Article
Reference
Top quark mass measurement in the lepton plus jets channel using a modified matrix element method
CDF Collaboration
CLARK, Allan Geoffrey (Collab.), et al.
Abstract
We report a measurement of the top quark mass, mt, obtained from pp collisions at s√=1.96 TeV at the Fermilab Tevatron using the CDF II detector. We analyze a sample corresponding to an integrated luminosity of 1.9 fb−1. We select events with an electron or muon, large missing transverse energy, and exactly four high-energy jets in the central region of the detector, at least one of which is tagged as coming from a b quark. We calculate a signal likelihood using a matrix element integration method, where the matrix element is modified by using effective propagators to take into account assumptions on event kinematics. Our event likelihood is a function of mt and a parameter JES (jet energy scale) that determines in situ the calibration of the jet energies. We use a neural network discriminant to distinguish signal from background events. We also apply a cut on the peak value of each event likelihood curve to reduce the contribution of background and badly reconstructed events. Using the 318 events that pass all selection criteria, we find mt=172.7±1.8(stat+JES)±1.2(syst) GeV/c2.
CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Top quark mass measurement in the lepton plus jets channel using a modified matrix element method. Physical Review. D , 2009, vol. 79, no. 07, p. 072001
DOI : 10.1103/PhysRevD.79.072001
Available at:
http://archive-ouverte.unige.ch/unige:38613
Disclaimer: layout of this document may differ from the published version.
Top quark mass measurement in the lepton plus jets channel using a modified matrix element method
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Y. Zheng,9,eand S. Zucchelli6a,6b (CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439
3University of Athens, 157 71 Athens, Greece
4Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
5Baylor University, Waco, Texas 76798
6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy
6bUniversity of Bologna, I-40127 Bologna, Italy
7Brandeis University, Waltham, Massachusetts 02254
8University of California, Davis, Davis, California 95616
9University of California, Los Angeles, Los Angeles, California 90024
10University of California, San Diego, La Jolla, California 92093
11University of California, Santa Barbara, Santa Barbara, California 93106
12Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
13Carnegie Mellon University, Pittsburgh, Pennsylvania 15213
14Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637
15Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia
16Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
17Duke University, Durham, North Carolina 27708
18Fermi National Accelerator Laboratory, Batavia, Illinois 60510
19University of Florida, Gainesville, Florida 32611
20Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
21University of Geneva, CH-1211 Geneva 4, Switzerland
22Glasgow University, Glasgow G12 8QQ, United Kingdom
23Harvard University, Cambridge, Massachusetts 02138
24Division of High Energy Physics, Department of Physics,
University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
25University of Illinois, Urbana, Illinois 61801
26The Johns Hopkins University, Baltimore, Maryland 21218
27Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany
28Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea;
Seoul National University, Seoul 151-742, Korea; Sungkyunkwan University, Suwon 440-746, Korea;
Korea Institute of Science and Technology Information, Daejeon, 305-806, Korea;
Chonnam National University, Gwangju, 500-757, Korea
29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720
30University of Liverpool, Liverpool L69 7ZE, United Kingdom
31University College London, London WC1E 6BT, United Kingdom
32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
34Institute of Particle Physics: McGill University, Montre´al, Que´bec, Canada H3A 2T8;
Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6;
University of Toronto, Toronto, Ontario, Canada M5S 1A7;
and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3
35University of Michigan, Ann Arbor, Michigan 48109
36Michigan State University, East Lansing, Michigan 48824
37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
38University of New Mexico, Albuquerque, New Mexico 87131
39Northwestern University, Evanston, Illinois 60208
40The Ohio State University, Columbus, Ohio 43210
41Okayama University, Okayama 700-8530, Japan
42Osaka City University, Osaka 588, Japan
43University of Oxford, Oxford OX1 3RH, United Kingdom
44aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
44bUniversity of Padova, I-35131 Padova, Italy
45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France
46University of Pennsylvania, Philadelphia, Pennsylvania 19104
47aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy
47bUniversity of Pisa, I-56127 Pisa, Italy
47cUniversity of Siena, I-56127 Pisa, Italy
47dScuola Normale Superiore, I-56127 Pisa, Italy
48University of Pittsburgh, Pittsburgh, Pennsylvania 15260
49Purdue University, West Lafayette, Indiana 47907
50University of Rochester, Rochester, New York 14627
51The Rockefeller University, New York, New York 10021
wOn leave from J. Stefan Institute, Ljubljana, Slovenia.
