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Lecture 2: Time-Dependent Measurements with Flavor and CP Samples oReconstruction of B meson samples...
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Transcript of Lecture 2: Time-Dependent Measurements with Flavor and CP Samples oReconstruction of B meson samples...
Lecture 2: Time-Dependent Measurements with Flavor
and CP Samples o Reconstruction of B meson sampleso Lifetimes and B0 oscillation
measurements with flavor eigenstate decay
Aug 5-7, 2002 D.MacFarlane at SSI 2002 2
z ~ 260 m
0tagB
ee
4S
K
0recB
B-Flavor Tagging
cβγz/ΔtΔ
Exclusive B Meson
Reconstruction
0
SK
/J
0 0rec fl avB B (flavor eigenstates) lifetime, mixing analyses0 0
rec CPB B (CP eigenstates) CP analysis
Experimental Technique for B Factories
(4S) produces coherent B pair: t t
Time-integrated asymmetries are zero
0
0
( )
( )
tag
rec
B B t
B B t
Aug 5-7, 2002 D.MacFarlane at SSI 2002 3
Main Variables for B Reconstruction
For exclusive B reconstruction, two nearly uncorrelated* kinematic variables are used:
* *B beamE E E
2 2* *BbeamESm E p
2 2 2 2
2
2 2 2 2
ES
beamE E E
m pbeam beamB
pm
* * *( , ),B B beamE Ep B candidate (energy, 3-momentum) and beam energy in (4S) frame
Signal at E ~ 0
Signal at mES ~ mB
Resolutions
10 40 MeVE
22.6 MeV/ cESm
“Energy-substituted
mass”
* If E were zero, the variables would be fully correlated; however, E is typically at least 5 times larger than beam and so dominates E
Aug 5-7, 2002 D.MacFarlane at SSI 2002 4
Example for Hadronic B Decays
mES
E
sidebands
signal region
B0 J/KS
, 3 ,0 3ESB mES Em E m
Defined outside signal region in
Si
or
Si
de
gnal
r to
Region:
estimat
deb
e b
and Re
ackgro
gion:
unds
mES [GeV/c2]
E [
MeV
]
Aug 5-7, 2002 D.MacFarlane at SSI 2002 5
Continuum Background Suppression Separate 2-jet continuum from spherical BB
events via event shape variables
Ratio of second-to-zeroth order Fox-Wolfram moments (R2):
B decays
B decays
Continuum
Continuum
R2
Angle of thrust axis of “rest of the event” wrt B candidate direction
(T)
cosT
Aug 5-7, 2002 D.MacFarlane at SSI 2002 6
Select intermediate mesons using either mass or mass difference:
After selection, candidates are constrained to nominal masses
Inclusive Open Charm States
D*+ D0+
D0 K-+
D0 K+-
m(K-+) [GeV/c2] m [GeV/c2]
Aug 5-7, 2002 D.MacFarlane at SSI 2002 7
Inclusive Charmonium Signals/J e e /J
(2 ) /
/
S J
J
(2 ) /
/
S J
J e e
Aug 5-7, 2002 D.MacFarlane at SSI 2002 8
Flavor Eigenstate Neutral B Sample
0 (*)1( , , )B D h h a 0 *0/ ( )B J K K
Ntag = 23618Purity = 84%
Ntag = 1757Purity = 96%
* 0 0 0
0
, , , ,,
S
S
D D D K K K KD K K
Charm decay modes
B decay modes
BBAABBARAR81.3 fb81.3 fbBBAABBARAR81.3 fb81.3 fb
mES [GeV/c2] mES [GeV/c2]
0( ) 28%BF D ( ) 12%BF D
0( ) 4.1%BF B
Self-TaggingModes
Aug 5-7, 2002 D.MacFarlane at SSI 2002 9
Flavor Eigenstate Charged B Sample
(*)0B D (*)1/ , (2 ) , ,C CB J K S K K K
Ntag = 15915Purity = 87%
Ntag = 6245Purity = 94%
*0 0 0 0 0, , , , SD D D K K K K
Charm decay modes
