBRs–– Principal challenge background suppressionPrincipal challenge background suppression

�� Detailed selections studies as for Detailed selections studies as for DalitzDalitz analysisanalysis–– LHCbLHCb--20062006--066066

�� The suppressed modes have yields varying from 0 The suppressed modes have yields varying from 0 to 500 depending on the strong parametersto 500 depending on the strong parameters–– 780 background events predicted 780 background events predicted

1.81.8

0.60.6

B/SB/S

50050082008200BB±±→→(h(h−−hh++))DDKK±±

4000400056,00056,000BB±±→→(K(K±±ππ ))DDKK±±

BB--factory yields factory yields

(~1/4 final data set)(~1/4 final data set)

Signal yield/2 Signal yield/2

fbfb--11ChannelChannel

±

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19th December 200719th December 2007 RAL SeminarRAL Seminar 3535

Sensitivity from 2Sensitivity from 2--bodybodyδD= -25o – fit results from 1000 toy 2 fb-1 experiments :

9.49.49.39.38.68.68.68.67.57.58.68.69.59.5σσσσσσσσγγγγγγγγ ((°°))

252516.616.68.38.300--8.38.3--16.616.6--2525δδδδδδδδDD ((°°))

Br0 0.05 0.1 0.15 0.2

Ent

ries/

0.00

4

0

50

100

150

200

250

)° (B

δ90 100 110 120 130 140 150 160 170

°E

ntrie

s/2

0

10

20

30

40

50

60

70

80

(πK

δ-80 -60 -40 -20 0 20 40 60 80

°E

ntrie

s/3

0

50

100

150

200

250

)°(γ20 30 40 50 60 70 80 90 100

°E

ntrie

s/2

0

20

40

60

80

100

δδδδδδδδDD constraint leads to constraint leads to

a 0.5a 0.5--1.01.0°°°°°°°° reduction reduction

in in σσσσσσσσγγγγγγγγ

Also important for D Also important for D

mixing mixing

measurementsmeasurements

γδD

δBrB

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19th December 200719th December 2007 RAL SeminarRAL Seminar 3636

FourFour--body ADSbody ADS�� BB→→D(K D(K ππππππ)K )K can also be used for ADS style analysiscan also be used for ADS style analysis

�� Similar yields to 2Similar yields to 2--body body –– slightly worse B/Sslightly worse B/S–– LHCbLHCb--20072007--004004

�� However, need to account for the resonant substructure in However, need to account for the resonant substructure in DD→→KKππππππ–– made up of made up of DD→→K*K* ρρ, K, K−−aa11(1260)(1260)++,.,,.,……

–– in principle each point in the phase space has a different stronin principle each point in the phase space has a different strong phase g phase associated with it associated with it -- 3 and 4 body 3 and 4 body DalitzDalitz plot analyses exploit this very plot analyses exploit this very fact to extract fact to extract γγ from amplitude fitsfrom amplitude fits

�� Atwood and Atwood and SoniSoni ((hephep--ph/ph/0304085) show how to modify the usual 0304085) show how to modify the usual ADS equations for this caseADS equations for this case–– Introduce Introduce coherence parameter coherence parameter RRK3K3ππwhich dilutes interference term which dilutes interference term

sensitive to sensitive to γγ

�� RRK3K3ππ ranges from ranges from �� 1=coherent (dominated by a single mode) to 1=coherent (dominated by a single mode) to

�� 0=incoherent (several significant components)0=incoherent (several significant components)

�� Can slice and dice phase space to find most coherent regionsCan slice and dice phase space to find most coherent regions

)cos(2)())(( 33

3232 γδδπππ ππ

ππ −+++∝→Γ −+−−+− KDBK

KDB

KDBD RrrrrKKB

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19th December 200719th December 2007 RAL SeminarRAL Seminar 3737

�� Measurements of the rate of K3Measurements of the rate of K3ππ versus different tags at CLEOversus different tags at CLEO--c allows c allows

direct access todirect access to RRK3K3ππ andand δδK3K3ππ

1.1. Normalisation from CF KNormalisation from CF K−−ππ++ππ++ππ−− vs. Kvs. K++ππ−−ππ−−ππ++ and Kand K−−ππ++ππ++ππ−− vs. Kvs. K++ππ−−