vWith visitors from Bergische Universita¨t Wuppertal, 42097 Wuppertal, Germany.
uWith visitors from University of Virginia, Charlottesville, VA 22904.
tWith visitors from IFIC(CSIC-Universitat de Valencia), 46071 Valencia, Spain.
sWith visitors from Texas Tech University, Lubbock, TX 79409.
rWith visitors from University de Oviedo, E-33007 Oviedo, Spain.
qWith visitors from University of Notre Dame, Notre Dame, IN 46556.
pWith visitors from Nagasaki Institute of Applied Science, Nagasaki, Japan.
oWith visitors from University of Manchester, Manchester M13 9PL, United Kingdom.
nWith visitors from Queen Mary, University of London, London, E1 4NS, United Kingdom.
mWith visitors from Universidad Iberoamericana, Mexico D.F., Mexico.
lWith visitors from University of Edinburgh, Edinburgh EH9 3JZ, United Kingdom.
kWith visitors from University College Dublin, Dublin 4, Ireland
jWith visitors from University of Cyprus, Nicosia CY-1678, Cyprus.
iWith visitors from Cornell University, Ithaca, NY 14853.
hWith visitors from University of California Santa Cruz, Santa Cruz, CA 95064.
gWith visitors from University of California Irvine, Irvine, CA 92697.
fWith visitors from Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy.
eWith visitors from Chinese Academy of Sciences, Beijing 100864, China.
dWith visitors from University of Bristol, Bristol BS8 1TL, United Kingdom.
cWith visitors from Universiteit Antwerpen, B-2610 Antwerp, Belgium.
bWith visitors from University of Massachusetts Amherst, Amherst, Massachusetts 01003.
aDeceased.
52aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Italy
52bSapienza Universita` di Roma, I-00185 Roma, Italy
53Rutgers University, Piscataway, New Jersey 08855
54Texas A&M University, College Station, Texas 77843
55aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, Italy
55bUniversity of Trieste/Udine, I-33100 Udine, Italy
56University of Tsukuba, Tsukuba, Ibaraki 305, Japan
57Tufts University, Medford, Massachusetts 02155
58Waseda University, Tokyo 169, Japan
59Wayne State University, Detroit, Michigan 48201
60University of Wisconsin, Madison, Wisconsin 53706
61Yale University, New Haven, Connecticut 06520 (Received 24 December 2008; published 10 April 2009) We report a measurement of the top quark mass,mt, obtained fromppcollisions at ffiffiffi
ps
¼1:96 TeVat the Fermilab Tevatron using the CDF II detector. We analyze a sample corresponding to an integrated luminosity of1:9 fb1. We select events with an electron or muon, large missing transverse energy, and exactly four high-energy jets in the central region of the detector, at least one of which is tagged as coming from abquark. We calculate a signal likelihood using a matrix element integration method, where the matrix element is modified by using effective propagators to take into account assumptions on event kinematics. Our event likelihood is a function ofmtand a parameter JES ( jet energy scale) that determines in situthe calibration of the jet energies. We use a neural network discriminant to distinguish signal from background events. We also apply a cut on the peak value of each event likelihood curve to reduce the contribution of background and badly reconstructed events. Using the 318 events that pass all selection criteria, we findmt¼172:71:8ðstatþJESÞ 1:2ðsystÞGeV=c2.
