Gerhard Raven 1

Measurement of CP Violation in B Measurement of CP Violation in B DecaysDecays

with the BaBar detectorwith the BaBar detector

Nikhef ColloquiumDecember 7th 2001

Gerhard Raven University of California, San Diego

Gerhard Raven 2

OutlineOutline

• What is CP (a)symmetry?• B mesons and CP violation in the Standard Model• How can we measure CP Violation?• Brief introduction to PEP-II and the BaBar detector• Overview of the measurement technique

– B reconstruction– B0, B+ Lifetime measurement– Measurement of B0B0 Mixing Frequency– Time Dependent CP Asymmetries

• sin(2)• sin(2eff)

• Summary and Outlook

Gerhard Raven 3

Discrete SymmetriesDiscrete Symmetries

• In general if a physical law is symmetric under a transformation, then there is a conserved quantity

• 3 important discrete symmetries in Particle Physics

• Parity, P– Parity reflects a system through the origin.

Converts right-handed coordinate systems to left-handed ones.– Vectors (momentum) change sign but axial vectors (spin) remain

unchangedx x L L

• Charge Conjugation, C– turns a particle into its anti-particle e e

• Time Reversal, T– Changes, the sign of the time; t t

all time dependent quantities,e.g. momentum, change sign

Symmetry Operation Conserved Quantity

Translation in Space Linear Momentum, p

Rotation in Space Angular Momentum, L

Translation in Time Energy, E

Change of Phase Electrical Charge, q

Gerhard Raven 4

Why is CP Violation interesting?Why is CP Violation interesting?

• Universe is matter dominated– Where has the anti-matter gone?

• In 1967, Sakharov showed that the generation of a net baryon number requires:1. Baryon number violating processes

(e.g. proton decay)2. Non-equilibrium state during the

expansion, therefore unequal number of particles and anti-particles

3. C and CP symmetry Violation

• Standard Model CP-violation is unlikely to be sufficient to explain matter asymmetry in the universe– It means there is something beyond

SM in CP violation somewhere, so a good place to work

-4 -6N(anti-Baryon) 10 -10

N(Baryon)

Gerhard Raven 5

Weak Interactions and Symmetry ViolationWeak Interactions and Symmetry Violation

• In 1957 violation of parity was observed– Asymmetry in decays of 60Co 60Ni e– Electrons produced mostly in one hemisphere

• C is violated too!– only left-handed neutrinos and right-handed anti-neutrinos

• (assuming massless neutrinos )

• In 1964 CP violation was observed in the weak decay of neutral K mesons– Ks (CP = 1)

– Kl (CP = -1)

– Observed Kl (0.2%) CP violation!

• Theoretically difficult to precisely interpret CP violation results in neutral K systems

• B Mesons expected to show CP violation– good testing ground for possible sources of CP violation

Gerhard Raven 6

The Weak Interactions of QuarksThe Weak Interactions of Quarks

• The coupling strength at the vertex is given by gVij

– g is the universal Fermi weak coupling

– Vij depends on which quarks are involved

– For leptons, the coupling is just g• For 3 generations, the Vij can be

written as a 3x3 matrix– This matrix is referred to as

the CKM matrix

• We can view this matrix as rotating the quark states from a basis in which they are Mass eigenstates to one in which they are Weak eigenstates

ud us ub

CKM cd cs cb

td ts tb

V V V

V V V

V V V

V

b W

cgVcb

b

s

d

VVV

VVV

VVV

b

s

d

tbtstd

cbcscd

ubusud

Gerhard Raven 7

CPCP Violation via the CKM matrix Violation via the CKM matrix

• The CKM matrix is a 33 complex unitary matrix• Requires 4 independent, physical parameters to describe it:

– 3 real numbers & 1 complex non-trivial phase

• The existence of the complex coupling (phase) gives rise to CP violation

– All CP violating observables are possible due to interference between different decay amplitudes involving a weak phase

If there were only 2 quark generations, the corresponding 22 matrix would be all real No CP violation

– CP violation is possible in the Standard Model with at least 3 generations

Gerhard Raven 8

The CKM Matrix: Wolfenstein The CKM Matrix: Wolfenstein parameterizationparameterization

Complex phase

λ =Vus = sin(cabbibo) = 0.2205 ±0.0018A =Vcb/ λ2 = 0.83±0.06

* * * 0ud ub cd cb td tbV V V V V V

Out of 6 triangles, this one (together with the “tu” one) is “special”:

•It has all sides O(3)•Large phases potentially large CP asymmetries

=

Wolfenstein parameterization uses the observed hierarchy of the CKM elements and pushes the complex phase to the smallest elements

Unitarity

Gerhard Raven 9

Unitarity of the CKM MatrixUnitarity of the CKM Matrix• The sides and the angles of this triangle can be determined

experimentally in B decays

Also see Peter Kluits colloquium last month for measurements of the magnitude of the sides

Gerhard Raven 10

CPCP violating observables for B mesons violating observables for B mesons

• As mentioned, need at least two amplitudes with different phases• In B decays, we can consider

two different types of amplitudes:– Those responsible for decay

– Those responsible for mixing

• This gives rise to three possiblemanifestations of CP violation:– Direct CP violation

• (interference between two decay amplitudes)– Indirect CP violation

• (interference between two mixing amplitudes)

– CP violation in the interferencebetween mixed and unmixed decays

d

bW

d

uu

d

B0

B0 B0

b

b d

d

u,c,t

u,c,t

W W

Gerhard Raven 11

CP violation in decayCP violation in decay

Requires two decay amplitudes– Eg. K+-:

“easy” to measure– ACP = N(K+-) – N(K-+) / N(K+-) + N(K-+)– Asymmetry expected to be small

• Large asymmetry requires ~equal amplitudes…– But difficult to interpret:

• How large is the penguin contribution? • What is the relative phase?

