Article
Reference
Measurement of the top quark mass using template methods on dilepton events in pp collisions at s√=1.96 TeV
CDF Collaboration
CAMPANELLI, Mario (Collab.), et al.
Abstract
We describe a measurement of the top quark mass from events produced in pp collisions at a center-of-mass energy of 1.96 TeV, using the Collider Detector at Fermilab. We identify tt¯
candidates where both W bosons from the top quarks decay into leptons (eν, μν, or τν) from a data sample of 360 pb−1. The top quark mass is reconstructed in each event separately by three different methods, which draw upon simulated distributions of the neutrino pseudorapidity, tt longitudinal momentum, or neutrino azimuthal angle in order to extract probability distributions for the top quark mass. For each method, representative mass distributions, or templates, are constructed from simulated samples of signal and background events, and parametrized to form continuous probability density functions. A likelihood fit incorporating these parametrized templates is then performed on the data sample masses in order to derive a final top quark mass. Combining the three template methods, taking into account correlations in their statistical and systematic uncertainties, results in a top quark mass measurement of [...]
CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the top quark mass using template methods on dilepton events in pp collisions at s√=1.96 TeV. Physical Review.
D , 2006, vol. 73, no. 11, p. 112006
DOI : 10.1103/PhysRevD.73.112006
Available at:
http://archive-ouverte.unige.ch/unige:38349
Disclaimer: layout of this document may differ from the published version.
Measurement of the top quark mass using template methods on dilepton events in p p collisions
at
p s
1:96 TeV
A. Abulencia,23D. Acosta,17J. Adelman,13T. Affolder,10T. Akimoto,55M. G. Albrow,16D. Ambrose,16S. Amerio,43 D. Amidei,34A. Anastassov,52K. Anikeev,16A. Annovi,18J. Antos,1M. Aoki,55G. Apollinari,16J.-F. Arguin,33 T. Arisawa,57A. Artikov,14W. Ashmanskas,16A. Attal,8F. Azfar,42P. Azzi-Bacchetta,43P. Azzurri,46N. Bacchetta,43 H. Bachacou,28W. Badgett,16A. Barbaro-Galtieri,28V. E. Barnes,48B. A. Barnett,24S. Baroiant,7V. Bartsch,30G. Bauer,32
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A. Zanetti,54I. Zaw,21F. Zetti,46X. Zhang,23J. Zhou,52and S. Zucchelli5 (CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439, USA
3Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain
4Baylor University, Waco, Texas 76798, USA
5Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
6Brandeis University, Waltham, Massachusetts 02254, USA
7University of California, Davis, Davis, California 95616, USA
8University of California, Los Angeles, Los Angeles, California 90024, USA
9University of California, San Diego, La Jolla, California 92093, USA
10University of California, Santa Barbara, Santa Barbara, California 93106, USA
11Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
12Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
13Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
14Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
15Duke University, Durham, North Carolina 27708
16Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
17University of Florida, Gainesville, Florida 32611, USA
18Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
19University of Geneva, CH-1211 Geneva 4, Switzerland
20Glasgow University, Glasgow G12 8QQ, United Kingdom
21Harvard University, Cambridge, Massachusetts 02138, USA
22Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
23University of Illinois, Urbana, Illinois 61801, USA
24The Johns Hopkins University, Baltimore, Maryland 21218, USA
25Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany
26High Energy Accelerator Research Organization (KEK), Tsukuba, Ibaraki 305, Japan
27Center for High Energy Physics: Kyungpook National University, Taegu 702-701; Seoul National University, Seoul 151-742;
and SungKyunKwan University, Suwon 440-746; Korea
28Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
29University of Liverpool, Liverpool L69 7ZE, United Kingdom
30University College London, London WC1E 6BT, United Kingdom
31Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
32Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
33Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7
34University of Michigan, Ann Arbor, Michigan 48109, USA
35Michigan State University, East Lansing, Michigan 48824, USA
36Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
37University of New Mexico, Albuquerque, New Mexico 87131, USA
38Northwestern University, Evanston, Illinois 60208, USA
39The Ohio State University, Columbus, Ohio 43210, USA
40Okayama University, Okayama 700-8530, Japan
41Osaka City University, Osaka 588, Japan