DOI:10.1103/PhysRevD.79.072001 PACS numbers: 14.65.Ha
I. INTRODUCTION
The top quark mass,mt, is an important parameter in the standard model of particle physics. Since the discovery of the top quark in 1995, there have been many reported measurements of its mass, all from the CDF and D0 experi- ments at the Fermilab Tevatron [1]. The standard model relates the top quark andWboson masses to the mass of the predicted Higgs boson via loop corrections. Precision mea- surements ofmtand theWboson massmW, in conjunction with many other precision electroweak measurements, thus provide constraints on the value of the Higgs boson mass [2].
The measurement reported here usespp collision data corresponding to an integrated luminosity of 1:9 fb1, collected by the CDF II detector during Run II of the Fermilab Tevatron collider at ffiffiffi
ps
¼1:96 TeV. Inpp col- lisions, top quarks are produced predominantly asttpairs, and present measurements within the standard model framework indicate that the top quark decays to aWboson and abquark nearly 100% of the time [3]. TheW boson can decay into either a charged lepton and a neutrino (‘‘leptonic decay’’) or a quark-antiquark pair (‘‘hadronic decay’’). We select events in which one of the W bosons decays leptonically and the other decays hadronically, where the lepton in the leptonic decay is required to be an electron or muon; this channel is referred to as the
‘‘leptonþjets’’ channel. Decays ofW bosons into a tau lepton are not explicitly included in our model, although some events containing a tau lepton which decays into an
electron or muon do pass our selection criteria and amount to approximately 7% of thettsignal. In general, an event in our candidate sample has four high-energy jets (two of which come from the parton shower and hadronization associated with the quarks from the hadronic W boson decay and two from the parton shower and hadronization of the b quarks), a charged electron or muon, and an unobserved neutrino. For a given Tevatron integrated lu- minosity, the leptonþjets channel allows for more precise measurements than channels in which both W bosons decay leptonically or hadronically, as it offers the best balance of available statistics and sample purity. The most recent mt measurements obtained at the Tevatron using the leptonþjets topology are reported in Ref. [4].
The method we use to extract the top quark mass from a sample of candidatettevents is a modified matrix element integration method. The matrix element approach to the top quark mass measurement [5] is based on integrating over the tree-level phase space of the process, where each kinematic configuration of the tree-level partons is weighted by the matrix element squared and by the proba- bility that the detector observables can be produced by the final-state particles. With an appropriate normalization factor, this integral defines the probability to see an event with this configuration in the detector. By multiplying the individual event probabilities, we obtain a likelihood, as a function ofmt, of seeing the event sample observed in our detector.
In theory, the distributions of the invariant masses of the top quark and theW boson decay products are dominated
by propagator-induced terms in the matrix element squared. The top quark and the W boson widths are rela- tively narrow in comparison with their respective masses.
This leads to nearly pure relativistic Breit-Wigner distri- butions for the invariant masses of their decay products.
Compared to this theoretical prediction, finite resolution of the detector measurement naturally results in a widening of the observed distributions. We describe the widening due to an imperfect measurement of magnitudes of jet mo- menta in terms of detector transfer functions. Effects of other uncertainties, such as finite angular resolutions, are modeled by replacing the Breit-Wigner terms in the matrix element squared with empirically determined distributions called ‘‘effective propagators’’ in this paper. This modifi- cation of the matrix element improves the observation model forttevents.
The matrix element used in this work [6] includes tt production, from both quark-antiquark and gluon-gluon collisions, and decay into the leptonþjets channel.
Since we do not know which jet observed in our detector corresponds to which parton in the matrix element, we calculate the likelihood for each possible assignment of jets to partons and sum the likelihood over all permuta- tions. Each permutation includes a weight, which takes into account the probability that the permutation is con- sistent with the observed information on whether the jet has been tagged or not as ab-jet. Tagging ofb-jets is done by the displaced vertex technique discussed in Sec.III. For each permutation, the matrix element integration is per- formed over the seven kinematic variables in the event that remain after a set of simplifying assumptions.
We improve the precision of the method by introducing another parameter into our likelihood, the jet energy scale (JES). This is a scale factor which multiplies the energy of all jets. The uncertainty on the jet energy scale is the major source of systematic uncertainty on the top mass measure- ment; by including JES as a parameter in the likelihood, we can use theWboson decay to hadrons in thettdecay chain to providein situcalibration, thus reducing the systematic uncertainty due to JES. Our final likelihood calculated for each candidate event is thus a function of both the top quark mass and JES.