B decay modes
BBAABBARAR81.3 fb81.3 fbBBAABBARAR81.3 fb81.3 fb
mES [GeV/c2] mES [GeV/c2]
0( ) 28%BF D
0( ) 1.2%BF B
Self-TaggingModes
Aug 5-7, 2002 D.MacFarlane at SSI 2002 10
Golden Sample: (cc)KS CP Eigenstates
(2S)Ks
c1Ks
0/ ( )SJ K
0 0 0/ ( )SJ K
0(2 ) ( )SS K
01 ( )SC K
BBAABBARAR81.3 fb81.3 fbBBAABBARAR81.3 fb81.3 fb
Ncand = 974Purity = 97%
Candidates & purity for mES > 5.27 GeV/c2
Ncand = 150Purity = 97%
Ncand = 170Purity = 89%
Ncand = 80Purity = 95%
Aug 5-7, 2002 D.MacFarlane at SSI 2002 11
Selecting candidates for B J/KL
KL detected by nuclear interactions in EMC or IFRo EMC neutral clusters with energy between 0.2 and 2.0 GeV
• Veto clusters forming 0s with any other photon (E > 30 MeV)
• Remove clusters (E > 1 GeV) containing two distinct bumpso IFR neutral clusters are 2 or more RPC layers that are
unmatched to any projected charged tracko Only able to determine angle of KL wrt interaction point, not
energy
B candidates formed from mass-constrained J/ l+l- and KL candidateso Since there should be missing momentum along KL direction, cut
on difference between observed and expectedo Use cuts on J/ l+l- helicity angle (sin2h for signal) and B
candidate polar angle (sin2 wrt to z-axis)
Aug 5-7, 2002 D.MacFarlane at SSI 2002 12
Final Candidate Selection Apply constraint of
known mB mass & KL direction to determine momentum pKL
Search for signal in the one remaining variable expressed as:
signalbkg
EMC
Remove
measured – expected missing pt [GeV/c]
22 2 2
/2
/
L L
L L
B K KJ
K KJ
m E m p
p p d
* * */
* * */
LK beamJ
B
E E E E
p
LKJp p
LKd
Aug 5-7, 2002 D.MacFarlane at SSI 2002 13
CP Eigenstate Sample: B J/KL
BBAABBARAR81.3 fb81.3 fbBBAABBARAR81.3 fb81.3 fb
Signal
J/ Bkg
Fake J/ Bkg
0/ LJ K
Ncand = 988Purity = 55%
Estimated with MC
Estimated with sidebands
Resolution of about 10 MeV for E after mB
constraint
Aug 5-7, 2002 D.MacFarlane at SSI 2002 14
Sample B0 J/ KL Event
KL
Aug 5-7, 2002 D.MacFarlane at SSI 2002 15
One More Mode for CP Sample
*0 0 0 SJ/ψK K
Ncand = 147 Purity 81%
P VV: mixture of statesCP
BBAABBARAR81.3 fb81.3 fbBBAABBARAR81.3 fb81.3 fb
2
1 2 ,
| | f raction of -odd
D R
R A CP
( ) ( )(16.0 3.2 1.4 )%stat systR BABAR PRL 87, 241801 (2001)
( ) ( )(19.1 2.3 2.6 )%stat systR BELLE hep-ex/0205021
Conclude: J/ mostly CP even
Aug 5-7, 2002 D.MacFarlane at SSI 2002 16
Angular Analysis at BABAR
K* modes without
0
K* modes with 0
Projections of fits for amplitudes and rescattering phases:
22 20 , , , ,A A A
Aug 5-7, 2002 D.MacFarlane at SSI 2002 17
Time-Dependent Analysis Strategies
Measurements
Hig
her p
recisio
n
Factorize the analysis into building blocks Incre
asin
g co
mple
xity
a) Reconstruction of B mesons in flavor eigenstates
b) B vertex reconstruction
0/ Lif etimesB B
0 0 MixingB B c) Flavor Tagging + a + b
AsymmetriesCP d) Reconstruction of neutralB mesons in CP eigenstates + a + b + c
Analysis Ingredient
Aug 5-7, 2002 D.MacFarlane at SSI 2002 18
Measurement of B0 and B+ Lifetime
