helicity of w bosons in top quark decays at cdf
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Helicity of W bosons in Top Quark Decays at
CDFShulamit Moed, University of
GenevaOutline:
Introduction
Motivation
Overview of W helicity studies
1D measurement of W helicity fractions with 955pb-1 of data
2D measurement of W helicity fractions with 955pb-1 of data
Summary
2
Why is top quark interesting?
Youngest member of the SM family
Striking characteristic: HUGE mass , at EWSB scale (Yukawa coupling ~1) - what does this tell us?
Unique opportunity to probe bare quark properties (spin? charge?)
Top special relation to the Higgs boson
Is top the gateway to new physics?
Top chargeTop spinTop lifetimeTop mass
Branching ratiosRare decaysNon-SM decaysDecay kinematicsW helicityAnomalous coupling|Vtb|
Production cross sectionResonance productionProduction kinematicsSpin polarization
3
The Tevatron
Main Injector
Tevatron
DØCDF
Chicago
p source
Booster
W helicity result
with 955 pb-1
p-pbar collisions with 1.96TeV
center-of-mass energy.
Until LHC turns on - the only place to study top quark
4
Top production at the Tevatron
q
q
t
t
t
t
g
g
Top pair production
Main mechanism for top physics at Tevatron
Single top production Not yet observed different final states than pair production Larger background
For top mass = 175 GeV
@ √√s= 1.96 TeVs= 1.96 TeV: pb
pblumisyststat
tt
tt
8.07.6
)(4.0.)(6.0.)(5.03.7
~85% ~15%
(theory)
CDF combined
~1 top event every 10 BILLION inelastic collisions
L
NN bkgobs
tt
geometric and kinematic acceptance
selected eventsestimated bkg
5
t-tbar Final States
Top decays before hadronizing
~10-25 s (due to large mass)
Vtb~1; Mtop>MW+Mb: Decays to real W
BR(tWb) ~ 100%
all-jets44%
dilepton5%
lepton+jets15%
lepto
n+
jets
15
%e jets
e
jets
Final states are classified by the decay of the W’sBR(Wl) = 1/3BR(Wqq) = 2/3In all cases, the final state has 2 b quarks
Lepton+jets
Di-lepton
All hadronic
6
Lepton+Jets Channel
Best compromise higher statistics than dilepton, less background than all-hadronic Purity of the l+jet channels is not that high (S:B ~1:3)
Increase S:B by using b-tagging Fully reconstruct the event
Detected objects for full event reconstruction:
4 energetic jets
1 isolated charged lepton
Missing Et for the neutrino
Do not know with certainty the correct assignment between parents and decay products
??
7
Muon system
CMP ; CMU |η|<0.6
CMX 0.6<|η|<1.0
The CDF detector
Tracking system: Silicon detector -> b tagging COT : central outer trackerEff. for charged particle tracks: ~100% for |η|<1.0 ~40% for |η|≈ 2.0
calorimeters
Excellent lepton ID:~80% eff. for central electrons~90% eff. for high Pt muons
Up to |η|<3.6
z
x
y)2/tan(ln
pseudorapidity
8
W helicity in top quark decays
bWVt
igtb
5122
PJH
SM top decays via the weak interaction
V-A coupling like all other fermions:
t
spin=1/2
W
spin=1
b
spin=1/2
Helicity:
22
2
0
0
00
2
)()()(
)(
tw
t
RL
mm
mf
WWW
Wf
The longitudinal fraction:
This measurement:
Test of the SM, non-zero V+A?