– Difficult to disentangle contributions…• To get a feeling for the relative weight, compare +-and K+-:

• Br(K+-) >> Br()!

::

Gerhard Raven 12

BB00 B B00 mixing: ARGUS, 1987 mixing: ARGUS, 1987

• Fully reconstructed mixed event and dilepton studies demonstrate mixing

• Integrated luminosity 1983-87:– 103 pb-1

0*122

*2

02

10*

111*1

01

,

,

DDDB

DDDB

Gerhard Raven 13

CP violation in mixingCP violation in mixing

Mixing between B0 and B0 can be described can by effective Hamiltonian:

12 describes B0 f B0 via on-shell statesThis is rare: the branching ratios of CP

states is very smallM12 describes B0 f B0 via off-shell states

CP violation can occur in the interference between the on-shell and off-shell amplitudes, and leads to However, for B0 mesons, 12 is very small: mixing is dominated by m=2M12

Little CP sensitivity…

0 012 12

* * 0 012 12

Mass Eigenstates 2

L

H

M M B pB qBiH

M M B pB qB

Prob(B0 B0) Prob(B0 B0) |q/p|1

Gerhard Raven 14

CP violation in the inference between mixing and CP violation in the inference between mixing and decaydecay

CP

CP

CP

2f

f 2f

1 | λ |

1 | λ |C

CP

CP

CP

ff 2

f

2Im λ

1 | λ |S

CP CP4 ff cos(( , ) e [1 ]in) s ( )tC dP df B f t tt Sm mC

0

0

:

:phys CP

phys CP

f B f

f B f

CP

CP

CP

ff

f

Aqλ

p A Amplitude ratio

Mixing Phase

0 0Prob( ( ) ) Prob( ( ) )

1CP

phys CP phys CP

f

B t f B t f

In order to have CP Violation

Time evolution of initial B0 (or B0) mesons into a final CP eigenstate

•A single decay amplitude is sufficient•Mixed decay has taken the role of the 2nd amplitude•Thus interfering amplitudes are comparable by construction•and large CP asymmetries are possible!!!

Gerhard Raven 15

Time Dependent Time Dependent CPCP Asymmetry Asymmetry

C CPP

0 0

0 0

f f

( ( ) ) ( ( ) )( )

( ( ) ) ( ( ) )

- sin(s( o )c )

CP

CP CPphys physf

CP CPphy

d

s p

d

hys

B t f B t fA t

B t f B t f

SC m t m t

From the time evolution of the B0 and B0 states we can define the time-dependent asymmetry to be

CP

CP

CP

2f

f 2f

1 | λ |

1 | λ |C

Probe of direct CP violation since it requires

CPfλ 1

CP

CP

CP

ff 2

f

2 Im λ

1 | λ |S

Sensitive to the phaseof even without directCP Violation

Im = 0.75||=1

Gerhard Raven 16

Golden Decay Mode: BGolden Decay Mode: B00 J/J/KK00SS

• Theoretically clean way to measure the phase of (i.e. sin2)• Clean experimental signature• Branching fraction: O(10-4)

• “Large” compared to other CP modes!

0L,S

2

J/ Kλ i

CPe

0K

b

c

s

c

d

/J

d

Time-dependent CP asymmetry

sin 2( ) sin( ) CP CPA t m t

u,c,t

0B

u,c,t

W W0

Bd

b 0 0

0 0

/

/CP S

LCP

B J K

B J K

K0 mixing

CP = +1

B0 J/ K0L

CP = -1 B0 J/ K0

S

B0 (2s) K0S

B0 c1 K0

S

“Golden Modes”

Gerhard Raven 17

B meson productionB meson production

• Electron-Positron collider: e+e- (4s) B0B0

– Only 4s resonance can produce B meson pair – Low B0 production cross-section: ~1 nb– Clean environment, coherent B0B0 production

B-Factoryapproach

B0B0 thresholdOff On

)MeV(ME )S4(CM

PEP-II BABAR

BB

thre

shold

28.0hadr

bb

Gerhard Raven 18

(4S): Coherent B(4S): Coherent B00BB00 production production

• B0B0 system evolves coherentlyuntil one of them decays– CP/Mixing oscillation clock only starts

ticking at the time of the first decay, relevant time parameter t:

– B mesons have opposite flavour at time t=0– Half of the time CP B decays first (t<0)

• Integrated CP asymmetry is 0:

• Coherent production requires time dependent analysis

At tcp=0

B0

B0

At t=0

B0

B0

t = tCP - tOtherB

Coherent

Incoherent

-

+ +

-t(ps)

t(ps)

Gerhard Raven 19

A Symmetric Collider won’t work…A Symmetric Collider won’t work…

• CP asymmetry is a time-dependent process– ACP t between two B decays, t ~ ps

– In reality one measures decay distance between two B decays

• In symmetric energy e+e- collider, where (4S) produced at rest, daughter B’s travel ~ 20m– Too small a distance to discern with today’s detector

technology

l 40 m

Btag BCP

5.3 GeV 5.3 GeV

e+

Gerhard Raven 20

Solution: Boost the CMS!Solution: Boost the CMS!