3. Reconstruct inclusively the vertex of the “other” B meson (BTAG)
4. Compute the proper time difference t5. Fit the t spectra
(4s)
= 0.55
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
Aug 5-7, 2002 D.MacFarlane at SSI 2002 19
B Decay Time (ps)
perfectresolution
B-Lifetimes: Time Distributions
Production point of B meson
is known with good accuracy
Proper time difference
obtained from distance z
between the two B vertices
LEP/CDF
B Factories
B Decay Time Difference (ps)
perfectresolution
Control of the resolution function at
negative times
B Decay Time (ps)
finiteresolution
Fit the parameters of the
resolution function together with the lifetime
finiteresolution
B Decay Time Difference (ps)
Aug 5-7, 2002 D.MacFarlane at SSI 2002 20
Vertex and z Reconstruction
Brec vertex
Brec daughters
z
1.Reconstruct Brec vertex from Brec daughters
Beam spot
Interaction Point
Brec direction
Btag direction
2.Reconstruct Btag direction from Brec vertex & momentum, beam spot, and (4S) momentum = pseudotrack
Btag Vertex
tag tracks, V0s
3.Reconstruct Btag vertex from pseudotrack plus consistent set of tag tracks
4.Convert from Δz to Δt, accounting for (small) B momentum in (4S) frame
Result: High efficiency (97%) and σ(Δz)rms ~ 180μm versus <|Δz|> ~ βγcτ = 260μm
Aug 5-7, 2002 D.MacFarlane at SSI 2002 21
Conversion from z to ttagrec
rec tag,rec ,tag
rec tagwhere and are in diff erent f rames
Bz z
zzt t t m
p p
t t
Proper time difference:
* * * *rec rec tag rec rec rec rec tag
Since one is f ully reconstructed and two mesons are correlated:( ) cos ( )
B Bz c t t c t t
Boost Approximation *,rec ,tag (4 ),Neglect , take : B z z S zp p p
zp t
c
rec tag
rec tag
Do not know ( ), but can compute average event-by-event:
Bt
t t t
t t t
Improved Boost Approximation *r
*rec
ec
Since cos 0, z
tc
0.2% effect
Average B Approximation 0* * * *rec rec rec reccos ( | |)
Bz c t c t
Improves resolution by 5% in quadrature
Aug 5-7, 2002 D.MacFarlane at SSI 2002 22
Actual Δt Signal Resolution Function
(Δtmeas-Δttrue)/σ(Δt)
Signal MC: Δt resolution function
Asymmetric RF:Tracks from long-lived charm in tag
vertex
~0.6 ps
Event-by-event σ(Δt) from vertex
errors
σ(Δz) [cm]
Empirical Models with parameters fit to data: Gaussian convolved with an exponential [lifetime] or Triple Gaussian [mixing, CP]
Aug 5-7, 2002 D.MacFarlane at SSI 2002 23
Effect of Charm Tracks on t
D flight direction
bias
(ztag)
Charm
tracks
ztag
Prompt B
tracks
ttrue
tmeas
zrec
tmeas – ttrue < 0
t > 0
z axis
D flight direction
bias
(ztag)
Charm
tracks
ztag
Prompt B
tracks
ttrue
tmeas
zrec
tmeas – ttrue < 0
t < 0
Underlying principle: tag vertex dominates
resolution
Aug 5-7, 2002 D.MacFarlane at SSI 2002 24
Gaussian-Exponential t Resolution Model
(1
( ; ) (0, )
(0, ) )
ˆ
()t
t t
R t G
G E
a f S
f S
Parameters:
ˆ , ,a f S
f = fraction in core Gaussian componentS = scale factor for estimated event-by-event errors = effective lifetime for charm bias component
Core Gaussian
Gaussian convolved with exponential