Our model is designed to fit leptonþjets tt events where the final objects observed in the event come directly fromttdecays. We thus need to take into account non-tt events orttevents where some of the observed objects do not originate from tt decay. The probability that a tt candidate event is background is estimated using a neural network output that is a function of several shape and kinematic variables, and then their expected contribution to the likelihood is subtracted from the total likelihood. In addition, we cut on the magnitude of the peak of the likelihood for an event to further reduce background and badly modeled events.
We multiply the individual likelihood curves from each event to get an overall likelihood. Because of the assump-
tions made, and the presence of background events, the extraction of a mass value and its uncertainty needs a calibration, which we obtain from Monte Carlo simulated events.
Section IIis a brief description of the CDF II detector and its use for the measurements needed in this analysis.
Section IIIdefines the data sample used for this analysis and the estimated background. Section IV describes the likelihood construction forttsignal events. Section Vex- plains how non-tt events are incorporated into the like- lihood function. Section VI describes how the method is tested and calibrated. Section VII covers the systematic uncertainties. SectionVIIIsummarizes the results obtained by applying the method to the data. Finally, Section IX gives the conclusions.
II. THE CDF II DETECTOR
A complete description of the CDF II detector and its use in lepton, jet, and secondary vertex reconstruction can be found elsewhere [7]. Here, we describe the components that are essential for this analysis and how they are used.
The CDF II detector is a general-purpose detector with a cylindrical geometry featuring forward-backward symme- try and axial symmetry around the beam pipe. The CDF coordinate system uses a cylindrical system centered at the interaction point with the z (longitudinal) axis along the proton beam direction,rthe distance to the beam line, and the azimuthal angle around the beam line. We also use, the polar angle from the beam line. The pseudorapidity of a particle three-momentum is defined in terms of the polar angle by¼ lnðtanð=2ÞÞ. For a particle with momentum p and energy E, we define the transverse momentum pT and the transverse energy ET as psin andEsin, respectively. The detector covers the complete solid angle inandup tojj ¼3:6.
The innermost part of the detector consists of the charged particle tracking detectors, which are immersed in a 1.4 T magnetic field provided by a superconducting solenoid oriented parallel to the beam line. Calorimeters and muon systems outside the solenoid provide lepton measurement and identification in addition to jet momen- tum measurements. The tracking detectors and calorime- ters together provide identification of jets from heavy (charm and bottom) quarks.
The first component of the tracking system is a series of silicon microstrip detectors between radii of 1.5 and 28 cm.
The innermost layer (L00) [8] is a single-sided layer of silicon attached directly to the beam pipe, providing a position measurement very close to the collision point.
Five layers of double-sided microstrip detectors (SVXII) cover up tor¼10:6 cmin thejj<1:0region [9]. Each layer has one side with strips oriented parallel to the beam line to provide measurements in ther-plane and one side at a stereo angle to provide three-dimensional measure- ments; two layers have strips at a 90 angle and three
layers have strips at a 1.2 angle. The ISL [10] is an additional set of silicon microstrip detectors located out- side of SVXII to provide measurements at larger distances from the beam line, thus improving the silicon tracking. It consists of one layer at r¼22 cm in the central region (jj<1:0) and two layers atr¼20 cmandr¼28 cmin the forward region (1:0<jj<2:0). The typical resolu- tion of these detectors in the r- plane is 11m. The impact parameter resolution of this system is ðd0Þ 40m, of which approximately 35m is due to the transverse size of the Tevatron interaction region. Outside of the silicon layers lies the central outer tracker (COT) [11], an open-cell drift chamber detector, which provides coverage forjj<1:0. Multiple wire planes, each with 12 sense wires, are grouped in 8 superlayers which extend to a radius of 137 cm. The superlayers alternate between hav- ing wires parallel to the beam axis and wires skewed by a 2stereo angle, thus providing up to 96 points for track reconstruction. Together with the additional constraint coming from the primary vertex position, these tracking elements provide a resolution on the track transverse mo- mentum,pT, ofðpTÞ=pT 0:1%pT=ðGeV=cÞ.