42University of Oxford, Oxford OX1 3RH, United Kingdom
43University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
44LPNHE-Universite de Paris 6/IN2P3-CNRS
45University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
46Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena and Scuola Normale Superiore, I-56127 Pisa, Italy
47University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
48Purdue University, West Lafayette, Indiana 47907, USA
49University of Rochester, Rochester, New York 14627, USA
50The Rockefeller University, New York, New York 10021, USA
51Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University of Rome ‘‘La Sapienza,’’ I-00185 Roma, Italy
52Rutgers University, Piscataway, New Jersey 08855, USA
53Texas A&M University, College Station, Texas 77843, USA
54Istituto Nazionale di Fisica Nucleare, University of Trieste/Udine, Italy
55University of Tsukuba, Tsukuba, Ibaraki 305, Japan
56Tufts University, Medford, Massachusetts 02155, USA
57Waseda University, Tokyo 169, Japan
58Wayne State University, Detroit, Michigan 48201, USA
59University of Wisconsin, Madison, Wisconsin 53706, USA
60Yale University, New Haven, Connecticut 06520, USA (Received 30 January 2006; published 13 June 2006)
We describe a measurement of the top quark mass from events produced inppcollisions at a center-of- mass energy of 1.96 TeV, using the Collider Detector at Fermilab. We identifyttcandidates where bothW bosons from the top quarks decay into leptons (e,, or) from a data sample of360 pb1. The top quark mass is reconstructed in each event separately by three different methods, which draw upon simulated distributions of the neutrino pseudorapidity,ttlongitudinal momentum, or neutrino azimuthal angle in order to extract probability distributions for the top quark mass. For each method, representative mass distributions, or templates, are constructed from simulated samples of signal and background events, and parametrized to form continuous probability density functions. A likelihood fit incorporating these parametrized templates is then performed on the data sample masses in order to derive a final top quark mass. Combining the three template methods, taking into account correlations in their statistical and systematic uncertainties, results in a top quark mass measurement of 170:16:0stat:
4:1syst:GeV=c2.
DOI:10.1103/PhysRevD.73.112006 PACS numbers: 14.65.Ha, 13.85.Ni, 13.85.Qk
I. INTRODUCTION
The top quark, the weak isospin partner of the bottom quark, was first observed by the CDF and D0 collabora- tions in pp collisions produced at the Fermilab Tevatron [1]. During Run I operation from 1992 to 1995, CDF
acquired 109 pb1 of data at a center-of-mass energy of 1.8 TeV, and performed the first measurements of top quark properties. Since the start of Run II at the Tevatron in 2001, CDF has collected integrated luminosities several times that of Run I. Increased top production from a higher collision energy and improved acceptance of the upgraded . . .
detector have further enhanced the Run II top quark yield.
This larger sample size allows for more precise studies of the characteristics of the top quark.
As with all quarks, the top quark mass is not predicted by theory, and therefore represents a free parameter in the standard model which must be experimentally determined.
Tevatron Run I measurements yielded a top quark mass of 178:04:3 GeV=c2 [2], approximately 40 times heavier than the next heaviest quark, the bottom quark. Such a large mass, close to the electroweak symmetry breaking
scale v
p2
GF1=2246 GeV, suggests that the top quark may play a special role in this process [3]. The subsequently large contribution to quark-loop corrections of electroweak parameters from the heavy top quark pro- vides for powerful tests of the standard model. In particu- lar, a precise measurement of the top quark mass, coupled with that of theWboson, leads to tighter constraints on the as yet unobserved Higgs boson [4].
At the Tevatron, inpp collisions with a center-of-mass energy of 1.96 TeV, top quarks are produced mainly intt pairs, throughqq annihilation (85%) and gluon-gluon fusion. Because of its large width and correspondingly short lifetime (1025 s), the top quark decays before any hadronization can take place, so that its existence as a
‘‘free quark’’ can be studied without the complication of lower energy QCD effects. In the framework of the stan- dard model, each top quark decays almost exclusively to an on-shellW boson and a bottom quark. The bquark sub- sequently hadronizes into a jet of particles, while the W decays either to aqq0 or a lepton-neutrino pair. Thus, the decays of theWbosons determine the characteristics of att event and, consequently, the event selection strategy.