Motivated by inclusion of charm decay products in determination of Btag vertex, creating a small bias in the mean residual t distribution
Outlier component (measurement error not applicable) added explicitly to PDF used in likelihood fit with one additional free
parameter foutlier
where truet t t Event-by-event
uncertainties from vertex fits (t)
0.2 0.20.3 0.3, ,0.2 %, 0.2 %sig outlier bk outlierff
0.69 0.07,1.21 0.07,1.04 0 2ˆ . 4a
Aug 5-7, 2002 D.MacFarlane at SSI 2002 25
Method for Extracting Lifetime
Global unbinned maximum likelihood technique
• Includes probability-density functions (PDFs) for signal & backgrounds
• Incorporates model for t resolution function for signal & backgroundPrimary advantages:
• Incorporates all correlations between parameters describing dataset
• Extracts maximum statistical precision for desired result
Cautions:
• Need to build reasonable model that incorporates physical correlations
• Need to thoroughly test the model with Monte Carlo simulation to verify complete understanding
Aug 5-7, 2002 D.MacFarlane at SSI 2002 26
Likelihood Function for Lifetime Fits
sig,i , ˆ, ; ), ˆ( ;2
i B
i
| Δt | / τ
i t i BB
eH (Δt a) R Δt a
τ
, ,, , ,
, ,, , ,
(1 )
(1 ) (1 )
i sig i sig isig outlier sig outlier outlier i
sig i bk ibk outlier bk outlier outlier i
P p f H f O
p f H f O
Signal model:
,bk,i ,0
,0 ,0
ˆ, ; , ,
( ) (1 )2
ˆ( ; )i bk
i t i bk bk| Δt | / τ
ibk bkbk
iR Δ
H (Δt f b)e
f t fτ
t b
Background model:
Outlier model: outlier,i (0,10 ps)i GO (Δt )
Two single-sided exponentials convolved with signal Gaussian resolution function
Prompt and lifetime components convolved with separate background Gaussian resolution
function
Gaussian with zero mean and fixed 10 ps width
Probability Density Function (PDF):
Likelihood Function:
Assign probabilities for individual events to be signal (psig,i) or background (1- psig,i),
based on observed mES value and a separate global fit to the mES distribution
for the sample Sum PDFs for charged and neutral samples
for a combined fit with a total of 19 free parameters
00 0 0 0
0 , , 0 ,0, ,0
, , ,0, ,
ˆˆln ln ( , , ; , , , , , , )
ˆˆln ( , , ; , , , , , , )
i i t i sig i bk bksig outlier bk outlierBi
i i t i sig i bk bksig outlier bk outlierBi
L P t p a b ff f
P t p a b ff f
Likelihood Function
Aug 5-7, 2002 D.MacFarlane at SSI 2002 29
Signal and Background Probabilities
signal: 6967 95purity 90 %
signal: 7266 94purity 93 %
Gaussian
ARGUS function
mES (GeV/c2)
wrong-charge contamination
mES (GeV/c2)
psig,i ~ 0 psig,i ~ 0.9
Background properties from
sideband events BBAABBARAR20.6 fb20.6 fbBBAABBARAR20.6 fb20.6 fb
Neutral Neutral BB Mesons Mesons
Charged Charged BB Mesons Mesons
2(1 )20 0( ; , ) 1 , where /ESx
BES ES ES ES ESA m m A m x e x m m
ARGUS background function:
Aug 5-7, 2002 D.MacFarlane at SSI 2002 30
B-Lifetime Measurements
Good agreement with previous lifetime measurements
Excellent control of the time resolution function (parameterization, tails)
0
0
1.546 0.032 0.022 ps1.673 0.032 0.023 ps