+e-e

Coherent BB pair

z

Δ zΔ tβγ c

B

Btag

z

Start the Clock

| | 260Bz c m

This can be measured using a silicon vertex detector!

4s

()(4S) = 0.56

Brec

Gerhard Raven 21

Asymmetric B FactoriesAsymmetric B Factories

= 0.56, s = M(4S)

Collisions every 4.2 nsLarge currents!

HER LER

Energy (GeV) 9.0 3.1

Number of bunches

1658 1658

Beam Current (A) 1.0 2.1

Gerhard Raven 22

PEP-IIPEP-II

PEP-II delivered : 63 fb-1

BABAR recorded : 60 fb-1 (incl. 6.5 fb-1 off peak) 60 Million B meson pairs “on

tape”!

•PEP-II top luminosity: 4.3 x 1033cm-2s-1 (design 3.0 x 1033)

•Best shift: 102 pb-1

•Best day: 282 pb-1

•Best month: 6 fb-1

•Average logging efficiency: > 96%

October 99 December 5, 2001

30/fb usedfor CP and

mixing

20/fb usedfor lifetime

off-peak

Gerhard Raven 23

KEK-B has reached 5.5 1033cm-2s-1! (design 1034)

Extrapolation suggest both machines will have delivered ~100 fb-1 by the time of ICHEP 2002 – we live in interesting times!

KEK-B performanceKEK-B performance

peak luminosity = 5.447 × 1033 /cm2/sec integrated luminosity :

shift = 101.9 /pb day = 280.8 /pb 24h = 287.7 /pb 7days = 1801. /pb month = 4760. /pb

Gerhard Raven 24

The BaBar DetectorThe BaBar Detector

Cerenkov Detector (DIRC)

144 quartz bars11000 PMs

1.5 T solenoid Electromagnetic Calorimeter

6580 CsI(Tl) crystals

Drift Chamber40 stereo layers

Instrumented Flux Returniron / RPCs (muon / neutral hadrons)

Silicon Vertex Tracker5 layers, double sided strips

e+ (3.1 GeV)

e- (9 GeV)

SVT: 97% efficiency, 15 m z hit resolution (inner layers, perp. tracks)

SVT+DCH:(pT)/pT = 0.13 % pT + 0.45 %

DIRC: K- separation 4.2 @ 3.0 GeV/c 2.5 @ 4.0 GeV/c EMC: E/E = 2.3 %E-1/4 1.9 %

Gerhard Raven 25

Silicon Vertex DetectorSilicon Vertex Detector

• 5 Layer AC-coupled double sided silicon detector

• SVT Located in high radiation area • Radiation hard readout electronics (2Mrad)

• 97% hit reconstruction efficiency• Hit resolution ~15 μm at 00

e- beam e+ beam

Gerhard Raven 26

Silicon Vertex DetectorSilicon Vertex Detector

Beam pipe

Layer 1,2Layer 3

Layer 4Layer 5

Beam bending magnets

Readoutchips

Gerhard Raven 27

Drift ChamberDrift Chamber

• 40 layers of wires inside 1.5 Tesla magnetic field

• Measurement of charged particle momentum• Limited particle identification from ionization

loss

Gerhard Raven 28

Cerenkov Particle Identification SystemCerenkov Particle Identification System

• Čerenkov light in quartz– Transmitted by internal reflection– Rings projected in standoff box– Detected by PMTs– Essential for Kaon ID >2 GeV

Gerhard Raven 29

ElectroMagnetic CalorimeterElectroMagnetic Calorimeter

• 6580 CsI(Tl) crystals with photodiode readout

• About 18 X0, inside solenoid

• Excellent energy resolution, essential for 0

= 5.0%

)%1.007.085.1()%3.003.032.2()(

4

EE

E

0

Gerhard Raven 30

Instrumented Flux ReturnInstrumented Flux Return

• Up to 21 layers of RPCs sandwiched between iron plates

• Muons identified above 500 MeV

• Neutral Hadrons (KL) detected

Gerhard Raven 31

Event Topology and Analysis StrategyEvent Topology and Analysis Strategy

+e-e

Brec

z

Btag

zExclusive B Meson and Vertex Reconstruction

Exclusive B Meson and Vertex Reconstruction

-π

0sK +π

+μ

-μ

Tag vertex reconstructio

n

Tag vertex reconstructio

n

FlavorTaggingFlavor

Tagginge+

K-

Gerhard Raven 32

Analysis StrategyAnalysis Strategy

Measurements• B±/B0 Lifetimes

• B0 B0-Mixing

• CP-Asymmetries• sin(2)• sin(2eff)

Analysis Ingredient• Reconstruction of B

mesons in flavor eigenstates

• B vertex reconstruction

• Flavor Tagging + a + b

• Reconstruction of neutralB mesons in CP eigenstates + a + b + c

Hig

her p

recisio

n

Incre

asin

g co

mple

xity

Factorize the analysis in building blocks

Gerhard Raven 33

Blind AnalysisBlind Analysis•All analysis were done “blind” to eliminate possible experimenters’ bias

–In general, measurements of a quantity “X” are done with likelihood fits – blinding done by replacing “X” with “X+R” in likelihood fits

–R is draw from a Gaussian with a width a few times the expected error

–Random number sequence is “seeded” with a “blinding string”

–The reported statistical error is unaffected

–It allows all systematic studies to be done while still blind

–The sin(2b) result was “unblinded” 1 week before public announcement this summer!