2.2. CP CP eigenstateseigenstates::

3.3. KK−−ππ++ππ++ππ−− vs. Kvs. K−−ππ++ππ++ππ−−::

4.4. KK−−ππ++ππ++ππ−− vs. Kvs. K−−ππ++::

Determining the coherence factorDetermining the coherence factor

( )[ ]ππ

πππ δπ 3

3323

3 cos21):3( KDK

KD

KDCP

CFK RrrCPK m+ΓΓ=±Γ

00--40 per mode 40 per mode K3K3ππ//KKππ DCSDCS

200200ππ++ππ−−

500500KK ++KK −−

650650KK 00SSππ

00

50005000KKππ CFCF

37003700K3K3ππ CFCF

Expected 800 pbExpected 800 pb−−1 1 yieldyieldK3K3ππ tag sidetag side

[ ]233 3

1)3:3(πππππ

KRKK DCS

KCFK −ΓΓ=Γ −−

( )

++ΓΓ≈Γ −− π

ππ δππππ

π

π

π 32

33 cos21):3(3

33 KDr

r

r

rDCSK

CFK K

KD

KD

KD

KD RKK

ππ ~ Assume KDδ

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19th December 200719th December 2007 RAL SeminarRAL Seminar 3838

Determining the Determining the

coherence factorcoherence factor�� Analysis underway 10% effects in CP Analysis underway 10% effects in CP

modes so great care withmodes so great care with

–– Background subtractionBackground subtraction

–– Efficiency calculation Efficiency calculation

�� Estimate of current sensitivity with the Estimate of current sensitivity with the addition of addition of KK00

LLππ0 0 and fand further CP tags i.e.urther CP tags i.e.

KK00SSηη to be addedto be added

�� Further information in mixed CP SCS tags Further information in mixed CP SCS tags such assuch as KK00

SSππ++ππ−−

� σσσσstat ~ 0.1 with 800 pb-1

�� Binned analysis to determine the most Binned analysis to determine the most coherent regionscoherent regions

δD

K3π

RK3π

Excluded bylikesign

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19th December 200719th December 2007 RAL SeminarRAL Seminar 3939

ConclusionConclusion--LHCbLHCb

�� LHCb has estimated 2 fbLHCb has estimated 2 fb--11 sensitivity to sensitivity to γγ in in BB±±→→DKDK±± withwith–– DD→→KK00

SSππ++ππ−− -- σσγγ =7=7--1212°°

–– DD→→KK−−ππ+ + and and DD→→hh++hh−− -- σσγγ =7.5=7.5--9.59.5°°–– DD→→KK−−ππ++ππ++ππ−− will add additional informationwill add additional information

�� Not the whole story with theoretically clean Not the whole story with theoretically clean measurements:measurements:–– BB00→→DKDK* * σσγγ ~ 9~ 9°° [LHCb[LHCb--20072007--050]050]–– BBss→→DDssKK σσγγ++φφs s ~ 10~ 10°° [LHCb[LHCb--20072007--041]041]

�� A few degree precision onA few degree precision on γγ by the end of by the end of LHCbLHCb

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4040

Conclusion Conclusion CLEOcCLEOc

�� CLEOCLEO--c measurements essential to fulfilling c measurements essential to fulfilling this goalthis goal

�� But there is much more that can be doneBut there is much more that can be done

�� Full amplitude analysis of 4Full amplitude analysis of 4--body should yield body should yield ultimate precision ultimate precision –– Need DCS model, which can be accessed via CP tags at Need DCS model, which can be accessed via CP tags at

CLEOcCLEOc

–– Also will guide division of phase space for binned Also will guide division of phase space for binned coherence factor analysiscoherence factor analysis

�� Other modes that can be used:Other modes that can be used:–– DD→→KK−−ππ+ + ππ0 0 (Coherence analysis underway)(Coherence analysis underway)–– DD→→KK00

SSKK++KK−− and and DD→→KK00

SSKK++ππ−−

–– DD→→KK−−KK++ππ++ππ−− and and DD→→KK00SSππ

−− ππ+ + ππ0 0

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4141

Additional slidesAdditional slides

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4242

)4/c2 (GeV2ππm

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

|Sum

(BW

)|

0

20

40

60

80

100

Aside: KAside: K--matrix matrix

�� BreitBreit WignerWigner description of broad description of broad overlapping resonances overlapping resonances violates violates unitarityunitarity and requires nonand requires non--physical physical σσ′′

�� KK--matrix description preserves matrix description preserves unitarityunitarity

�� First studies (Lauren Martin/JL) of First studies (Lauren Martin/JL) of LHCb LHCb γγ fit with one Kfit with one K--matrix matrix parameterisation of the parameterisation of the ππππ SS--wave wave –– Difference between assuming KDifference between assuming K--

matrix and BW model consistent with matrix and BW model consistent with BB--factory observationsfactory observations