/ 1.082 0.026 0.012
B
B
B B
(error PDG2000 ~ 0.03 ps, stat+syst)
BABAR PRL 87, 201803 (2001)
Proof of principle for time-dependent analysis at B Factories
background
BBAABBARAR20.7 fb20.7 fbBBAABBARAR20.7 fb20.7 fb
Aug 5-7, 2002 D.MacFarlane at SSI 2002 31
B-Lifetime Measurements
Good agreement with previous lifetime measurements
Excellent control of the time resolution function (parameterization, tails)
0
0
1.554 0.030 0.019 ps1.695 0.026 0.015 ps
/ 1.091 0.023 0.014
B
B
B B
(error PDG2000 ~ 0.03 ps, stat+syst)
Belle PRL 88, 171801 (2002)
Proof of principle for time-dependent analysis at B Factories
background
BelleBelle29.1 fb29.1 fbBelleBelle
29.1 fb29.1 fb
Aug 5-7, 2002 D.MacFarlane at SSI 2002 32
Measurement of B0B0 Mixing
3. Reconstruct Inclusively the vertex of the “other” B meson (Btag)
5. compute the proper time difference t
(4s)
= 0.55
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
3. Reconstruct Inclusively the vertex of the “other” B meson (Btag) 4. Determine the flavor of Btag to separate Mixed and Unmixed events
Tag B
z ~ 110 m
5. compute the proper time difference t 6. Fit the t spectra of mixed and unmixed events
Aug 5-7, 2002 D.MacFarlane at SSI 2002 33
0B D
0 ,B DX D K X
0 0, sB D X D D
Methods for B Flavor Tagging
0 *,B D D K
Many different physics processes can be used
Secondary lepton
K
Kaon(s)
Soft pions from D* decays
, Fast charged tracks
Primary lepton
b c sW W
Aug 5-7, 2002 D.MacFarlane at SSI 2002 34
Use charge correlations with decay products to define two physics categorieso “Lepton”o “Kaon”
Multivariable techniques used to combine PID, kinematic variables, correlations, event informationo e.g., primary lepton without PID,
soft pions from D* decays
o Multivariable analysis with neural network techniques: “NT1”, “NT2” categories
0B D 0 ,B DX D K X
0 0, sB D X D D
Flavor Tagging for Mixing Study
* 1.0[1.1] GeV/ c f or [ ]p e
No confl icting Lepton tag, 0ikaons
q
Aug 5-7, 2002 D.MacFarlane at SSI 2002 35
Electron ID at BABARo Match track to EMC
clustero 0.89 < EEMC/p < 1.2
o EM shower shape requirements
o DCH dE/dx and DIRC Cherenkov angle consistent with electron hypothesis
eff e=91%, misid=0.13%
Aug 5-7, 2002 D.MacFarlane at SSI 2002 36
Electron ID at Belleo Match track to ECL clustero EECL/p ratio requirement
o EM shower shape requirements, track-cluster matching
o DCH dE/dx, TOF, ACC consistent with electron hypothesis
eff e=94%, misid=0.5%
Aug 5-7, 2002 D.MacFarlane at SSI 2002 37
Muon ID at BABARo # int. lengths in IFR >2.2o Difference in measured
and expected int. length <1
o Match bet’n extrapolated track and IFR hits
o Requirements on average and spread of # of IFR hits per layer
eff =75%, misid=2.5%
Aug 5-7, 2002 D.MacFarlane at SSI 2002 38
Muon ID at Belleo Difference in measured
and expected rangeo Match bet’n extrapolated
track and KLM hitso Likelihood based selection
eff =90%, misid=1%
Open = Loose; Closed = Tight
Effi
cie
ncy
Pio
n f
ake r
ate
Aug 5-7, 2002 D.MacFarlane at SSI 2002 39