Gerhard Raven 34

Measurement of BMeasurement of B00 and B and B++ Lifetime Lifetime

3. Reconstruct Inclusively the vertex of the “other” B meson (BTAG)

4. compute the proper time difference t5. Fit the t spectra

(4s)

= 0.56

Tag B

z ~ 110 m Reco Bz ~ 65 m

+z

t z/c

K0

D-

--

K+

1. Fully reconstruct one B mesonin flavor eigenstate (BREC)

2. Reconstruct the decay vertex

Gerhard Raven 35

Fully-Reconstucted B sampleFully-Reconstucted B sample

Cabibbo-favored hadronic decays

“Open Charm” decays

Neutral B Mesons

Charged B Mesons

%38purity

9400N 00 B/B

%85purity

8500NB/B

ducb

( )b c c s

Flavor eigenstates Bflav : for lifetime and mixing measurements

0 *0/ ( )B J K K / , (2 )B J K S K [GeV]

30 fb-1

0( )B D π 0

1( )B D π /ρ /a

Hadronic decays into final stateswith Charmonium

ESm

22cm

B

s = - p

2

Gerhard Raven 36

Vertex and Vertex and t Reconstructiont Reconstruction

Reconstruct Brec vertex from charged Brec daughters

Determine BTag vertex from charged tracks not

belonging to Brec

Brec vertex and momentum

beam spot and (4S) momentum

High efficiency (97%) Average z resolution is 180 m (<|z|> ~ ct = 260 m) Conversion of z to t takes into account the (small) B

momentum in (4S) frame

t resolution function measured directly from data

Beam spot

Interaction Point

BREC Vertex

BREC daughters

BREC direction

BTAG direction

TAG Vertex

TAG tracks, V0s

z

* * * *cos ( )rec rec rec recz c t c t 0* * * *cos ( | |)rec rec rec rec Bz c t c t

Gerhard Raven 37

Vertex and Dt reconstruction: BelleVertex and Dt reconstruction: Belle

Gerhard Raven 38

BB Measurements in BaBar Measurements in BaBar

e-|t|/

Either Brec or Btag can decay first (this analysis)

BaBar

t resolution

e-t/

true t

B production point known eg. from beam spot

LEP/SLD/CDF/D0/LHC-B/…

Need to disentangle resolution function from physics !

measured t

Resolutionfunction Resolution

fcn+

lifetime

Resolution Function + Lifetime =

=

Gerhard Raven 39

t Signal Resolutiont Signal Resolution

(1 ) ( , )

( , )

( , )

tail outlier core t core

tail tail t tail

outlier outlier outlier

R f f G S

f G S

f G

(1 ) ( , 0)

( , 0) exp( / )

( , )

tail outlier t core

tail t bias

outlier outlier outlier

R f f G S

f G S t S

f G

high flexibility

small correlation with B)

z

Signal MC (B0)

t(meas-true)t

tracks from long-lived D’s in tag vertex asymmetric

RF

• event-by-event (t) from vertex errors• Resolution Function (RF) – 2 models:

– Sum of 3 Gaussians (mixing + CP analyses)

– Lifetime-like bias (lifetime analysis)

~0.6 ps

Gerhard Raven 40

Lifetime Likelihood FitLifetime Likelihood Fit

• Simultaneous unbinned maximum likelihood fit to B0/B+ samples

• 19 free parameters – (B+) and (B0) 2– t signal resolution

5– empirical background 12

description• Background parameters

determined from mES sideband

)2

Beam-Energy Substituted Mass (MeV/c5200 5210 5220 5230 5240 5250 5260 5270 5280 5290 5300

2E

ve

nts

/ 1

MeV

/c

0

200

400

600

800

1000

1200

1400 BABB0 mES

B0 BkgtmES<5.27 GeV/c2

t characteristics determined from data

Gerhard Raven 41

Neutral and Charged B meson LifetimesNeutral and Charged B meson Lifetimes

• Precision measurements:

t (ps)

0 = 1.546 0.032 0.022 ps

= 1.673 0.032 0.022 ps

/0 = 1.082 0.026 0.011

t RF parameterization, t outlier description

Common resolution function for B+ and B0

20 fb-1

PRL 87 (2001)

•2 % statistical error•1.5 % systematic error

t distribution well described!

bkgd

signal

+bkgd

outliers

Gerhard Raven 42

Comparison of Lifetime Ratio MeasurementsComparison of Lifetime Ratio Measurements

