Optimal Use of Information for Measuring Top Mass in lepton jets tt Events

1
Optimal Use of Information for Measuring Top Mass
in leptonjets tt Events

• Breese Quinn, Fermilab
• for the DØ Collaboration
• DPF2003

• General introduction
• Explanation of the optimized method used in the
  new Mt measurement
• Preliminary Run I measurement of Mt using
  optimized method
• Systematic errors
• Conclusions

2
Event topology and selections
DØ Statistics Run I (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 ?Wlt2
• Gives 91 events
• Ref. PRD 58 (1998), 052001 Mt
  173.3 ? 5.6 (stat) ? 5.5 (syst.) GeV
• After ?2 ? 77 events
• 29 signal
• 48 backg. (80 Wjets, 20 QCD)
• Additional cuts for this analysis
• 4 Jets only ? 71 events
• Background Prob. ? 22 events

3
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

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

Template(ximtB)
Template(ximtA)
Data gt mtB
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Approach for new Mt 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 into
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).

background- like event
P(mt)
signal-like events
?
?
?
Psignal
Pbackground
mt
For each event, signal and background
probabilities are added. The probabilities for
individual events are then multiplied together.
All jet permutations are considered.
5
Three differences between the two approaches
Template Method
Optimized 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).
  
• The full information contained in each event is
  contributed to the probability well-measured
  events contribute more than poorly-measured
  events.

6
The general method

• If the probability of an event can be calculated
  accurately, then the best estimate of a parameter
  will maximize a likelihood like
• Detector and reconstruction effects (e.g.
  fiducial regions) are multiplicative and lead to
  acceptance corrections independent of the
  parameter to be estimated
• The probability P(xa) can be calculated as

x the set of variables measured in the detector
y the set of parton level
variables dns the differential cross section
f(q) the
parton distribution functions W(y,x) transfer
function, the probability that a parton level set
of variables y will show up in the
detector as the set of variables x
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Transfer function W(x,y)
W(x,y) probability of measuring x when y was
produced (x measured 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 ? yj ? 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), the parameters were
extracted from MC simulation.
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Probability for tt events

• 5 integrals
• 20 degrees of freedom 2(in) 18(final)
• 15 constraints 3 (e) 8 (?1..?4) 3
  (PinPfinal) 1 (EinEfinal)
• Sum over the 12 jet permutations
• 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 These variables of integration
were chosen because M2 is almost negligible
except near the four Breit-Wigners peaks within
M2.
9
Signal and Background

• The background probability is defined only in
  terms of the main background
• Wjets (80)
• An adequate representation for the QCD multijet
  background (20).
• 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 ?.

10
Extra selection in Pbkg
PRD 58, 52001 (1998)
Wjets
ttbar_at_175GeV
DPsig/(PsigPbkg)
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
11
Signal and background probabilities a MC vs.
data comparison
Background probability comparison between data
(dots) and MC (histogram). Background (signal)
MC events are shown in blue (red). The MC S/B
ratio was set to the measured ratio S/B12/10 for
Pbkglt10-11 .
Signal probability comparison between data (dots)
and MC (histogram) in the form of a discriminant
DPsig/(PsigPbkg). The signal probability was
taken at its maximum value. The MC S/B ratio was
set to the measured ratio S/B12/10 for
Pbkglt10-11 .
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Top probability for data events
Right plots show -ln(Ptt) as a function of Mt
for 10-9ltPbkg lt10-8 (red arrows in lower
figure).
13
Top probability for data events
Right plots show -ln(Ptt) as a function of Mt
for 9.7x10-13 ltPbkg lt 9.0x10-12 (red arrows in
lower figure).
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Varying the background probability cut

• The top plot shows Mt as a function of the cut in
  the background probability (Pbkg). Mt is very
  stable over a change in the number of events (N)
  of more that a factor of 2, and a change in Pbkg
  of more that a factor of 10.
• The plots on the right show ln(L) as a function
  of Mt for each of the points in the plot above.
  The background enters mainly as a tail at low
  masses.

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Preliminary Result with DØ Run I data
DØ Preliminary
DØ Preliminary
Mt 179.9 ? 3.6 GeV ? SYST This optimized
method 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. Out of 22 events which pass the cuts,
the analysis gives a total of 12.5 3.0 t-tbar
events.
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Total Uncertainty
DØ Preliminary

• Determined from MC studies with large event
  samples
• Determined from data

This error will be significantly reduced in the
final result.
Total systematic 6.0 GeV Total 7.0 GeV
17
Tevatron Top quark mass measurements
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Check of Mw Future handle on Jet Energy Scale
DØ Preliminary
DØ Preliminary

• Mw can be measured in the same events where Mt is
  measured
• This can be very helpful for reducing the
  uncertainty in the jet energy scale
• DØ is currently studying this option for Run II.
  See the Proceedings of DPF2002 (Top quark
  physics) http//dpf2002.velopers.net/talks_pdf/120
  talk.pdf.

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Conclusions
DØ Preliminary
Mt 179.9 ? 3.6 (stat) ? 6.0 (syst.) GeV

• Significant improvement to the previous DØ
  measurement Mt 173.3 ? 5.6 (stat) ? 5.5 (syst.)
  GeV (LB analysis in PRD) - equivalent to 2.4
  times more data
• Correct permutation is always considered (along
  with the other 11)
• All features of the individual events are
  included, meaning well measured events contribute
  more information than poorly measured events.
• The possibility of checking the value of the W
  mass in the hadronic branch on the same events
  provides a new handle in Run II for controlling
  the largest systematic error, the jet energy
  scale.

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Two and three jet invariant masses
FWHM 40 GeV
Two (left plot) and three (right plot) jet
invariant mass distributions. The error bars
correspond to t-tbar MC events for which the jets
were matched to partons. The curves correspond
to our calculations for two different transfer
functions Wjet(x,y). The dashed-dotted line
corresponds to the transfer function used in the
final analysis.
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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
22
Acceptance Corrections
Likelihood
Detector Acceptance
Measured probability
Detector acceptance
Production probability
, and Ngen(N) is the number of
generated(accepted) events
23
Crosschecks on Ensemble Tests (12 signal10
background)
From the ensemble tests we estimate a 0.5 GeV
bias in the peak with respect to the generated
value
24
Crosschecks on Ensemble Tests (12 signal10
background)

• The most probable result of these experiments is
  Mt174.7 GeV
• top generated at Mt175.0 GeV

25
Crosscheck of linearity of response

• Test of linearity of response is with MC samples
  containing large numbers of events

26
Systematic error due to tt model
Herwig MC with official DØ simulation
Herwig MC with official DØ simulation
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
27
Systematic error due to background model

• Results for different VECBOS
• flavors Q2 scale of either ltptjetgt2 or
• M2W ,and with either HERWIG or
• ISAJET fragmentation.
• From left to right
• M2W and IS
• M2W and HW
• ltptjetgt2 and HW.
• The points with large error bars
• were calculated with 250s500b
• events, and the ones with small error
• bars with 400s800b events. The
• number of events is specified before
• the cut in Pbkg .
• The assigned systematic uncertainty
• is ?1.0 GeV

28
Extra selection in Pbkg
Pbkglt1E-11