Some Inputs to NN Tagger
Opening angle between input
track and thrust axis of recoil B
0
0
,
s
B D XD D
Sum of energy within 90o of estimated W
direction
Opening angle between input
track and missing
momentum vector
CMS momentum of input track
0B D
0B D
0B D
Aug 5-7, 2002 D.MacFarlane at SSI 2002 40
Flavor Tagging Performance in Data
Tagging category
Fraction of tagged
events(%)
Wrong tag fraction w (%)
Mistag fraction
difference w (%)
Q =
(1-2w)2 (%)
Lepton 10.9 0.3 9.0 1.4 0.9 2.2 7.4 0.5
Kaon 35.8 1.0 17.6 1.0 -1.9 1.5 15.0 0.9
NT1 7.7 0.2 22.0 2.1 5.6 3.2 2.5 0.4
NT2 13.8 0.3 35.1 1.9 -5.9 2.7 1.2 0.3
ALL 68.4 0.7 26.1 1.2
The large sample of fully reconstructed events provides the precise determination of the tagging parameters required in the CP fit
Highest “efficiency” Smallest mistag fraction
BBAABBARAR29.7 fb29.7 fbBBAABBARAR29.7 fb29.7 fb
Error on sin2 and md depend on the “quality factor” Q approx. as:
1sin 2
Q
Aug 5-7, 2002 D.MacFarlane at SSI 2002 41
Decay Time Difference (reco-tag) (ps)
UnMixedMixed
0
10
20
30
40
50
60
-8 -6 -4 -2 0 2 4 6 8
0
0 0 0 0
0 0 0unmixed
1
mixed
cos4
B
mixing, tag tagflav
| Δt | / τ
mixi
mixing, tag tagflav
ng, dB
fl
fl v
a
a
v
"f " (B B or B B )
"f "
ef (Δt) Δm Δt
τ
(B B or B B )
0
0 0 0 0
0 0 0unmixed
1
mixed
cos4
B
mixing, tag tagflav
| Δt | / τ
mixi
mixing, tag tagflav
ng, dB
fl
fl v
a
a
v
"f " (B B or B B )
"f "
ef (Δt) Δm Δt
τ
(B B or B B )
0 0 0
0 0 0
0
0
1 cos4
1 2
unmixe
mixed
( )
d
B
mixing, tag tagflav
mixing, tag tagf
| Δt | / τ
mixin
lav fla
g, dB
flav
v
"f " (B B or B B )
"f " (B
ω R Δe
f (Δt) Δm Δt
B or B B
τt
)
0 0 0
0 0 0
0
0
1 cos4
1 2
unmixe
mixed
( )
d
B
mixing, tag tagflav
mixing, tag tagf
| Δt | / τ
mixin
lav fla
g, dB
flav
v
"f " (B B or B B )
"f " (B
ω R Δe
f (Δt) Δm Δt
B or B B
τt
)
is the flavor mistag probability is the time resolution function
ωR( t)
B-Mixing Analysis:Time Distributions
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
realistic mistag probability,
finite time resolution
Aug 5-7, 2002 D.MacFarlane at SSI 2002 42
Triple-Gaussian t Resolution Model
Core Gaussian
Tail Gaussian
Outlier Gaussian
( ; ) ( , )
( , )
(
ˆ
, )
core core core
tatail
outlier
il tail
outlier outlier
R t f G
G
a
f
Gf
,
Bias
0
core
tail
outli
core c
tail
t
t
er
b
b
Widths
8 ps
core
tail tail
outlie
core t
t
r
S
S
(1 )tail outliercore fff
Parameters: ,, ,ˆ , ,core core ctail outlier taila ff S b b
f = fractions in tail and outlierS = scale factor for estimated
event-by-event errorsb = bias factor due to inclusion of
charm products in tag vertex
Event-by-event uncertainties from vertex
fits (t)
Aug 5-7, 2002 D.MacFarlane at SSI 2002 43
Monte Carlo
Correlation: (t) and residual t bias
z axis
ztag
Prompt B
tracks
Charm
tracks
D flight direction
(t) smallest, t
bias zero
(ztag) D flight direction
bias
(ztag)
Charm
tracks
ztag
Prompt B
tracks
(t) largest, t bias largest
Aug 5-7, 2002 D.MacFarlane at SSI 2002 44
Mistag fraction versus vertex error for kaon tags
Yet another correlation!