Single most precise measurement

Systematic error 1% in B+/B0

lifetime ratio

Gerhard Raven 43

Belle result from 5Belle result from 5thth KEK conference (end KEK conference (end Nov)Nov)

Gerhard Raven 44

Belle result from 5Belle result from 5thth KEK conference (end KEK conference (end Nov)Nov)

Gerhard Raven 45

Analysis Strategy (II)Analysis Strategy (II)

Measurements

• B±/B0 Lifetimes

• B0 B0-Mixing

• CP-Asymmetries

Analysis Ingredient

• Reconstruction of B mesons in flavor eigenstates

• B vertex reconstruction• Flavor Tagging + a + b

• Reconstruction of neutral

B mesons in CP eigenstates + a + b + c

Gerhard Raven 46

Measurement of BMeasurement of B00BB00 Mixing Mixing

3. Reconstruct Inclusively the vertex of the “other” B meson (BTAG) 4. Determine the flavor of BTAG to separate Mixed and Unmixed events

5. compute the proper time difference t 6. Fit the t spectra of mixed and unmixed events

(4s)

= 0.56

Tag B

z ~ 110 m Reco Bz ~ 65 m

+z

t z/c

K0

D-

--

K+

1. Fully reconstruct one B meson in flavor eigenstate (BREC) 2. Reconstruct the decay vertex

Gerhard Raven 47

MiU

xnmix 1 cos( )

4f (Δ t)

Bd

d

| Δ t |/τ

Bd

eΔm Δt

τ

t distribution of mixed and unmixed eventst distribution of mixed and unmixed events

Decay Time Difference (reco-tag) (ps)

UnMixedMixed

0

10

20

30

40

50

60

-8 -6 -4 -2 0 2 4 6 8

perfect flavor tagging & time

resolution

Decay Time Difference (reco-tag) (ps)

UnMixedMixed

0

10

20

30

40

50

60

-8 -6 -4 -2 0 2 4 6 8

realistic mis-tagging & finite time

resolution

Unmix

xMi

f (Δ t) 1 1 2 cos( ) ResolutionFunction4

Bd

d

d

| Δt |/τ

B

e tτ

mw Δ Δ

0 0

0 0

0 0

0 0Mixed:

Unmixed: tagflav

tagflav

tag flav

tagflav

or

or

B B

B B

B B

B B

w: the fraction of wrongly tagged events

md: oscillation frequency

Gerhard Raven 48

Extraction of Extraction of mmdd and Flavour Mistag and Flavour Mistag FractionsFractions

Fraction of Mixed Events as Function of time

Sensitive to mistag fraction measurement because the mixing has not started yet

At t=0 the observed ‘mixed’ events are only due to wrongly tagged events

Sensitive to md when the rate of change of the amplitude is at its maximum

Gerhard Raven 49

B Flavour tagging methodsB Flavour tagging methods

NN output

Not U

sed

For electrons, muons and Kaons use the charge correlation

b c

d d

l-

B0 D, D*

W-

0

0

l

l

B

B

Lepton Tag

b

d

B0

W- W+c s

K*0

d

0

0

0

0

kaons

kaons

Q

Q

B

B

Kaon Tag

Each category is characterized by the probability of giving the wrong answer (mistag fraction w)

Multivariate analysis exploiting the other kinematic information of the event, e.g., Momentum spectrum of the charged particles Information from non-identified leptons and kaons Soft from D* decay

Neural Network

Hierarchical Tagging CategoriesHierarchical Tagging Categories

Gerhard Raven 50

Flavour Tagging PerformanceFlavour Tagging Performance

Tagging category

Fraction of tagged

events(%)

Wrong tag fraction w (%)

Q = (1-2w)2 (%)

Lepton 10.9 0.3 8.9 1.3 7.4 0.5

Kaon 35.8 0.5 17.6 1.0 15.0 0.9

NT1 7.8 0.3 22.0 2.1 2.5 0.4

NT2 13.8 0.3 35.1 1.9 1.2 0.3

ALL 68.4 0.7 26.1 1.2 Smallest mistag fractionHighest “efficiency”The error on sin2 and m depend on

“the quality factor” Q:

1sin 2

Q

The large sample of fully reconstructed events provides the precise determination of the tagging parameters required in the CP fit

Gerhard Raven 51

Belle Flavour TaggingBelle Flavour Tagging

Gerhard Raven 52

Belle Flavour TaggingBelle Flavour Tagging

Gerhard Raven 53

Mixing Likelihood FitMixing Likelihood Fit

UnmixMix

f (Δ t) 1 1 2 cos( )4

Bd

d

| Δ t |/τ

Bd

e ΔtΔmw Rτ

Fit Parametersmd 1Mistag fractions for B0 and B0 tags 8Signal resolution function(scale factor,bias,fractions)8+8=16Empirical description of background t 19B lifetime fixed to the PDG value B = 1.548 ps

Unbinned maximum likelihood fit to flavor-tagged neutral B sample

44 total free parameters

All t parameters extracted from data

Gerhard Raven 54

Beware of Correlations!Beware of Correlations!• Difficult part of the md analysis are correlations• For this result, 2 correlation are not modeled in the

likelihood function– Between mES and t

• For mES close to mB, more background due to (incorrectly reconstructed) real B mesons

• For smaller mES, more continuum background• Leads to a 0.002 ps-1 correction determined from data

– Between mistag rate and resolution• Eg. “wrong” sign K± are mainly produced by D(*)D(*) decays• Higher charged multiplicity, no (or only low momentum) tracks from B

decay vertex different t resolution• Leads to a 0.007 ps-1 correction determined from MC

• Next generation of this measurement should / will have to model this in the likelihood…

Gerhard Raven 55

Mixing Likelihood Fit ResultMixing Likelihood Fit Result

md=0.516±0.016±0.010 ps-1

•BaBar internal review passed•currently in “final circulation”

•Numbers are final•To be submitted to PRL in the very near future (please don’t tell your friends on Belle just yet!)