The ‘‘all hadronic’’ mode, where both W’s decay into qq0pairs, occurs for44%ofttevents, but this topology is dominated by a large QCD multijet background. The most precise top quark mass measurements arise from the
‘‘leptonjets’’ mode (30% of events), where oneW decays hadronically while the other decays to either an electron or muon plus a neutrino, whose presence can be inferred from missing transverse energy in the detector. A third mode occurs when both W bosons from each top quark decay into leptons (e, , or ). Though this
‘‘dilepton’’ mode accounts for only 11% of tt events, such measurements are important in order to reduce the overall uncertainty on the top quark mass. Further, dilepton measurements test the consistency of top quark mass re- sults obtained using other decay modes, as the dilepton mode contains different background sources and, there- fore, represents an inherently different event sample.
Since all top quark mass measurements assume a sample composition ofttand standard model background events, any discrepancy among the measured top masses could indicate the presence of new physics processes.
This paper reports a measurement of the top quark mass with the CDF II detector by combining three analysis
methods for the dilepton channel. Each analysis selects candidatettdilepton decays using one of two complemen- tary event selection strategies, which differ in lepton iden- tification criteria and subsequent signal-to-background ratios. In each analysis a single, representative top quark mass for each event is reconstructed using different kine- matical assumptions in order to constrain the ttdilepton decay. The distributions of reconstructed top quark masses obtained from the data are compared with simulated mass distributions (templates) for signal and background events, and likelihood fits are used to arrive at a final top quark mass for each analysis technique. Accounting for correla- tions in statistical and systematic uncertainties, the results of the three analyses are then combined to determine the top quark mass in the dilepton channel using template methods.
II. DETECTOR AND EVENT SELECTION The data sample used for these analyses was collected by the Collider Detector at Fermilab [5] during Run II operation between March 2002 and August 2004. As de- picted in Fig. 1, the CDF II detector is an azimuthally and forward-backward symmetric apparatus designed to study pp reactions at the Tevatron. We use a cylindrical coor- dinate system about the proton beam axis in whichis the polar angle,is the azimuthal angle, and pseudorapidity is defined as lntan=2. The detector has a charged particle tracking system immersed in a 1.4 T magnetic field, aligned coaxially with the pp beams. The Run II Silicon Vertex Detector (SVX II) and Intermediate Silicon Layer (ISL) provide tracking over the radial range 1.5 to 28 cm [6]. A 3.1 m long open-cell drift chamber, the Central Outer Tracker (COT), covers the radial range from 40 to 137 cm [7]. The fiducial region of the silicon detector extends to pseudorapidityjj 2, while the COT provides coverage forjj&1.
FIG. 1. Elevation view of the CDF II detector, showing the inner silicon microstrip detector, Central Outer Tracker drift chamber, electromagnetic and hadronic calorimeters, and muon drift chambers and scintillation counters.
Segmented electromagnetic and hadronic sampling cal- orimeters surround the tracking system and measure the energy flow of interacting particles in the pseudorapidity range jj<3:6. This analysis uses the new end plug detectors [8] to identify electron candidates with 1:2<
jj<2:0in addition to the central detectors [9] for lepton candidates with jj<1:1. A set of drift chambers and scintillation counters [10] located outside the central had- ron calorimeters and another set behind a 60 cm iron shield detect muon candidates withjj&0:6. Additional cham- bers and counters detect muons in the region0:6 jj 1:0. Gas Cherenkov counters [11] located in the 3:7<
jj<4:7region measure the average number of inelastic ppcollisions per bunch crossing and thereby determine the beam luminosity.
The signature ofttdecays in the dilepton channel is two jets from the bquarks, two high-momentum leptons and large missing energy (due to the unobserved neutrinos) from theW decays, and the possibility of extra jets from initial or final-state radiation. The major backgrounds for dileptonttevents are from Drell-Yan dilepton production qq !Z=!ee; ; , W!‘ jets events where a jet ‘‘fakes’’ the signature of the second lepton, and diboson productionWW; WZ; ZZ.
