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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
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