EWSB – prediction of high longitudinal W fraction
9
What do we measureWhat do we measure? ?
bl
blbl
pp
EEpp )cos( *
We fully reconstruct the event using:
SM prediction of helicity fractions )assuming Mt=175GeV(:
longitudinal f0 = 0.7
left-handed f- = 0.3
right-handed f+ = 0
Left-handed longitudinal Right-handed
2* )cos1( 2* )cos1( )cos1( *2
V+A is suppressed
1/2
10
Sensitive Variables
cos(θ*)…
M2lb = 1/2 (M2
t – M2W)(1 + cos θ*)
Lepton-b invariant mass
Lepton transverse momentum
comp
lexity
11
Other W Helicity Measurements
LCF
F
.%95@27.0
74.0 22.034.00
RunI (Mlb)2 :
Early RunII:
1)7109( pbIntegrated luminosity=
Previously at CDF
D0 09/2006 370 pb-1
cos(θ*) method
LCf
f
AV
AV
.%95@23.0
057.008.0056.0
12
Analysis Overview
lepton+jets selection fully reconstruct the leptonic top
decay. calculate cos(θ*) construct templates for left-handed,
right handed and longitudinal W’s and background
fit helicity fractions using unbinned likelihood fitter.
correct for acceptance effects. estimate systematic uncertainties.
13
Event Reconstruction
Selection main features: only one isolated lepton with PT >20 GeV
at least 4 jets with ET > 15 GeV and |η|<2.0 (JETCLU with ΔR=0.4)
missing ET > 20 GeV
at least one jet is tagged with a secondary vertex tagging
veto on electrons from photon conversion
veto on events tagged by cosmic ray tagger
scalar sum of transverse energies of all reconstructed objects (Ht) > 200 GeV
Reconstructed objects – 4 jets + 1 lepton
24 permutations of possible combinations , which one we choose?
14
b-jet Tagging
Expect t W bb jet tagging is a very important tool.
- Every ttbar event contains 2 b-jets - Less than 20% of the dominant
background (W+jets) contains Heavy Flavor (b/c quarks)
B decay signature: displaced vertex Long life time c ~ 450 m: travels
Lxy~3mm before decaying
Require at least 1 jet tagged with the secondary vertex tagging algorithm.
Reduce permutations from 24 to 12!
b-tagb-tag
b-tagb-tag1.2 cm
CDF Event:CDF Event:
Close-up View of Layer 00 Silicon Close-up View of Layer 00 Silicon DetectorDetector
MET
15
Jet Energy Scale
Corrections applied to estimate the original parton energies from the observed jet energy in the calorimeter
Jets are corrected for:
η dependence correction – homogenous calorimeter response.
subtraction of energy due to pile-up of multiple interactions in the same bunch crossing.
correction for non-linearity and energy loss in the uninstrumented regions of the detectors.
Underlying event energy that falls inside the jet cone.
Jet energy radiating out of the jet cone.
Top specific corrections – flavor and topology of ttbar events.
16
Kinematical Fit
Provides constraints on W mass, t mass= anti-top mass etc.
Fit lowest Χ2 used to select the most likely combination
Χ2
2
2
2
2
2
2
2
2
4,
2,,2
t
tbl
t
tbjj
W
Wl
W
Wjj
jetsli i
measiT
fitiT MMMMMMMMPP
PT resolutions 1.5 GeV
2.5 GeV
MW , Mt = pole masses
efficiency ≈ 33%
17
Selected Data SampleSelected Data Sample
Use lepton+jets selection with at least one b-tagged jet and Ht>200GeV cut )to reduce QCD background( for events with njets >= 4:Data 220 events (89% signal fraction)
Total background 22.8 events
Process bkg events
fraction fraction
Mistag 9±1.35 39.5% 4.1%
W+h.f. 6.4±1.85 28% 2.9%
Single top 0.54±0.17 2.4% 0.25%
Diboson 1.36±0.07 6% 0.61%
QCD 5.5±1.08 24.1% 2.5%
Background composition
Scaled to 955pb-1
18
Monte Carlo Samples
Used HERWIG based samples with top mass of 175 GeV.
In these samples one the leptonic W is forced to a specific helicity (longitudinal, left handed or right handed).
The hadronically decaying W decays according to SM.
reconstructed
particle-level
19
ParameterizationsParameterizations
Comparison of signal and background fits used for likelihood fitter parameterizations.
Fit to 3rd order polynomial times exponential.