The data are derived from inclusive lepton triggers demanding central electrons with transverse energyET Esin >18 GeV, or central muons with transverse mo- mentum pT psin >18 GeV=c. Electrons in the end plug are required to haveET>20 GeV. Events must also have a missing transverse energyE6 T>15 GeV, calculated from the vector sumP
iEiTn~i, wheren~iis the unit vector in the azimuthal plane which points from the beam line to theith calorimeter tower.
The top quark mass analyses described here employ one of two sets of selection criteria developed for thettcross section measurement in the dilepton decay channel [12].
The first method, referred to as the dilepton (DIL) analysis, is similar to that used in the CDF Run I measurement [13], and requires both candidate leptons to be specifically iden- tified as either electrons or muons. A second
‘‘leptontrack’’ (LTRK) method increases the efficiency of the event selection (at the cost of a larger background) by requiring one well-identified lepton (electron or muon) in conjunction with an isolated track with large transverse momentum. This method recovers events where leptons fall in calorimeter or muon detector gaps, and increases the acceptance for single prong hadronic decays of thelepton from W! (approximately 20% of the total LTRK acceptance, compared with 12% for the DIL selection).
Both selection methods demand a ‘‘tight’’ lepton in combination with a ‘‘loose’’ lepton of opposite charge.
Requirements for the tight lepton are identical for both methods, but differ for the loose lepton. Tight leptons must have well-measured tracks, based on the numbers of silicon and drift chamber hits and reconstructed vertex position,
and haveET>20 GeV. Tight leptons must also satisfy the isolation requirement that the total calorimeterETwithin a
cone R
22
p 0:4 about the lepton trajec- tory not exceed 10% of the lepton’s ET. Tight electrons must have lateral and longitudinal electromagnetic shower profiles in the calorimeter consistent with electrons, while tight muons must point to muon chamber hits and have a calorimeter signature compatible with minimum-ionizing particles. For the DIL method, loose leptons must be well- identified electrons or muons with ET>20 GeV and no isolation requirement. Loose DIL electrons must be con- tained within the central calorimeter, while the muon chamber hit requirements for loose DIL muons are relaxed.
Loose leptons in the LTRK method, in contrast, are simply required to be well-measured and isolated tracks within jj<1 and having pT>20 GeV=c. The LTRK loose lepton isolation is determined from the pT sum of neigh- boring tracks within the cone R0:4 about the lepton track, which must not exceed 10% that of the lepton.
At least two jets are required per event, and are derived from looking for clusters of energy in calorimeter towers within a cone size of R0:4. This total jet ET is corrected for nonuniformities in the response of the calo- rimeter as a function of , effects from multiple pp collisions, and the hadronic jet energy scale of the calo- rimeter [14]. Jets are required to havejj<2:5andET>
15 GeV for the DIL analysis, or jj<2:0 and ET>
20 GeV for the LTRK method. The two highest ET jets for each event are assumed to stem from thebquarks; this assumption is true for 70% of simulatedtt events. For application in the top quark mass measurements, these jets are further corrected for energy deposited from the under- lying pp event or lost outside the search coneR0:4.
The momentum components of each b quark are then calculated from the measured jetETand angle by assuming abquark mass of5:0 GeV=c2. No explicit identification of bjets is used.
The final signature of a dilepton tt event is missing transverse energy E6 T in the calorimeter. For calorimeter tower clusters associated with an identified jet, the E6 T vector sum uses the transverse jet energy which has been corrected for calorimeter response and multiple pp colli- sion effects. The E6 T for events with an identified muon is further corrected by the measured muon momentum.
Dilepton tt events must satisfy the requirement E6 T>
25 GeV. FalseE6 T may arise through mismeasurement of the leptons or jets. Therefore, both DIL and LTRK methods require a minimum angular separationbetween lepton or jet trajectories and theE6 Tvector. For the DIL selection, events must have >20for all leptons and jets ifE6 T<
50 GeV. In the LTRK method, the E6 T vector cannot be within 5of either the tight lepton direction or the axis of the loose lepton, and jets must have >25for events withE6 T<50 GeV.