CL=44%

( ) ( )( )

( ) ( )

(1 2 )cos( )

unmixed mixedmix

unmixed mixed

N t N tA t

N t N t

w m t

Gerhard Raven 56

Cross Checks and Systematic ErrorsCross Checks and Systematic Errors

Gerhard Raven 57

mmdd Measurement in Comparison Measurement in Comparison

• Precision md measurement (3%) with Bflav sample is still statistically limited

• Systematic error under control (2%)– Dominated by uncertainty on B

– Followed by resolution fcn and tagging-vertexing correlations.

• Theoretical hadronic uncertainties limit extraction of |Vtd |

22 2 2 2 2

02( / ) | |

6 d d d

Fd w B t W B td B B

Gm m e S m m m V B f

2 2(210 40MeV)d dB BB f

My Average, using COMBOS

(PDG 2000)

Gerhard Raven 58

Recent Belle Result (5Recent Belle Result (5thth KEK topical KEK topical conference)conference)

Gerhard Raven 59

Recent Belle Results (5Recent Belle Results (5thth KEK topical KEK topical conference)conference)

Gerhard Raven 60

Analysis Strategy (III)Analysis Strategy (III)

Measurements

• B±/B0 Lifetimes

• B0 B0-Mixing

• CP-Asymmetries

Analysis Ingredient

• Reconstruction of B mesons in flavor eigenstates

• B vertex reconstruction

• Flavor Tagging + a + b

• Reconstruction of neutral B mesons in CP eigenstates + a + b + c

Gerhard Raven 61

Measurement of sin(2Measurement of sin(2))

3. Reconstruct Inclusively the vertex of the “other” B meson (BTAG) 4. Determine the flavor of BTAG to separate B0 and B0

5. compute the proper time difference t 6. Fit the t spectra of B0 and B0 tagged events

(4s)

= 0.56

Tag B

z ~ 110 m Reco Bz ~ 65 m

-z

t z/c

K0

KS0

-

+

1. Fully reconstruct one B meson in CP eigenstate (BREC)2. Reconstruct the decay vertex

+

Gerhard Raven 62

The CP SampleThe CP Sample

c1Ks

J/Ks

Ks(00)

J/K*0

(2S)Ks

J/Ks

Ks(+-)

After tagging:Sample tagge

d event

s

Purity CP

[J/, (2S), c1] KS

480 96% -1

J/ KL 273 51% +1

J/ K*0(KS0) 50 74% mixed

Full CP sample

803 80%

1999-2001 data 32 x 106

BB pairs29 fb-1 on peak

Before tagging requirement

mES(GeV/c2)

mES(GeV/c2) E=EB*-s/2 (GeV)

J/KL

Gerhard Raven 63

Example of a Fully Reconstructed Example of a Fully Reconstructed EventEvent

(2S) Ks

+- +-

• D*+ -

D +

K-+

• Exercise for the viewer/reader/listener: how many ways are there to flavour tag this event?– Bonus points: which

tag was actually used?

Gerhard Raven 64

A few words about J/A few words about J/K*K*00(K(KSS00))

J/ K*0(KS0) angular components:

• A|| : CP = +1

• A0 : CP = +1

• A : CP = -1 (define R = |A|2 )

CP asymmetry diluted by D = (1 - 2R)

R = (16.0 ± 3.2 ± 1.4) % (BABAR, to appear in PRL)

=> Effective f = 0.65 0.07 (includes acceptance corrections)

Sample used in R measurement (20.7fb-1) and the angular fit

Gerhard Raven 65

| |/

41 sin(2 )sin(

d

f

Bd

B

te

CP,f (Δt) m t

| |/

41 sin(2 )sin(

d

f

Bd

B

te

CP,f (Δt) m t

1 (1 2 )sin(

42 )sin

d

d

B

B|Δt|/τ

CP, f def (Δt) η Δm Δtwβ

τ

R1 (1 2 )sin(4

2 )sind

d

B

B|Δt|/τ

CP, f def (Δt) η Δm Δtwβ

τ

R

t Spectrum of CP eventst Spectrum of CP events

00tag BB 00

tag BB

perfect flavor tagging & time

resolution

Mistag fractions wAnd resolution function R

CP PDF

00tag BB 00

tag BB

realistic mis-tagging & finite time

resolution

1 (1 2 )cos( )4

dB

Bd|Δt|/τ

mixing, dwef (Δt) Δm Δt

τ

R1 (1 2 )cos( )