Tests of likelihood fit with full Monte Carlo shows bias of +0.0070.003 for md (about 40% of statistical
error!)
Mystery:
Resolved!2mistag rate scaled by tp
pt spectrum of wrong-sign kaons softer than those in correct-tag processes
2But: ( ) 1/ tt p Systematic difference in pt
leads to correlation
Aug 5-7, 2002 D.MacFarlane at SSI 2002 45
Fit Results for Signal Resolution Parameters
Run 1 Run 2
Score 1.37 0.09 1.18 0.11
bcore lepton 0.06 0.13 -0.04 0.16
bcore kaon -0.22 0.08 -0.25 0.09
bcore NT1 -0.07 0.15 -0.45 0.21
bcore NT2 -0.46 0.12 -0.20 0.16
btail -5.0 4.2 -7.5 2.4
ftail 0.014 0.020
0.015 0.010
foutlier 0.008 0.004
0.000 0.014
Non-zero bias for kaons
Aug 5-7, 2002 D.MacFarlane at SSI 2002 46
Additions to the Likelihood Function
1 2 1 2D w D w
12
w w w w w w
12
D D D D D D
0
0
,
,
11
2cos
co2
s1
1
dmixing,
dmixing,
tag B
tag B
f (Δt) Δm Δt
f
D D
D D(Δt) Δm Δt
1. Allow for difference in B0 vs B0 mistag rates
PDFs now depend on tag state as
well
2. Allow for prompt and non-prompt background components
Adds fractions for each tagging category, effective lifetime for non-prompt component, and “effective dilutions” for both
8 parameters
4+1+8 parameters
Aug 5-7, 2002 D.MacFarlane at SSI 2002 47
Blind Analyses Analyses were done “blind” to eliminate
possible experimenters’ biaso In general, measurements of a quantity “X” are done with
likelihood fits – blinding achieved by replacing “X” with “X+R” in likelihood fits
• R is drawn 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• Allows all systematic studies to be done while still blind
Aug 5-7, 2002 D.MacFarlane at SSI 2002 48
md Likelihood Fit
Combined unbinned maximum likelihood fit to t spectra of mixed and unmixed events in the B flavor sample
All t parameters extracted from data Correct estimate of the error and correlations
Fit Parameters # Main Sample
md 1 Signal
Mistag fractions for B0 and B0 tags
8 Signal
Signal resolution function 2x8 * Signal
Description of background t 5+8 Sidebands
Background t resolution 2x3 * Sidebands
B lifetime from PDG 2002 0 B = 1.548 ps
Total parameters 44
* 2 running periods
Aug 5-7, 2002 D.MacFarlane at SSI 2002 50
Final Tagged Mixing Sample
1097 34(96.0 0.7)%
signalNPurity
798 31(88.9 1.2)%
signalNPurity
3156 63(84.6 0.7)%
signalNPurity
1293 43(79.4 1.3)%
signalNPurity
Gaussian
ARGUS function
psig,i ~ 0 psig,i ~ 0.96
Background properties from
sideband events
Lepton KaonLepton
NT2NT1
Aug 5-7, 2002 D.MacFarlane at SSI 2002 51
1(0 516 0 016 0 010 ) ps d (stat) (syst)Δm . . . BABAR PRL 88, 221802 (2002)
Mixing with Hadronic Sample
BBAABBARAR29.7 fb29.7 fbBBAABBARAR29.7 fb29.7 fb
Precision measurement consistent with world average
Signal: mES>5.27
Bgnd: mES<5.27
Aug 5-7, 2002 D.MacFarlane at SSI 2002 52
)
1 2 cosd
mixing
B
A ( tω Δm Δt
Mixing Asymmetry with Hadronic Sample
Unfolded raw asymmetry
t [ps]
dm/π~
21~
Folded raw asymmetry
|t| [ps]
BBAABBARAR29.7 fb29.7 fbBBAABBARAR29.7 fb29.7 fb
Aug 5-7, 2002 D.MacFarlane at SSI 2002 53
Systematic Errors on md
[md]
Description of background events 0.004
Background fractions, sideband extrapolation
Background t structure and resolution
Peaking B+ background
t resolution and detector effects 0.005
Silicon detector residual misalignment
t resolution model
(t) requirement
Fit bias correction and MC statistics 0.003
Fixed lifetime from PDG2000 * 0.006
Total 0.010
* Now improved with PDG2002
Aug 5-7, 2002 D.MacFarlane at SSI 2002 54
Mixing in Hadronic Modes at Belle
1(0 528 0 017 0 011 ) ps d (stat) (syst)Δm . . .