The dominant source of background for both selection methods is from Drell-Yan qq!Z= !ee;
. . .
events. These events should have no realE6 T, and can only satisfy the selection criteria if there is mismeasurement of the lepton or jet ET. Therefore, additional selection re- quirements are imposed for events where the reconstructed invariant mass of the two lepton candidates lies within 15 GeV=c2 of the Z boson resonance. For these events, the DIL method requires a ‘‘jet significance’’ of>8, de- fined as the ratio ofE6 T to the sum of jetETprojected along the E6 T direction. The LTRK method increases the E6 T requirement toE6 T >40 GeV for dilepton events near the Z resonance. The DIL method further suppresses back- ground processes by requiring that the scalar sum of jetET, leptonpT, andE6 T (denoted byHT) exceed 200 GeV.
Table I summarizes the luminosity and expected num- bers of signal and background events for the DIL and LTRK selection methods, along with observed results from the inclusive lepton data set. The LTRK selection comprises a 6% greater luminosity since it is able to accept edilepton decays when muon detectors were not opera- tional. The acceptance and efficiency ofttsignal events are calculated with a full detector simulation using PYTHIA [15] Monte Carlo and assuming a production cross section of 6.1 pb, corresponding to a top mass of178 GeV=c2[16].
The Drell-Yan,W!‘ jets fakes, and diboson back- ground acceptances are estimated using a combination of Drell-Yan and Wjets data, and PYTHIA and ALPGENHERWIG [17,18] simulation. The total uncer- tainties for expected event yields include both the statisti- cal uncertainties of the Monte Carlo samples used, as well as systematic uncertainties from particle identification, jet energy measurement, and modeling of the tt signal and background. Applied to the inclusive lepton data set, the DIL selection observes 33 events, and the LTRK selection observes 46 events, representing upward fluctuations for both selections from the predicted numbers of events at the assumedttcross section. The DIL and LTRK data samples share 24 events in common, leading to a union of 55 events with a 44% overlap.
III. METHODS FOR TOP MASS MEASUREMENT Reconstruction of the top quark mass from dilepton events involves an underconstrained system. For leptons jets decays, the two components of E6 T generated by the single neutrino, along with other assumptions about thett event (e.g., equal masses for the t and t quarks, and invariant masses of the ‘ and qq0 systems equal to the W mass) are enough to allow a kinematically overcon- strained fit. For dileptonttevents, in contrast, the measured E6 T is due to two neutrinos, so that the decay assumptions are insufficient to constrain the event.
Specifically, for each ttevent, the kinematics are fully specified by 24 quantities: the four-momenta of the six final-state particles. Twelve three-momentum components of the twob-quarks and two leptons are measured by the detector, along with the two components ofE6 T. The four mass values of the final-state b-quarks and leptons are known, while the two neutrinos are assumed to be mass- less. Making three additional assumptions about thettand W boson decays
mb‘ mb‘ (1)
m‘ mW (2)
m‘ mW; (3)
results in only 23 measured, known, or assumed compo- nents of the system. Therefore, the top quark mass cannot be directly reconstructed from tt dilepton decays, but requires one additional kinematic assumption to constrain the system.
In practice, for each event we integrate over undeter- mined kinematical variables to obtain distributions giving the relative likelihood of different values of the top quark mass. The three mass analyses are distinguished by differ- ent choices of kinematical variable, different methods for determining the likelihood of each top quark mass, and different approaches to distilling the resulting information into one top quark mass per event. This section describes each technique in turn. We model thettdecay kinematics and optimize each method over a large range of top quark masses, using HERWIG Monte Carlo simulation with CTEQ5L [19] parton distribution functions. Potential biases in the reconstructed top quark masses are taken into account in the comparison of the measured distribu- tions with top quark mass templates derived using the same simulation, as discussed in Sec. IV.
A. Neutrino weighting algorithm (NWA) One method for estimating the top quark mass from dilepton events uses the Neutrino weighting algorithm (NWA). In Run I at the Tevatron, the NWA method was one of two techniques used by D0 [20], and was employed by CDF [21] to measure the top quark mass. The method TABLE I. Luminosity, expected tt signal and background
(with total uncertainties), and observed number of events for the DIL and LTRK selection methods. A tt cross section of 6.1 pb is assumed, corresponding to a top mass of178 GeV=c2.