4dB

Bd|Δt|/τ

mixing, dwef (Δt) Δm Δt

τ

R

Mixing PDFdetermined by theflavor sample

Gerhard Raven 66

Sin(2Sin(2) likelihood fit) likelihood fit

Combined unbinned maximum likelihood fit to t spectra of flavor and CP sample

45 total free parameters

All t parameters extracted from data Correct estimate of the error and correlations

Fit Parameterssin2 1Mistag fractions for B0 and B0 tags 8Signal resolution function 16Empirical description of background t 20B lifetime fixed to the PDG value B = 1.548 psMixing Frequency fixed to the PDG value md = 0.472 ps-

1

Global correlation coefficient for sin2b: 13%Different t resolution function parameters for Run1 and Run2

tagged flavor sample

tagged CP samples

Driven by

Gerhard Raven 67

Sin(2b) Fit ResultsSin(2b) Fit Results

Consistency of CP channels P(2) =

8%

sin2 = 0.59 ± 0.14

Cross-checks:Null result in flavor samples

Goodness of fit(CP Sample): P(Lmax>Lobs) >

27%

Phys. Rev. Lett. 87 091801 (2001)

Combined fit to all modes

Gerhard Raven 68

Raw CP AsymmetryRaw CP Asymmetry

sin2=0.56 ± 0.15 sin2=0.59 ± 0.20

Kaon tagsAll tags

Raw ACP

f = -1 events

Gerhard Raven 69

Raw CP Asymmetry for J/Raw CP Asymmetry for J/ K KLL

sin2=0.70±0.34

Backgroundcontribution

Gerhard Raven 70

Check “null” control sampleCheck “null” control sample

•Treat Bflav sample as CP•No asymmetry seen

•Analysis doesn’t create artificial asymmetries

Gerhard Raven 71

Consistency checksConsistency checks

sin2 measured in several t bins

sin2 vs. J/ decay mode and tagging category and flavor for

= -1 events

Combined CP=-1

Gerhard Raven 72

Is it possible to measure a very large Is it possible to measure a very large asymmetry?asymmetry?

• The answer is… yes! Suppose at a given time t’ you have

• Nevents < 0 is possible in the likelihood fit– The signal PDF can be negative in some regions– Requires having NO OBSERVED event in those regions– The only constraint on the PDF is the normalization

0 0

0 0

5( )

( 2)

( 25

5 )3.B B

B B

N NAsymmetry t

N N

1PDF

Gerhard Raven 73

Large sin2Large sin2in Bin B00 C1C1KKSS

• fit for B0/B0 t PDFs, not for ACP

• Large sin2 possible , because – No events where PDF<0

(eg. lepton tags)

– Sum of signal + background PDFs positive (eg. Kaon tags)

• Note: a single lepton B0-tag at t = -/2mwould bring sin2 from 2.6 to ~1/(1-2wlep) 1.1

• Measure sin2unbiased for low stat. samples and probability to obtain sin22.6 when true value 0.7 is 1~2%

Lepton tags

Kaon tags

t [ps]

B0 tags

B0 tags

B0 tags

B0 tags

t [ps]

Gerhard Raven 74

Systematic ErrorsSystematic Errors

Signal resolution and vertex reconstruction 0.03 Resolution model, outliers, residual misalignment of

the Silicon Vertex Detector Tagging 0.03

possible differences between BCP and Bflavor samples Backgrounds 0.02 (overall)

Signal probability, fraction of B+ background in the signal region, CP content of background

Total 0.09 for J/ KL channel; 0.11 for J/ K*0

Total = 0.05 for total sample

Error/Sample KS KL K*0 Total

Statistical 0.15 0.34 1.01 0.14

Systematic 0.05 0.10 0.16 0.05

Gerhard Raven 75

Belle sin(2Belle sin(211) result) result

Gerhard Raven 76

Belle sin(2Belle sin(211) result) result

Gerhard Raven 77

Belle sin(2Belle sin(211) result) result

Gerhard Raven 78

The New World AverageThe New World Average

Measurements assumed to be uncorrelated

New sin2 world average is 8 significant!

Gerhard Raven 79

Interpretation of the resultInterpretation of the result

One solution for is consistent with measurements

of sides of the unitarity triangle

Method as in Höcker et al,hepex/0104062 (see also many other recent global CKM analyses)

Error on sin2 is dominated by statistics and will decrease ~1/for the forseeable future…

Ldt

Gerhard Raven 80

Search for Direct CPSearch for Direct CP

To probe new physics (only use CP=-1 sample that contains no CP

background)|| = 0.93 ± 0.09 (stat) ± 0.03 (syst)

No evidence of direct CP violation due to decay amplitude interference (SCP unchanged in Value)

CP CPf fcos( sin(( )) - )CP df dC mA t St m t

CP

CP

CP

2f

f 2f

1 | λ |

1 | λ |C

CP

CP

CP

ff 2

f

2 Im λ

1 | λ |S

Without SM Prejudice :

If more than one amplitude present then |

| might be different from 1

Gerhard Raven 81

CP Violation in BCP Violation in B00++-- decays decays

u

u

d

bd

ub

u

| | 1 must fit for direct CPIm () sin2 need to relate asymmetry to

/( ) [1 sin( ) cos( )]

4t

d def t S m t C m t

Decay distributions f+(f-) when tag = B0(B0)