Outside the tracking system and the solenoid are seg- mented electromagnetic and hadronic calorimeters. The central calorimeter covers up tojj<1:1and has a pro- jective geometry consisting of towers segmented inand pointing toward the center of the detector. The central electromagnetic calorimeter (CEM) consists of alternating layers of lead plates and plastic scintillators, 18 radiation lengths deep. The energy detected in small contiguous groups of calorimeter towers is summed into electromag- netic clusters. These clusters are identified as electron candidates if they match a track reconstructed in the track- ing system and if very little energy is detected in the surrounding towers (i.e., if the cluster is isolated). The energy resolution for an electron with tranverse energy ET is given by ðETÞ=ET 13:5%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ET=GeV
p 2%.
Approximately at shower maximum are proportional strip and wire chambers (CES) which provide finer position resolution for electron and photon identification. The cen- tral hadronic calorimeter (CHA) is composed of alternating layers of iron plates and scintillators, 4.5 nuclear interac- tion lengths deep, again with projective geometry segmen- tation. A plug tile calorimeter covers the forward region with1:1<jj<3:6, consisting of a lead/scintillator elec- tromagnetic portion (PEM), scintillator strips at shower maximum (PES), and an iron/scintillator hadronic portion (PHA). An additional hadronic calorimeter (WHA) covers the region between the plug calorimeter and the central calorimeter and improves the hermeticity of the detector.
These calorimeters provide jet measurements with a reso- lution of approximately ðETÞ 0:1ET þ1:0 GeV [12].
In the central and forward regions, jets are reconstructed with a cone algorithm [12], which adds groups of electro-
magnetic (EEM) and hadronic clusters (EHAD) that fall within a cone of radiusR¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2þ2
p 0:4around
a seed tower with energy of at least 1 GeV. The jet energies are corrected for multiple primary interactions (pileup) and for detector effects including a calibrated nonlinearity in the calorimeter and average losses in nonsensitive regions of the calorimeter. The jet energies are also corrected for hadronic physics effects. Soft hadroproduction in the underlying event tends to increase the measured jet energy, while the limited cone size of the jet clustering algorithm gives rise to out-of-cone losses [13]. Uncertainties for each of these corrections contribute to the jet systematic uncer- tainty, and are used to assign an uncertainty on the top quark mass.
In the leptonþjets channel one of theWbosons decays into a lepton and a neutrino, which escapes undetected.
This results in less energy being measured in our detector than we would otherwise expect. We require this as a signature for ttevents. Specifically, we define a quantity, the missing ET (E6 T), to measure the resulting transverse energy imbalance as follows:
E6 T ¼
X
i2towers
ETin^Ti
; (1)
wheren^Ti is the unit vector in thex-yplane pointing from the primary vertex to a given calorimeter tower andETi is the uncorrected ET measured in that tower. Two correc- tions to this quantity are made. One is to account for muons, which, unlike other particles, typically deposit only a small fraction of their energy in the towers, and the other is to take into account the corrections applied to the raw energies of the jets. Details of these corrections can be found in Ref. [14].
Muon identification takes place in three separate sub- detectors. Two of these are in the central region: one set of four layers of drift chambers (CMU) located outside the central calorimeters (after 4.6 hadronic absorption lengths of material), and another set of four layers (CMP) located outside the magnet return yoke, which provides an addi- tional 60 cm of absorbing steel. Muon tracks in this region are required to pass through both detectors and are called CMUP muons. These two subdetectors cover the region jj 0:6. Muons in the region 0:6<jj<1:0 are de- tected by an additional set of four layers of drift chambers (CMX), completing the full fiducial region of the COT.
CMUP or CMX track segments are matched to tracks in the COT; in addition, the energy deposited in the CEM and CHA is required to be small.