Background model is a mix of Wbbpp, W4p and diboson sample.
longitudinal
background
left-handed
right-handed
20
The LikelihoodThe Likelihood
sN
isbbbbsbb pfpfbsPbGL
1
** ))(cos)1()(cos()|(),|(
Fitter to extract helicity fractions:
Use unbinned maximum likelihood fit. Pseudo experiments generated from ideal functions look fine. Tested ‘real’ pseudo experiments with arbitrary f0, f-, f+. (from templates) Tested ‘real’ pseudo experiments SM ttbar sample. (pythia) Fit residual and pull width look fine.
Gaussian bkg constraint
Poisson probability for number of observed events
shape information
pFFpFpFps )1( 000
longitudinal
left-handed
right-handed
Extract two results by fitting for:
F0 while F+=0
F+ while F0 is fixed to the SM value @Mt=175GeV
21
The likelihood Fitter – Linearity ChecksThe likelihood Fitter – Linearity Checks
MC input(f0, f+)
Fits(f0, f+)
(0.3, 0.0)(0.310.03, fixed)
(0.5, 0.0)(0.510.03, fixed)
(0.7, 0.0)(0.710.03, fixed)
(0.9, 0.0)(0.900.03, fixed)
(0.7, 0.0)(fixed, 0.00 0.001)
(0.7, 0.1)(fixed, 0.100.01)
(0.7, 0.2)(fixed, 0.200.01)
Expected stat. uncertainty for f0 : δf0 = 0.12 and for f+: δf+ = 0.058
Linearity checks and sensitivity with <S+B>=220 events: All fits are consistent with “no bias”.
22
The Likelihood Fitter – SM exampleThe Likelihood Fitter – SM example
Right-handed,
f0 fixed
Means and pulls for realistic pseudo experiments constructed with SM values:
Longitudinal,
f+ fixed
f+ = 0
F+ = 0.006
f0 = 0.7
F0 = 0.708
σ = 10.023σ = 0.990.023
23
Acceptance
In the fitter, all templates are normalized to 1, In the fitter, all templates are normalized to 1, butbut– –
our acceptance for WL≠ W0≠ WR
Cuts on lepton PT and isolation left (right) acceptance is smaller (larger) relative to the longitudinal W’s.
Applying an acceptance correction:
Recall:
24
Acceptance Correction
fff
fF
00
000
)1(
)1(1
)1()1(
).(
).(
0
00
0
00
0
RfR
fF
RF
FRFcorrection
allongitudinAcc
handedleftAccR
F0=measured fraction ; f0= true fraction
for the right-handed fraction:Correction for f+ is very small (~0.01) not applied.Instead – assign a 1% systematic.
αi = accptance for helicity i
25
Systematic UncertaintiesSystematic Uncertainties
We use realistic pseudo experiments to estimate systematic uncertainties while keeping the fit unchanged.
Source
Bkg model
JES
Signal model
ISR/FSR
MC statistics
Instantaneous luminosity
Lepton energy scale
Acceptance correction
Total syst.
δf0
±0.038
±0.013
±0.020
±0.009
±0.010
±0.020
±0.007
±0.001
±0.001
±0.053
δf+
±0.017
±0.010
±0.010
±0.006
±0.005
±0.010
±0.002
±0.002
±0.001
±0.027Expected stat. uncertainty 0.12 0.06
26
Results – Data FitResults – Data Fit
Fitting the data:
F0 = 0.65 (measured)
f0 = 0.60 ± 0.12 ± 0.06, (corrected) f+ = 0 fixed
f+ = -0.06 ± 0.06 ± 0.03, f0 fixed to SM value
@Mt=175 GeV
Fit for right-handed fraction
Fit for longitudinal fraction
27
Results - Likelihood CurvesResults - Likelihood Curves
For longitudinal fraction
For right-handed fraction
28
Results – Setting Upper Limit on fResults – Setting Upper Limit on f++
Bayesian method for setting a limit@95% C.L:
Model systematic uncertainties as a gaussian with =0, σ= 0.027 .
