Optimal Use of Information for Measuring Mt in lepton jets tt Events'

1
Optimal Use of Information for Measuring Mt in
leptonjets tt Events.

• Juan Estrada for the
• DØ Collaboration
• HCP 2002

• Published measurement of Mt at DØ
• The new approach for Mt measurement
• New preliminary measurement of Mt ( and check of
  MW)
• MC tests with the new approach
• Conclusions

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Event topology and selections

• DØ Statistics RunI (125 pb-1)
• Standard Selection
• Lepton Etgt20 GeV,?elt2,??lt1.7
• Jets ?4, ETgt15 GeV, ?lt2
• Missing ET gt 20 GeV
• ETW gt 60 GeV ?W lt2
• gives 91 events
• Ref. PRD 58 (1998), 052001
• After ?2 29 signal 48 backg. (0.8 Wjets and
  0.2 QCD)
• (77 events)
• Additional cuts for this analysis
• 4 Jets only 71 events
• Background Prob. 22 events

p
p
12 jet permutations/event
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Published measurements of Mtat DØ and CDF
A multidimensional (xi) template is obtained for
each value of the input mass, and the data sample
is then compared with those MC templates to find
the most likely value for mt
Template(ximtB)
Template(ximtA)

• A prescribed permutation is selected on basis of
  a kinematic fit.
• A few variables, containing most of the
  information, are selected for the templates.
• The background is accounted for using its own
  template.
• A likelihood is built to select the templates
  closest to the data.

Data gt mtB
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New approach for this measurement by DØ
The probability for each event being signal is
calculated as a function of the top mass. The
probability for each event being background is
also calculated. The results are combined in one
likelihood for the sample. (Similar to the
methods of Dalitz, Goldstein and Kondo, and Mt
measurement in the dilepton channel by DØ - PRD
60 52001 (1999).)
P(mt)
background event
signal event
?
?
?
Psignal
Pbackground
mt
For each event, signal and background
probabilities are added. The probabilities for
individual events are then multiplied together.
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Three differences between the two approaches
Template Method
New Method

• All the events are presented to the same
  template.
• The template corresponds to a probability
  distribution for the entire sample, using several
  variables calculated from MC simulations.
• The features of individual events are integrated
  (averaged) over the variables not considered in
  the template.

• Each event has its own probability distribution.
• The probability depends on all measured
  quantities (except for unclustered energy).
• Each event contributes with its own specific
  features to the probability, which depends how
  well is measured.

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Probability for tt events (d?)
2(in) 18(final) 20 degrees of freedom 3(e)
8(?1..?4) 4(PinPfinal)1(EinEfinal) 15
constraints 20 15 5 integrals Sum over 12
combinations of jets All values of the neutrino
momentum are considered ?1 momentum
of one of the jets m1,m2 top mass in the
event M1,M2 W mass in the event f(q1),f(q2)
parton distribution functions (CTEQ4) for qq
incident chann. q1,q2 initial parton
momenta ?6 six particle phase
space W(x,y) probability of measuring x when
y was produced in the collision We choose these
variables of integration because M2 is almost
negligible, except near the four peaks of the
Breit-Wigners within M2.
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Acceptance Corrections
Likelihood
Detector Acceptance
Measured probability
Detector acceptance
Production probability
where
, Ngen(N) is number of generated(observed) events
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Signal and Background

• The background probability is defined only in
  terms of the main backgound (Wjets, 80) which
  proves to be and adequate representation for
  multijet background.
• The background probability for each event is
  calculated using VECBOS subroutines for Wjets.
• The values of c1 and c2 are optimized, and the
  likelihood is normalized automatically at each
  value of ?.

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Transfer function W(x,y)
W(x,y) probability of measuring x when y was
produced (x jet variables, y parton variables)
where Ey energy of the
produced quarks Ex measured
and corrected jet energy pye
produced electron momenta pxe
measured electron momenta ?y j
?xj produced and measured jet angles
Energy of electrons is considered well measured.
And due to the excellent granularity of the D?
calorimeter angles are also considered as well
measured. A sum of two gaussians is used for the
jet transfer function (Wjet), parameters
extracted from MC simulation.
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S/B discrimination
One can define a discriminator, in the same way
as was done for the published analysis DPs/(PsP
bkg) We do not select on this variable, but
present it to show how well we can distinguish
signal from background.
PRD 58 52001, (1998)
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Extra selection in Pbkg
Pbkglt1E-11
Wjets
ttbar_at_175GeV
In order to increase the purity of signal another
selection is applied on Pbkg, with efficiencies
?signal 0.70, ?Wjets 0.30,
?multijets 0.23
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New preliminary Result with DØ RunI data
DØ Preliminary
DØ Preliminary
Mtpreliminary 179.9 ? 3.6 GeV ? SYST This new
technique improves the statistical error on Mt
from 5.6 GeV PRD 58 52001, (1998) to 3.6 GeV.
This is equivalent to a factor of 2.4 in the
number of events. 22 events pass our cuts, from
fit (12 s 10 b)
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Check of Mw with DØ RunI data
This can be very helpful for reducing the
uncertainty in the jet energy scale (JES) , DØ
has already been studying this option, for
reference see the Proceedings of DPF2002 (Top
quark physics) http//dpf2002.velopers.net/talks_p
df/120talk.pdf. Mw can be measured in the same
events where Mt is measured!
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Crosschecks on Ensemble tests (12s10b)
From the ensemble tests we estimate a 0.5 GeV
bias in the peak with respect to the generated
value
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Crosschecks on Ensemble tests (12s10b)
The most probable result of these experiments is
Mt174.7 GeV (top generated at Mt175.0 GeV).
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Crosscheck of linearity of response
Test of linearity of response is with MC samples
containing large numbers of events.
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Total Uncertainty
DØ Preliminary