The trigger system is used to record events with high-pT leptons. The trigger is a three-level filter in which the first two levels use specialized hardware and utilize only the detector subsystems with fast readout. The third level is a complete reconstruction of the event using the same soft- ware used for the offline reconstruction, but with less stringent cuts. The level 1 (L1) trigger uses information
from the calorimeter clusters and from the XFT (eXtremely Fast Tracker), which reconstructs tracks from the COT r- information with a momentum resolution given by ðpTÞ=pT 2%pT=ðGeV=cÞ [15]. The L1 central electron trigger requires a track with pT >
8 GeV=c pointing to a tower with ET >8 GeV and EHAD=EEM<0:125. The L2 trigger adds clustering in the CEM calorimeter and requires that a cluster with ET >
16 GeVmatches with apT>8 GeV=ctrack. The L1 and L2 muon triggers require a track with pT>4 GeV=c (CMUP) or pT>8 GeV=c (CMX) pointing to a track segment in the respective drift chamber system. A com- plete lepton reconstruction is performed in the L3 trigger, where ET>18 GeV is required for electrons and pT >
18 GeV=cis required for muons.
III. DATA SAMPLE AND BACKGROUND As mentioned previously, we search for events in the leptonþjets topology, where a ttpair is produced, each top quark decays into aW boson and abquark, and oneW boson decays leptonically and one hadronically. We thus identify our top quark candidates by selecting events with four high-energy jets, a high-energy electron or muon, and E6 T from a neutrino. Specifically, we require either an electron with ET >20 GeV or a muon with pT >
20 GeV=cin the central region (jj<1:0) of the detector.
Electron and muon identification criteria are discussed in Ref. [7]. For the neutrino, we requireE6 T>20 GeVin the event. We require exactly four jets withET>20 GeVand pseudorapidity jj<2:0. The jet ET is corrected for pileup, inhomogeneities of the detector, and nonlinear calorimeter response as a function of jet pT and [13].
The additional corrections (underlying event and out-of- cone losses) are not used in the analysis, but their uncer- tainties are taken into account in evaluating the systematic uncertainties on the final result.
Non-ttevents that contain aW boson and four jets are able to pass the aforementioned selection cuts. However, most of these events do not containbquarks in their final state, whilettevents will nearly always have twobquarks.
The b quarks from top quark decay hadronize into B-hadrons with energies on the order of several tens of GeV, due to the high mass of the parent top quark. Since the B-hadron decay time is approximately 1.5 ps, it is possible to reconstruct secondary vertices within a jet using the charged particles from the B decay [16]. A jet with an identified secondary vertex is called a b-tagged jet.
Therefore, to further increase thettpurity of the sample, we require that at least one of the jets must be tagged as a b-jet using a secondary vertex tagging algorithm.
The outline of theb-tagging algorithm used,SECVTX, is as follows: first, the charged particle tracks in the jet are subjected to selection cuts to ensure that a quality second- ary vertex can be reconstructed. There must either be at least three tracks withpT 0:5 GeV=cwhere at least one
of the tracks must be 1 GeV=c, or at least two tracks withpT 1 GeV=c. Once the secondary vertex is recon- structed using the tracks, the distance in the x-y plane between the primary and secondary vertices is projected onto the direction of the jet; this quantity is referred to as L2D (see Fig.1). A jet is tagged if L2D>7:5L2D, where L2D, the uncertainty onL2D, is approximately 190m.
Forb-jets produced inttdecay, theb-tagging efficiency is about 40%, while light jets are misidentified asb-jets with a rate of less than 2%. For more details see Ref. [16].
In1:9 fb1 of data we find 371ttcandidate events that pass the above selection requirements, 284 of which have oneb-tag and 87 of which have more than oneb-tag (see Table I); 207 of the candidate events contain an electron and 164 contain a muon. The background to thett signal consists of three main sources: a) events where aW boson is produced in conjunction with heavy flavor quarks (bb, cc, or c); b) events where a W boson is produced along with light flavor quarks where a light flavor jet has been incorrectly tagged with ab-tag (mistag); c) QCD events, which do not contain aWboson (non-Wevents) but have a jet mimicking a lepton, a jet with ab-tag, andE6 T. There are also smaller contributions from single top quark produc- tion, diboson (WW,WZ, orZZ) production, andZþjets production. The estimated number of background events for each of these sources is derived with the method used for the cross section measurement [17].