–– Draft available from CPWG webpageDraft available from CPWG webpage

�� Explore different physical KExplore different physical K--matrix matrix parameterisation to evaluate parameterisation to evaluate systematic rather than introduce systematic rather than introduce σσ′′will reduce model uncertaintywill reduce model uncertainty

σ

(GeV)ππ2M

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 22

|F1|

0

20

40

60

80

100

120

140

160

5 pole K-matrix

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4343

No background with No background with

predicted 2 fbpredicted 2 fb--1 1 yieldyield5000 experiments

Input parametersγ=60°, rB=0.1 and δB=130°

The four Cartesian coordinates and normalization are free parameters

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

pull-x-4 -3 -2 -1 0 1 2 3 4 5 6

Ent

ries/

0.2

0

50

100

150

200

250

300

350

400

/ ndf 2χ 28.62 / 37

Constant 7.0± 396.4 Mean 0.01421± 0.04355 Sigma 0.010± 1.001

pull-y-4 -3 -2 -1 0 1 2 3 4 5 6

Ent

ries/

0.2

0

50

100

150

200

250

300

350

400 / ndf 2χ 32.91 / 35

Constant 6.7± 384.3

Mean 0.01466± 0.01154

Sigma 0.01± 1.03

pull+x-4 -3 -2 -1 0 1 2 3 4 5 6

Ent

ries/

0.2

0

50

100

150

200

250

300

350

400 / ndf 2χ 70.26 / 42

Constant 7.0± 384.7

Mean 0.01455± 0.03719

Sigma 0.011± 1.012

pull+

y-4 -3 -2 -1 0 1 2 3 4 5 6

Ent

ries/

0.2

0

50

100

150

200

250

300

350

400 / ndf 2χ 60.92 / 42

Constant 6.9± 375.9

Mean 0.01483± -0.04989

Sigma 0.012± 1.034

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4444

Toy experiment results: Toy experiment results: γγ (2 fb(2 fb−−11))

1.041.040.0490.049±±0.0150.01512.612.612.712.760.760.7±±0.20.2DDππ + + DK+ DK+ PS (50:50) PS (50:50) (B/S=0.7)(B/S=0.7)

1.051.050.0640.064±±0.0150.01512.512.512.812.860.860.8±±0.20.2DDππ + + PS PS (B/S=0.7)(B/S=0.7)

1.111.110.0490.049±±0.0160.01612.212.212.812.860.760.7±±0.20.2DDππ + + DK DK (B/S=0.7)(B/S=0.7)

1.041.040.0880.088±±0.0150.0158.88.88.88.860.760.7±±0.10.1DDππ

1.071.070.0750.075±±0.0150.0157.87.88.18.160.760.7±±0.10.1AccAcc

1.051.050.0450.045±±0.0150.0157.87.87.97.960.560.5±±0.10.1No No bckbck

Pull RMSPull RMSMean pullMean pullMean Mean σσRMSRMSMeanMeanScenarioScenario

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4545

Toy experiment results: Toy experiment results: γγ (10 fb(10 fb−−11))

0.970.970.0380.038±±0.0150.0155.65.65.45.460.2260.22±±0.080.08DDππ + + DK+ DK+ PS (50:50) PS (50:50) (B/S=0.7)(B/S=0.7)

1.001.000.0450.045±±0.0150.0155.55.55.55.560.2660.26±±0.080.08DDππ + + PS PS (B/S=0.7)(B/S=0.7)

1.011.010.0300.030±±0.0150.0155.75.75.75.760.1860.18±±0.080.08DDππ + + DK DK (B/S=0.7)(B/S=0.7)

1.031.030.0540.054±±0.0150.0153.93.94.04.060.2260.22±±0.060.06DDππ

1.011.010.0360.036±±0.0150.0153.43.43.53.560.1360.13±±0.050.05AccAcc

1.031.030.0500.050±±0.0150.0153.43.43.53.560.1760.17±±0.050.05No No bckbck

Pull RMSPull RMSMean pullMean pullMean Mean σσRMSRMSMeanMeanScenarioScenario

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4646

Toy experiment results: Toy experiment results: rr BB (2 fb(2 fb−−11))

0.980.980.1860.186±±0.0150.0150.0200.0200.0200.0200.10380.1038±±0.00030.0003DDππ + + DK+ DK+ PS (50:50) PS (50:50) (B/S=0.7)(B/S=0.7)

0.990.990.1750.175±±0.0150.0150.0190.0190.0200.0200.10350.1035±±0.00030.0003DDππ + + PS PS (B/S=0.7)(B/S=0.7)