• I. Determined from MC studies with large event
  samples

II. Determined from data
We will reduce this error in our final result (Mw)
Total systematic 6.0 GeV Total 7.0 GeV
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Systematic Uncertainty JES
At DØ we studied the JES in MC and data using a
sample of ?jet PRD 58 52001, (1998), as a
result we have a function that matches the JES in
MC and data. To estimate the error in Mt due to
the JES, we did the analysis of data with and
without this correction and the difference is
assigned as a systematic uncertainty ?5.6
GeV This is our dominant error, but DØ plans to
reduce it using the observed Mw.
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Conclusions

• Mtpreliminary 179.9 ? 3.6 (stat) ? 6.0 (syst.)
  GeV
• Significant improvement to our previous
  measurement with Mt 173.3 ? 5.6 (stat) ? 5.5
  (syst.) GeV (LB analysis in PRD) is equivalent to
  2.4 times more data
• Correct permutation is always considered (with
  the other 11)
• All features of individual events are included,
  thereby well measured events contribute more
  information than poorly measured events.
• Discrimination of signal to background improves
  dramatically.
• The possibility of checking the value of the W
  mass in the hadronic branch on the same events
  provides a new handle on controlling the largest
  systematic error, namely, the jet energy scale.

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Background probability in Data
Comparison of (10signal 12 background) MC and
data sample. FIN
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Discriminator in Data (PR4)
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Number of events for signal and backg.
Mt190 GeV
Because of gluon radiation, 12 of the signal
events looks more like background than signal.
When only events with good jet-parton matching
are used, this is resolved (not a problem). The
expected purity for Mt175 GeV is 0.58
(0.51/0.580.88).
Mt175 GeV
Mt160 GeV
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MC ensemble test (24s 40 b) with additional cut
lt24gt signal lt40gt background w/Pbkg cut
Mt peak 174.3 GeV mean173.8 GeV width 4.2
GeV (symmetric 68) lt?gt4.5 GeV ?pull
0.97 ltNs/Ngt0.51
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MC ensemble test (24s 40 b)
lt24gt signal lt40gt background
Mt peak 174.8 GeV mean173.1 GeV width 4.1
GeV (symmetric 68) lt?gt4.2 GeV ?pull
1.02 ltNs/Ngt0.31
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MC ensemble test (20s 44 b)
Mt peak174.9 GeV mean172.6 GeV width4.7
GeV (symmetric 68) lt?gt4.8 GeV ?pull
1.08 ltNs/Ntotgt0.29
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Comparing ensemble tests
stat.err.
GeV
uncertainty from JES
mass
data
expected
PRD 58 52001, (1998)
(new PR4)
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Effect of QCD background
24s40b (32W8QCD) No systematic error is
included for the multijet background that is not
explicitly included in the calculation of our
probability.
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DØ top mass analysis (leptonjets) From PRD 58
52001, (1998)
?Mt (GeV)
DØ studied the problem in detail to produce
multidimensional templates than conserve most of
the information without introducing a bias in Mt,
and used for this analysis advanced techniques.
This is a very successful analysis but we
decided to go even further
Mt (GeV)
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Published top mass analysis (leptonjets), plots
Jet energy smearing is the dominant factor in the
mass resolution. Hatched correct
permutation Open all permutation.
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W mass
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JES issue

• We use a Monte Carlo simulation of the detector
  to build the transfer function (or the templates
  in previous analyses)
• It is essential to check that the energy scale in
  this MC simulation is representative of that in
  the detector. This can be done easily for the
  electromagnetic showers using Z?ee- decays. It
  is not so easy to do for hadronic showers.
• In our previous analysis, the JES introduced an
  uncertainty of 2.5 in Mt . Now we want to reduce
  this uncertainty using the mW peak in the top
  decays.