The contributions for the various types of background shown in TableIare estimated as follows. First, we define a pretag event sample, which comprises all events that pass all the signal selection requirements except for the b-tag requirement; our final tagged samples are thus subsets of the pretag sample. For all samples, the expected number of events for diboson, Zþjets, and single top quark back- grounds, as well as the tt signal, are estimated using
Primary vertex
Secondary vertex
Jet axis
L2D
FIG. 1 (color online). A view of ab-jet in thex-yplane.L2D, the distance between the primary and secondary vertices pro- jected onto the jet axis, along with its uncertainty, is used to determine whether a jet originates from a heavy flavor quark.
Monte Carlo (MC) simulated events assuming the theo- retical cross sections. To simulate the signal, we generatett events at a variety of top quark masses from152 GeV=c2 to 190 GeV=c2 (needed for our top mass analysis) using thePYTHIAMC generator version 6.216 [18]. As a cross- check we also use tt signal events generated with the
HERWIGgenerator version 6.510 [19]. For the number of expectedttevents used in the background estimate we use
a top mass of175 GeV=c2, with a calculatedttproduction cross section of6:70:8 pb[20].
The non-W contribution is estimated by a fit to the observed E6 T distribution of expectedE6 T distributions for non-W events (which lie mostly in the lowE6 T region) and Wþjets events. These distributions are taken from data sidebands (either events with leptons which fail to meet the isolation requirements, or from ‘‘antielectron’’ samples, which are electron candidates failing two other selection requirements) and from simulated MC events. This fit is performed separately for the pretagged and tagged samples to obtain the expected number of events in each.
The Wþjets background contribution to the pretag sample is taken as the remainder after subtracting all the above pretag contributions. The relative contribution of Wþheavy flavor events to the pretagWþjets contribu- tion is estimated with MC simulation. We use MC events generated with the ALPGEN [21] generator (version 2.10 prime) along with PYTHIA version 6.325 to perform the parton shower and hadronization. TheALPGENprogram is used to generate samples with specific numbers of partons in the matrix element; this decreases the time to generate TABLE I. Summary of observed data and predictedttsignal
and background contributions as a function of b-tags in the event.
Background 1 tag 2tags
Non-W QCD 13:811:5 0:51:5
Wþlight flavor (mistag) 16:33:6 0:30:1 DibosonðWW; WZ; ZZÞ,Zþjets 5:50:4 0:50:1 Wþbb, cc, c 26:110:2 3:41:4
Single top 3:00:2 0:90:1
Total background 64:716:3 5:52:6
Predictedttsignal 182:624:6 69:411:2
Events observed 284 87
(GeV) ET
50 100 150 200 250
Event fraction
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
(GeV) ET
50 100 150 200 250
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
0.18 1.9 fb-1 data
2) signal (172 GeV/c t
t
W + light mistag W + heavy flavor single top non-W QCD
K-S CL = 0.39 1st jet ET
(GeV) ET
20 40 60 80 100 120 140 160 180 0
0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22
(GeV) ET
20 40 60 80 100 120 140 160 180
Event fraction
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
0.22 1.9 fb-1 data
2) signal (172 GeV/c t
t
W + light mistag W + heavy flavor single top non-W QCD
K-S CL = 0.10 2nd jet ET
(GeV) ET
20 40 60 80 100 120
Event fraction
0 0.05 0.1 0.15 0.2 0.25 0.3
(GeV)
ET E (GeV)ETT (GeV)
20 40 60 80 100 120
Event fraction
0 0.05 0.1 0.15 0.2 0.25
0.3 1.9 fb-1 data
2) signal (172 GeV/c t
t
W + light mistag W + heavy flavor single top non-W QCD
K-S CL = 0.58 3rd jet ET
20 30 40 50 60 70 80 90
Event fraction
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
4th jet ET
20 30 40 50 60 70 80 90
Event fraction
0 0.1 0.2 0.3 0.4 0.5 0.6
0.7 1.9 fb-1 data
2) signal (172 GeV/c t
t
W + light mistag W + heavy flavor single top non-W QCD
K-S CL = 0.95 4th jet ET
FIG. 2. Comparison of data and MC predictions for the selected events. The confidence level obtained from a K-S test on the two distributions is indicated on the histogram. The plots show, in order, the correctedETof the leading jet, 2nd jet, 3rd jet, and 4th jet in our events.