DIL LTRK
Luminosity 340 pb1 360 pb1
Expectedtt 15:71:3 19:41:4
Drell-Yan 5:51:2 8:73:3
W!‘ jets fakes 3:51:4 4:01:2
Diboson 1:60:3 2:00:4
Total background 10:51:9 14:73:6
Total expected 26:22:3 34:13:9
Observed 33 46
therefore provides a baseline for CDF Run II measure- ments, and is applied to the360 pb1LTRK event sample.
The strategy of the algorithm is to solve for the neutrino and antineutrino momenta, independently of the measured missing energy, by making additional assumptions about the ttdecay. The neutrino/antineutrino solutions are then compared with the measuredE6 T through a weight function in order to create a probability distribution for the event as a function of top quark mass.
The NWA weight function is constructed as follows. We assume values for the top quark andW boson masses, the pseudorapidities of the neutrino and antineutrino, and the lepton-jet pairings associated with the top/antitop decays.
We apply energy-momentum conservation to the top quark decay and obtain up to two possible solutions for the 4- momentum () of the neutrino. We repeat this procedure on the antitop decay, resulting in up to four possible pairs of neutrino-antineutrino solutions;. Each of the four solutions is assigned a probability (weight, wi) that it describes the observed missing transverse energy compo- nents E6 x and E6 y within their uncertainties x and y, respectively
wiexp
E6 xpx px2 22x
exp
E6 ypy py2 22y
: (4)
We use x y15 GeV, which is obtained from tt Monte Carlo simulation generated with mt 178 GeV=c2. In practice, however, the performance of the algorithm is insensitive to the particular choice ofE6 T resolution.
Given the assumed top quark mass and assumed neu- trinovalues, any of the four solution pairs; havea prioriequal probability. We therefore sum the four weights
wmt; ; ; ‘-jet X4
i1
wi: (5) Not knowing which are the true neutrino’s in our event, we repeat the above steps for many possible; pairs.
As seen in the upper plots of Fig. 2, Monte Carlo tt simulation indicates that the neutrino’s are uncorrelated, and follow a Gaussian distribution centered at zero with a width near one. Since the neutrinowidth varies little with top quark mass (as shown in the lower plot of Fig. 2), we assume a constant width for all top quark masses corre- sponding to the value of 0.988 obtained from the mt 178 GeV=c2sample. To ensure symmetry and smoothness, we scan the neutrino distributions from 3 to 3 in steps of 0.1, and each; pair is assigned a probability of occurrenceP; derived from a Gaussian of width 0.988. Each trial ; pair contributes to the event according to its weight (Eq. (5)) and probability of occur- rence,P;
wmt; ‘-jet X
;
P; wmt; ; ; ‘-jet: (6) Since we do not distinguishbjets frombjets, both possible lepton-jet pairings are summed. Thus, the final weight becomes a function only of the top quark mass, after integrating over all other unknowns
Wmt ‘X-jet2
‘-jet1
wmt; ‘-jet: (7)
We scanmtfrom 80 to380 GeV=c2in steps of1 GeV=c2. Figure 3 shows the resulting normalized weight distribu- tion from Eq. (7) after applying the NWA method to a HERWIGMonte Carlottevent, with a simulated top quark mass of170 GeV=c2. We choose one indicative top quark mass for each event, selecting the most probable value (MPV) of the weight distribution as that which best ex- plains the event as attdilepton decay.
For a given event, there exists a small probability that the kinematics of the decay will fail to produce a solution for any scanned top quark mass. This efficiency for finding a solution is thus an additional event selection criterion.