1.161.160.2150.215±±0.0160.0160.0200.0200.0200.0200.10310.1031±±0.00030.0003DDππ + + DK DK (B/S=0.7)(B/S=0.7)

1.021.020.1230.123±±0.0150.0150.0140.0140.0140.0140.10150.1015±±0.00020.0002DDππ

1.131.130.1750.175±±0.0160.0160.0130.0130.0140.0140.10170.1017±±0.00020.0002AccAcc

1.021.020.1430.143±±0.0150.0150.0130.0130.0130.0130.10170.1017±±0.00020.0002No No bckbck

Pull RMSPull RMSMean pullMean pullMean Mean σσRMSRMSMeanMeanScenarioScenario

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4747

Toy experiment results: Toy experiment results: rr BB (10 fb(10 fb−−11))

0.980.980.0770.077±±0.0150.0150.0090.0090.0090.0090.10070.1007±±0.00010.0001DDππ + + DK+ DK+ PS (50:50) PS (50:50) (B/S=0.7)(B/S=0.7)

0.990.990.0930.093±±0.0150.0150.0090.0090.0090.0090.10080.1008±±0.00010.0001DDππ + + PS PS (B/S=0.7)(B/S=0.7)

0.970.970.1010.101±±0.0150.0150.0090.0090.0090.0090.10090.1009±±0.00010.0001DDππ + + DK DK (B/S=0.7)(B/S=0.7)

0.980.980.0490.049±±0.0150.0150.0060.0060.0060.0060.10030.1003±±0.00010.0001DDππ

1.011.010.0510.051±±0.0150.0150.0060.0060.0060.0060.10030.1003±±0.00010.0001AccAcc

1.001.000.0560.056±±0.0150.0150.0060.0060.0060.0060.10030.1003±±0.00010.0001No No bckbck

Pull RMSPull RMSMean pullMean pullMean Mean σσRMSRMSMeanMeanScenarioScenario

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4848

AcceptanceAcceptance

�� Acceptance in each bin calculated as a weighted average of the Acceptance in each bin calculated as a weighted average of the acceptance function used for model dependent studiesacceptance function used for model dependent studies–– 15% relative difference amongst bins15% relative difference amongst bins

�� Modifies the fit function:Modifies the fit function:

�� Average Average γγ uuncertainty increases to 8.1ncertainty increases to 8.1°°

( )[ ]

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

2),,(

22322

22222

2

−+−

−+

−+−+

±±−±±±±±

+−×==

±++=

∫mmmm

K

dDmmmmf

ysxcKKKrKhhyxN

i

Di

iiiiiBiii

i εε

ε

εmCan be

calculatedfrom Dπ

)° (γ20 30 40 50 60 70 80 90 100

°E

ntrie

s/2

0

100

200

300

400

500

Mean 60.68

RMS 8.102

)° (γσ0 2 4 6 8 10 12 14 16 18 20

°E

ntrie

s/0.

5

0

100

200

300

400

500

600

700

800

900

Mean 7.805

RMS 1.362

Pullγ-4 -3 -2 -1 0 1 2 3 4 5 6

Ent

ries/

0.2

0

50

100

150

200

250

300

350

400

Mean 0.07258

RMS 1.066

γ σ(γ) Pull

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19th December 200719th December 2007 RAL SeminarRAL Seminar 4949

Background Background

�� 3 types of background to consider 3 types of background to consider

–– BB→→D(KD(KSSππππ))ππ (B/S = 0.24)(B/S = 0.24)

�� rrBB(D(Dππ)) O(10O(10--33) ) so so DalitzDalitz plots are likeplots are like DD00 andand DD00 forfor BB−− andand BB++ ,,respectivelyrespectively

–– CombinatoricCombinatoric (B/S<0.7)(B/S<0.7)--mixtures of two types consideredmixtures of two types considered

1.1. DKDKcombcomb: real : real DD→→ D(KD(KSSππππ)) combined with a bachelor combined with a bachelor KK

��DalitzDalitz plot an even sum of plot an even sum of DD00 andand DD00 decaysdecays

2.2. PSPScombcomb:: combinatoriccombinatoric DD with a bachelor with a bachelor KK

��Follows phase spaceFollows phase space

�� Integrate background Integrate background PDFsPDFs used in modelused in model--dependent analysis over each dependent analysis over each

bin, then scaled to background level assumed:bin, then scaled to background level assumed:

iicomb

iiiiicomb

iii

PPSN

KKDKN

KDN

+∝

±

±±±

±±±

)(

)()(

)(

21

mmεε

επ

fractional area of Dalitz space covered by bin

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Systematic related to Systematic related to

acceptanceacceptance�� The acceptance varies over the The acceptance varies over the DalitzDalitz planeplane