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The likelihood in the mW-mt plane
The likelihood is also a function of mW, and one
could look at it in two dimensions. This can
provide a new handle on the systematic
uncertainty coming from the Jet Energy Scale
(JES). using MW. These are contours of constante
likelihood calculated for a MC sample of 30
signal events.
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Handle on JES from MW
After performing the measurement, our knowledge
of Mt is contained in
We assume that there is an unknown multiplicative
factor FJES for all jet energies. The likelihood
can be regarded as a 3D function that can be
integrated on the two variables (FJES,,MW) that
we do not want to measure. Because DØ has
information on FJES (from independent checks)
with an uncertainty of 2.50.5, this can be used
in our prior. The width in the prior for MW will
be the systematic error on the evaluation of MW
from our likelihood (this is still to be
determined).
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Results for Different Priors
Each line corresponds to a different width of the
prior for MW. The x-axis is the width for the
FJES prior. As the prior information on FJES
weakens (to the right), the value of Mt is
pegged purely to MW.
?top (linear scale)
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Energy corrections DØ-RunI
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Our published analysis

• MC events are generated according to production
  probability (models in Herwig for signal and
  Vecbos for Wjets) and ran through the detector
  simulation to get
• ? parameter to be measured (i.e. mt)
• x (x1,,x15) all measured variables for the
  event
• The variables containing most on mass are
  selected and used in the analysis, and the rest
  are integrated/averaged over generated events.
• In general, a maximum likelihood is in general
  used to obtain the most probable value of ?.

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Transfer function Wjet(x,y)
Models the smearing in jet energies from effects
of radiation, hadronization, measurement
resolution and jet reconstruction algorithm
These effects produce asymmetry
Correcting on average, and considering these
distributions to be single Gaussians, can
underestimate jet energies
Use 2 Gaussians, one to account for the peak and
the other to fit the asymmetric tails,
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Test of the Transfer Function in tt events
Angular decay of the W
Top Mass
Histogram HERWIG events after full DO
reconstruction, using the standard
criteria Solid Line Calculated by using the
transfer function on partons Dashed Same as
solid, but with a variant transfer function
In black HERWIG events passed through full DO
reconstruction, with standard Run-1 criteria In
red PYTHIA events (partons) after applying
transfer function and standard Run-1 riteria
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Check of the Transfer Function in Wjets
3 jets invariant mass
Invariant mass of three jets using W4-jets
events from VECBOS ISAJET without requiring
matching to initial partons. (Smooth curve, same
as before.)
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Helicity of the W - MC Studies

• Uses the full probability calculation
• Sums over all jet combination
• Sums over all neutrino solutions
• Uses W(x,y)
• Obtain F00.65?0.17

Using 30 events
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Testing new approach via linearity of response in
MC experiments
24 (tt) 24 (tt) 40 (Wjets) From this fit
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Number of events for signal and backg.
Because of radiation 20 of the signal events
look more like background than signal. When only
events with good jet-parton matching are used,
this is resolved (not a problem).
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Our published top mass analysis (leptonjets)

• Four variables are used to parameterize signal
  and background probabilities (missing Et, A,
  HT2/Hz,x4). These variables are chosen to
  minimize the correlation with mt . A
  discriminant is defined as
• A kinematic fit is performed to each event, and
  the permutation with best ?2 is selected (correct
  in 40 of the cases) and mfit is obtained for
  each event (the longitudinal momentum of the
  neutrino is also obtained from this constrained
  fit). Events with bad fit (?2gt10) are rejected.
• P is parameterized in 2 dimensions (mfit,?).
  Templates are obtained for different values of
  the MC input top mass, and then compared with
  data in a likelihood function.

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Advance Analysis Techniques at DØ

• At DØ we have used advance analysis techniques
  for the measurement of the mass of the top quark
  with Run I data. The analysis presented here is a
  continuation of our effort to the maximal amount
  of information available for the analysis. This
  analysis is also part of our effort in preparing
  tools for precision Run II analyses.
• The Tevatron has an advance analysis group
  (http//projects.fnal.gov/run2aag/) A variety of
  different techniques are being investigated
• Neural Networks
• Inverse Monte Carlo Techniques
• Support Vector Machines
• Robustness of Confidence Limits

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Matrix Element
no ttbar spin correlation included
sqt sine of angle between q and t in the q q CM
b top quark's velocity in the q q CM
gs strong coupling constant
Leptonic decay
Hadronic decay
Mt, MW pole mass of top and W mt top mass in
any event men ,mdu invariant mass of the en and
du (or cs) system Gt ,GW width of top and W gW
weak coupling constant ?(cos jeb,db) angular
distribution of the W decay
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Testing this in Run 1 DØ MC
Examples of product likelihood functions. Each
example corresponds to one experiment with the
statistics that DØ collected during Run 1
(PR4). The signal(HERWIG) and background
(VECBOS) events were run through the full DØ Run
1 simulation.
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Systematic due to ttbar model
u fraction of events in the experiment where all
the jets can be matched with partons from top
quark decays. Increasing the fraction u,
effectively turns on radiation and hadronization
effects. The systematic uncertainty is ?1.5
GeV (Each point corresponds to the maximum of a
likelihood for a large event sample).
Herwig MC with official DØ simulation