Studies of simulated tt dilepton events show that this NWA efficiency for signal is 99.8%, and independent of generated top quark mass. Applying the NWA method to Monte Carlo background samples shows that the efficiency for finding a kinematical solution varies between sources,
η Neutrino
-5 -4 -3 -2 -1 0 1 2 3 4 5
)ηEvents / (0.2
0 200 400 600 800 1000
1200 mt = 178 GeV/c2 = 0.988 σ
η Neutrino
-5 -4 -3 -2 -1 0 1 2 3 4 5
ηAntineutrino
-5 -4 -3 -2 -1 0 1 2 3 4 5
= 178 GeV/c2 mt
2) Top Mass (GeV/c
140 160 180 200 220
WidthηNeutrino
0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2
= 0.988 σ
FIG. 2. Neutrinodistribution with Gaussian fit (upper left) and neutrino vs antineutrino(upper right) from aHERWIGtt sample withmt178 GeV=c2. Lower plot showswidth as a function of generated top quark mass, compared with fit value at mt178 GeV=c2(horizontal line).
. . .
ranging from 94%–100%, with an average background efficiency of 96%.
B. Full kinematic analysis (KIN)
A second method for determining the top quark mass in the dilepton channel, called the Full Kinematic Analysis (KIN), is applied to the 340 pb1 DIL selection sample.
The KIN method resolves the underconstrained dileptontt decays by introducing an additional equation for the lon- gitudinal momentum of the tt system, ptzt. With the 6- particle final state constrained, the KIN method solves the resulting kinematic equations numerically to determine the top quark mass for each event.
Ideally, the quantityptztshould be determined theoreti- cally, and should be virtually independent of the top quark mass. Studies from Monte Carlo simulation over a range of top quark masses from140–200 GeV=c2show thatptzthas a Gaussian behavior, with a mean of zero and a width near 180 GeV=c. This width increases by roughly 10% across the top quark mass range studied. The validity of our Monte Carlo simulation can be tested with data from leptonjets tt events, where ptzt can be reconstructed explicitly. Figure 4 compares ptzt from the leptonjets data sample withttand background Monte Carlo samples, showing good agreement between data and simulation. The leptonjets event selection, using secondary vertex b-quark identification, and subsequent backgrounds are similar to those of the leptonjets cross section measure- ment [22].
Using the measured momenta of theb-quarks and lep- tons, the two components of the measuredE6 T, and assump- tions about the six final-state particle masses, the additional constraint on ptzt, along with constraints on the W andtt decays, lead to the following set of kinematic equations:
pxpxE6 x py py E6 y ptzptz0180 GeV=c mtmt mW80:4 GeV=c2 p~bp~W p~t
~
pbp~W p~t p~lp~p~W
~
plp~p~W:
(8)
These equations have two solutions, which are determined through an iterative procedure. If solutions cannot be found by using the above assumptions for the top and bottom quark masses, these requirements are relaxed, and we accept solutions where mW 80:43:0 GeV=c2 and mtmt2:0 GeV=c2.
The iterative procedure employed, Newton’s Method [23], solves equations of the form fx 0. The method requires an initial guess forxwhich is reasonably close to the true root. The local derivative f0xis then computed and extrapolated to zero, providing a better approximation for the root. This procedure is repeated according to
xn1 xn fxn
f0xn; (9) until a satisfactory solution is found. The method is ex- tended to a system of kequations Fx ~ fix~ by deter- mining the kk Jacobian matrix JijFx ~ @f@xi~x
j , where i1; k;j1; k. In actuality, the method solves the linear equations
JFx~n x~n1x~n Fx~n; (10) for the unknown x~n1x~n, in order to avoid having to compute the inverse ofJFx~n.
(GeV/c)
t t
pz
-600 -400 -200 0 200 400 600
Events / (100 GeV/c)
0 10 20 30 40
= 192 GeV/c) σ
l+jets data ( (8.7 pb) t t
EW, single top W+light flavor non-W W+heavy flavor
FIG. 4. Comparison of tt longitudinal momentum between leptonjets data (with associated Gaussian fit) and standard model processes. The data corresponds to a sample of318 pb1. The tt signal uses PYTHIA Monte Carlo with mt 178 GeV=c2, corresponding to a cross section of 8.7 pb.
2) Top Mass (GeV/c
100 150 200 250 300 350
)2 Weight / (1 GeV/c
0 0.01 0.02
event weight MPV
FIG. 3. NWA weight distribution as a function of top quark mass hypothesis (from Eq. (7)) for aHERWIG Monte Carlott event withmt170 GeV=c2. The vertical line denotes the most probable value (MPV) ofmt chosen by the method.