events with high jet multiplicity. Since each sample con- tains a different number of partons (for instance, theWþ bb sample contains Wþbbþ0p, Wþbbþ1p, and Wþbbþ 2p contributions), we combine the separate samples using their expected fractions, and remove over- laps using theALPGENjet-parton matching along with a jet- based heavy flavor overlap removal algorithm [17]. Finally, applying heavy flavor and light flavorb-tag efficiencies we obtain the estimated Wþjets contributions to the final sample.
The single top quark contribution is generated using the MadGraph/MadEvent [22] package along withPYTHIAfor the parton shower and hadronization. Since their expected contribution is small, we do not use separate MC samples for diboson or Zþjets backgrounds, but rather merge them into theWþlight flavor total. All MC samples are simulated using the CDF II detector response simulation package [23].
Table I summarizes the data sample composition as a function of the number of tagged jets in the event. The total number of expected background events in our data sample isNbg¼70:316:5out of 371 observed events.
We test our background model by comparing selected kinematic distributions in the data with those expected by our model, by adding the MC samples used for thettsignal and backgrounds and the data samples used for the QCD background according to their predicted proportions.
Figures2and3show the comparisons. All of these plots require exactly four jets withET>20 GeVandjj<2:0, but in Fig.3, we also show the number of jets with lower energies for an additional comparison between data and MC. For each quantity, we perform a Kolmogorov- Smirnov (K-S) test comparing the data and MC samples;
in all cases, the resulting confidence level shows a good agreement, which validates the use of the MC generators and the QCD background used in this analysis.
IV. SIGNAL LIKELIHOOD
The matrix element method allows for efficient incor- poration of the theoretical assumptions about the process under study into the data analysis. The phase space inte- gration procedure can be viewed as a Bayesian margin- alization of the event probability over all unobserved
(GeV) ET
20 40 60 80 100 120 140 160 180 200
Event fraction
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18
0.2 1.9 fb-1 data
2) signal (172 GeV/c t
t
W + light mistag W + heavy flavor single top non-W QCD
K-S CL = 0.51 Missing ET
Number of jets
4 5 6 7 8 9 10
Event fraction
0 0.1 0.2 0.3 0.4 0.5 0.6
0.7 1.9 fb-1 data
2) signal (172 GeV/c t
t
W + light mistag W + heavy flavor single top non-W QCD
K-S CL = 0.27
| < 2.4 η > 12 GeV and | Number of jets with ET
(GeV) ET
50 100 150 200 250
Event fraction
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16
data 1.9 fb-1
2) signal (172 GeV/c t
t
W + light mistag W + heavy flavor single top non-W QCD
K-S CL = 0.45 b-tagged jet ET
(GeV/c) pT
20 40 60 80 100 120 140 160 180 200
Event fraction
0 0.05 0.1 0.15 0.2
0.25 1.9 fb-1 data
2) signal (172 GeV/c t
t
W + light mistag W + heavy flavor single top non-W QCD
K-S CL = 0.56 Lepton pT
FIG. 3. Comparison of data and MC predictions for the selected events. The confidence level obtained from a K-S test on the two distributions is indicated on the histogram. The plots show, in order, the eventE6 T, the total number of jets withET>12 GeVand jj<2:4in the event, theET for all jets with ab-tag, and the leptonpT.