C0, S= sin2

i2f

)(i2f

f

f eeAA

pq

C 0, S= sin2eff

Weak phase (only tree diagram)Additional phase from penguin diagram

penguin diagramtree diagram

Gerhard Raven 82

BB,K,K,K,KKK Data Sample Data Sample

Lepton

Kaon

NT1 NT2

Likelihood Analyis with high reconstruction efficiency: Loose selection criteria yield 9741 two-prong candidates in 30.4 fb-1 (includes 97% background, almost entirely from continuum)

•sum of +-/K+- mES distributions by tagging category •particle ID used in likelihood fit for /K separation

Gerhard Raven 83

BBKK Likelihood Fit Likelihood Fit

– 8 event types – Sig and Bkg: +- , K+ , K-+ , K+K-

measure also direct CP violation in charge asymmetry

– Discriminating variables – mES, E , Fisher (Event shapes),

Cerenkov angles, t– Mistag rates and t signal resolution

function same as in sin2 fit (uses also untagged events to improve BR measurements)

– Empirical background parameters determined from mES sidebands

– md, B0 lifetime fixed to PDG values

A = N(K-+)-N(K+) / N(K-+)+N(K+)

Simultaneous extended unbinned ML fit to the yields and CP asymmetries:

Gerhard Raven 84

CP Sample: CP Sample: /K/K Candidates Candidates

L = 30.4 fb-

1

Events after likelihood ratio cuts

Total Yields from fit:

Measured Branching Ratios (using 20 fb-1):+-: ( 4.1+1.0+0.7 )10-6

K+-: (16.7+1.6+1.6)10-6

K+K-: <2.5 10-6 (90%CL)

K+

K-

K+

K-

Background (incl. crossfeed)Tagged events

Gerhard Raven 85

BB00 Asymmetry Result Asymmetry Result

• Measurement compatible with no CP in B0

• Statistically limited due to small branching fraction• Need ~500fb-1 for (S) ~ 0.10-0.15

To appear in PRD Rapid To appear in PRD Rapid CommunicationsCommunications

0.530.56

0.450.47

( ) 0.03 0.11

( ) 0.25 0.14

( ) 0.07 0.08 0.02CP

S

C

A K

Gerhard Raven 86

Summary and OutlookSummary and Outlook

• New precision measurements of B0/B+ lifetimes and B0B0 mixing frequency md

• Measurement of flavor-tagged, time-dependent B decays at asymmetric B factory has become established technique

• BaBar observes CP violation in the B0 system at 4 level

– Probability is < 3 x 10-5 to observe an equal or larger value if no CP violation exists

– Corresponding probability for only the CP = -1 modes is 2 x 10-

4

sin(2) = 0.59 ± 0.14 ± 0.05

0 = 1.546 0.032 0.022 ps = 1.673 0.032 0.022 ps0 / = 1.082 0.026 0.011

md = 0.516 ± 0.016 ± 0.010 ps-1

Gerhard Raven 87

Summary and Outlook (II)Summary and Outlook (II)

• First measurement of time-dependent CP asymmetry in rare B decay mode B

• The study of CP violation in the B system has started:– sin(2) will very soon become precision measurement (

unitarity triangle constraints will be limited by other CKM parameters)

– Need to compare sin(2) from different decay modes to test standard model

• With anticipated 100 fb-1 by summer, error in sin(2) will be 0.08 and for the asymmetry in B error will be ~0.3

0.530.56

0.450.47

( ) 0.03 ( ) 0.11( )

( ) 0.25 ( ) 0.14( )

S stat syst

C stat syst

Gerhard Raven 88

Summary and Outlook (III)Summary and Outlook (III)

• 37 years after the discovery of CP violation in Kaon decays, a 2nd system with CP violation is found – and its study is just beginning…

• The Standard Model prediction of a single phase as the source of CP violation seems right (sofar -- given the current experimental data…)

• New physics and its contribution to CP violation in B decays are possible, but remain to be discovered…

• Current experimental measurements of CP violation in weak interactions are very unlikely to explain the CP asymmetry observed in the universe…

Gerhard Raven 89

Luminosity Outlook of PEP-II & BaBarLuminosity Outlook of PEP-II & BaBar

0

100

200

300

400

500

600

Year

Inte

gra

ted

Lu

mi [

fb-1

]

0

2

4

6

8

10

12

14

16

18

Pea

k L

um

i [10

**33

]

Yearly Lumi

Cumulative Lumi

Peak Lumi

Yearly Lumi 2 23 40 45 62 100 100 170

Cumulative Lumi 2 25 65 110 172 272 372 542

Peak Lumi 1 2 4 5 6 8.5 11 16

1999 2000 2001 2002 2003 2004 2005 2006

Expect >500 fb-1 by 2007

Gerhard Raven 90

Changes between Run1 and Run2Changes between Run1 and Run2

• First publication in March 2001

• Changes since then:– More data (run 2): 23 32 BB pairs– Improved reconstruction efficiency– Optimized selection criteria takes into account CP

asymmetry of background in J/KL

– Additional decay modes C1KS and J/K*0

– Improved vertex resolution for reconstructed and tag B

sin(2) = 0.34 ± 0.20 (stat) ± 0.05 (syst)PRL 86 (2001) 2515