BELLEBELLE29.1 fb29.1 fbBELLEBELLE29.1 fb29.1 fb
Aug 5-7, 2002 D.MacFarlane at SSI 2002 55
1. Fully reconstruct one B meson in CP eigenstate (Brec)2. Reconstruct the decay vertex
1. Fully reconstruct one B meson in CP eigenstate (Brec)2. Reconstruct the decay vertex
5. compute the proper time difference t 6. Fit the t spectra of B0 and B0 tagged events5. compute the proper time difference t 6. Fit the t spectra of B0 and B0 tagged events
Measurement of sin2
3. Reconstruct Inclusively the vertex of the “other” B meson (Btag) 4. Determine the flavor of Btag to separate B0 and B0
(4s)
= 0.56
Tag B
z ~ 110 m Reco Bz ~ 65 m
-z
t z/c
K0
KS0
-
+
+
Aug 5-7, 2002 D.MacFarlane at SSI 2002 56
0 0
0 0( ) 1 2 sin2 sintag tagCP d
tag tag
N(B B ) N(B B )A t ω β Δm Δt
N(B B ) N(B B )
( ) 1 2 cosmixing d
N(unmixed) N(mixed)A t ω Δm Δt
N(unmixed) N(mixed)
Time-Dependent CP Asymmetries
Use the large statistics Bflav data sample to determine the mistag probabilities and the parameters of the time-resolution function
0 0/ SCPB J K
Time-dependence ofCP-violating asymmetry in
0 0- mixingB B Time-dependence of
(Assuming no confusion of Brec state)
Aug 5-7, 2002 D.MacFarlane at SSI 2002 57
Summary Precision measurements of lifetimes and B0
oscillations have been performed at the B Factorieso Require the development of all techniques for B reconstruction,
determination of vertex separation, tagging of the recoil B state at decay, unbinned maximum likelihood fitting and validation procedures
o Results are in excellent agreement with previous results and represent some of the single most-precise measurements available
mmdd = 0.516 = 0.516 ± ± 0.016 (stat)0.016 (stat) ± ± 0.010 (syst) ps0.010 (syst) ps-1-1
BELLE preprint-02/020, hep-ex/0207022, to appear in PLB
BABAR PRL 88, 221802 (2002)
mmdd = 0.528 = 0.528 ± ± 0.017 (stat)0.017 (stat) ± ± 0.011 (syst) ps0.011 (syst) ps-1-1
Tomorrowo Apply tools to measurement of CP violation in neutral B decays
Aug 5-7, 2002 D.MacFarlane at SSI 2002 58
Bibliography: Lecture 2
1. [lifetime] BABAR Collab., B.Aubert et al., PRL 87, 201803 (2001)2. [lifetime] Belle Collab., K.Abe et al., PRL 88, 171801 (2002)3. [mixing] BABAR Collab., B.Aubert et al., PRL 88, 221802 (2002)4. [mixing] Belle Collab, T.Tomura et al., hep-ex/0207022, to appear
in PLB5. [mixing] BABAR Collab., B.Aubert et al., hep-ex/0201020, to
appear in PRD