�� The relative acceptance in each bin can be measured using the BThe relative acceptance in each bin can be measured using the B→→DDππcontrol sample with DK selection applied without bachelor K PID control sample with DK selection applied without bachelor K PID

�� With the DC04 selection expect 60k events/2 fbWith the DC04 selection expect 60k events/2 fb--11

–– Relative relativeRelative relative--efficiency uncertainty 1efficiency uncertainty 1--4%/4%/∆δ∆δD D bin with 2 fbbin with 2 fb--11

–– Increased statistics reduces errorIncreased statistics reduces error

�� Toy MC study smearing bin efficiencies in event generation by thToy MC study smearing bin efficiencies in event generation by this is amount leads to an additional 1amount leads to an additional 1°° uncertainty without background and uncertainty without background and 3.23.2°° uncertaintyuncertainty with with DKDKcombcomb B/S=0.7B/S=0.7

–– Small effect compared to statistical uncertaintySmall effect compared to statistical uncertainty

�� NB: the efficiency related to the PID of the bachelor NB: the efficiency related to the PID of the bachelor ππ/K can be /K can be factored out and will be determined from the Dfactored out and will be determined from the D**→→D(KD(Kππ))ππ data to better data to better than one percentthan one percent--ignore at presentignore at present

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

S

22222

i

i

i

Di KK

dDmmmmfi

πππεε →∝=

−+−+∫

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Asymmetry in efficiency in Asymmetry in efficiency in

DalitzDalitz spacespace�� Considered charge asymmetries in the efficiency Considered charge asymmetries in the efficiency

across the across the DalitzDalitz plane plane

–– εε(m(m22++, m, m2 2

−−))≠≠εε(m(m22−−, m, m2 2

++))

�� Generated with the efficiency biased relative to Generated with the efficiency biased relative to

one another depending on whether the event one another depending on whether the event

hadhad mm22++>m>m2 2

−− oror mm22++<m<m2 2

−−

�� Maximum bias onMaximum bias on γγ induced wasinduced was <1<1°° forfor

10% 10% relative effect and full backgroundrelative effect and full background

�� 10% effects would be evident in the D10% effects would be evident in the Dππ samplesample

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ResolutionResolution

�� ∆δ∆δD D binning has some narrow regions in binning has some narrow regions in DalitzDalitz spacespace

�� Investigation of how resolution on the Investigation of how resolution on the DalitzDalitz variables might affected the variables might affected the extraction of extraction of γγ

�� 10 MeV10 MeV22/c/c4 4 resolution (DC04) on resolution (DC04) on DalitzDalitzvariables and generated toy variables and generated toy experiments with this smearingexperiments with this smearing

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

�� Fit results on toy experiments Fit results on toy experiments where resolution included in where resolution included in generation but ignored in fit found generation but ignored in fit found no significant bias (<0.5no significant bias (<0.5°°) on ) on γγ

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Background fractionsBackground fractions

�� CombinatoricCombinatoric background rate will be determined background rate will be determined from from B B and and DD mass sidebands which will cover at mass sidebands which will cover at least 2least 2--3 times the area of the signal region3 times the area of the signal region–– Use 10Use 10×× in DC04 background studies but this will probably in DC04 background studies but this will probably

be unrealistic with databe unrealistic with data

�� If background distributions relatively flat in masses If background distributions relatively flat in masses one can estimate that this leads to B/S will be one can estimate that this leads to B/S will be determined absolutely to around 0.01 or betterdetermined absolutely to around 0.01 or better

�� Toy studies suggest that there is no impact on Toy studies suggest that there is no impact on γγprecision with this kind of uncertaintyprecision with this kind of uncertainty

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

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Background compositionBackground composition

�� For favoured mode background For favoured mode background

dominated by dominated by BB→→DDππ–– 14 14 ×× larger BFlarger BF

–– Power of the RICHPower of the RICH

�� For suppressed For suppressed combinatoriccombinatoric

dominates (green)dominates (green)

�� For For BB→→D(hh)KD(hh)Kmore even more even

mixture of comb. andmixture of comb. and DDππ–– BB→→D(KK)K D(KK)K has significant nonhas significant non--

resonantresonant BB→→KKK KKK componentcomponent

5.2 5.25 5.3 5.35 5.40

1000

2000

3000

4000

5000

5.2 5.25 5.3 5.35 5.40

100

200

300

400

500

No RICH

RICH

DK

0.5 fb-1

B mass (GeV)