- Have verified f+ systematic independent of f+
Convolute with likelihood
- as expected the effect is small, dominated by statistics.
f+<0.11@95% C.L
W systematics
w/o systematics
29
Expected Statistical Uncertainty
Assuming no improvements, stat~syst with 4fb-1.
30
2D Fit – First Simultaneous f0, f+ measurement !
000
0
0
0
11 FF
F
f
000
0
0
11 FF
F
f
Same data, same reconstruction, same templates etc.
fit for f0 and f+ simultaneously, rather than:
Fixing f+ to 0 (=SM) and fitting for f0
Fixing f0 to 0.7 (=SM) and fitting for f+
---> Less precision, but a more general result
when fixing one fit parameter to its SM value (1D fit), the correction is either simple (f0) or negligible (f+)
With the increasing luminosity:
Interest in a model independent measurement
V+A coupling bounded by CLEO bsγ data at a level that cannot be reached even at the LHC.
No assumption on helicity fractions while fitting, probe any deviation from SM (super-symmetry, dynamical electroweak symmetry breaking models, Extra dimensions ….)
31
Uncertainties for Simultaneous Fit
Systematics
statistical
0.25
0.10
Compared with 1D fit –
0.053 for f0
0.027 for f+
Compared with 1D fit –
0.12 for f0
0.06 for f+
Expected sensitivity from 1000 SM p.e:
32
2D Fit Results
f0 0.740.25(stat)0.06(syst)
f 0.060.10(stat)0.03(syst)
33
Limit on f+?
Form probability surface Find contour of constant
probability that captures 95% of the volume under the surface
No systematics in likelihood shape.
but for 2D fit: stat syst = stat
34
Summary
Results: 1D fit
f0 = 0.6 ± 0.12(stat.) ± 0.06(sys.), f+ = 0 fixed
f+ = -0.06 ± 0.06(stat.) ± 0.03(sys.), f0 fixed to SM
value @175GeV
f+ < 0.11 @ 95% C.L (including systematics)
2D fit
First simultaneous measurement of right-handed and longitudinal W helicity fractions! Improvement of CDF 1D results of longitudinal and right handed W fractions. Our knowledge of t-W-b vertex is still statistically limited. CDF now factor of 2 better than previous measurements. However still factor of 2 above current systematics - This is worth doing as a 4 fb-1 analysis on CDF. Measurement consistent with SM predictions – top decay is of V-A nature. Current status - working towards a publication .
f0 0.740.25(stat)0.06(syst)
f 0.060.10(stat)0.03(syst)
35
Back up slides
36
Top Mass Dependence
Top mass is not constrained in this analysis.
Fit to a linear function yields a correction of 0.5% for a 1σ variation of the top mass (3 GeV).
37
Systematic Uncertainties – BackgroundSystematic Uncertainties – Background
Background shape systematic:
Assume 100% W4p or 100% Wbb2p
Add 25% special QCD sample
Vary q2 for W sample
reminder - estimated ~5 QCD events out of 220
Special QCD sample Multi-jet trigger
0.8<em<0.95
Ntracks>3
38
Background Dominated SamplesBackground Dominated Samples
Comparison of 0-tag sample and bkg model
We have a reasonable background model
39
Systematic Uncertainties – MC StatisticsSystematic Uncertainties – MC Statistics
Statistical uncertainty of the parameterizations is not propagated through the analysis systematic uncertainty:
Re-fitting templates 1000 times, Poisson fluctuate the bins around central value.
Draw pseudo-experiments from the different fits.
Take difference in RMS of fitted values as a systematic :
δf0=0.02 δf+=0.01
40
Systematic Uncertainties - PDF
difference between MRST72 and CTEQ5L.
difference between MRST75 and MRST72.
variation of the 20 CTEQ6M eigenvectors.
21
220
1
))]()([(2
1
i
ii SFSFF
41
2D Pull Distributions
42
955pb-1 – Data/MC Comparison
43
955pb-1 – Data/MC Comparison
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