Article
Reference
Top Quark Mass Measurement in the lepton+jets Channel Using a Matrix Element Method and in situ Jet Energy Calibration
CDF Collaboration
CLARK, Allan Geoffrey (Collab.), et al.
Abstract
A precision measurement of the top quark mass mt is obtained using a sample of tt events from pp collisions at the Fermilab Tevatron with the CDF II detector. Selected events require an electron or muon, large missing transverse energy, and exactly four high-energy jets, at least one of which is tagged as coming from a b quark. A likelihood is calculated using a matrix element method with quasi-Monte Carlo integration taking into account finite detector resolution and jet mass effects. The event likelihood is a function of mt and a parameter ΔJES used to calibrate the jet energy scale in situ. Using a total of 1087 events in 5.6 fb−1 of integrated luminosity, a value of mt=173.0±1.2 GeV/c2 is measured.
CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Top Quark Mass Measurement in the lepton+jets Channel Using a Matrix Element Method and in situ Jet Energy Calibration.
Physical Review Letters , 2010, vol. 105, no. 25, p. 252001
DOI : 10.1103/PhysRevLett.105.252001
Available at:
http://archive-ouverte.unige.ch/unige:39117
Disclaimer: layout of this document may differ from the published version.
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Top Quark Mass Measurement in the lepton þ jets Channel Using a Matrix Element Method and in situ Jet Energy Calibration
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J. C. Yun,15A. Zanetti,53aY. Zeng,14and S. Zucchelli6b,6a
(CDF Collaboration)
1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China
2Argonne National Laboratory, Argonne, Illinois 60439, USA
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, USA
6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy
6bUniversity of Bologna, I-40127 Bologna, Italy
7University of California, Davis, Davis, California 95616, USA
8University of California, Los Angeles, Los Angeles, California 90024, USA
9Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
10Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
11Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
12Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia
13Joint Institute for Nuclear Research, RU-141980 Dubna, Russia
14Duke University, Durham, North Carolina 27708, USA
15Fermi National Accelerator Laboratory, Batavia, Illinois 60510, USA
16University of Florida, Gainesville, Florida 32611, USA
17Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy
18University of Geneva, CH-1211 Geneva 4, Switzerland
19Glasgow University, Glasgow G12 8QQ, United Kingdom
20Harvard University, Cambridge, Massachusetts 02138, USA
21Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland
22University of Illinois, Urbana, Illinois 61801, USA
23The Johns Hopkins University, Baltimore, Maryland 21218, USA
24Institut fu¨r Experimentelle Kernphysik, Karlsruhe Institute of Technology, D-76131 Karlsruhe, Germany
25Center 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;
Chonbuk National University, Jeonju 561-756, Korea
26Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
27University of Liverpool, Liverpool L69 7ZE, United Kingdom
28University College London, London WC1E 6BT, United Kingdom
29Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain
252001-2
30Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
31Institute 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
32University of Michigan, Ann Arbor, Michigan 48109, USA
33Michigan State University, East Lansing, Michigan 48824, USA
34Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
35University of New Mexico, Albuquerque, New Mexico 87131, USA
36Northwestern University, Evanston, Illinois 60208, USA
37The Ohio State University, Columbus, Ohio 43210, USA
38Okayama University, Okayama 700-8530, Japan
39Osaka City University, Osaka 588, Japan
40University of Oxford, Oxford OX1 3RH, United Kingdom
41aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
41bUniversity of Padova, I-35131 Padova, Italy
42LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France
43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
44aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy
44bUniversity of Pisa, I-56127 Pisa, Italy
44cUniversity of Siena, I-56127 Pisa, Italy
44dScuola Normale Superiore, I-56127 Pisa, Italy
45University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
46Purdue University, West Lafayette, Indiana 47907, USA
47University of Rochester, Rochester, New York 14627, USA
48The Rockefeller University, New York, New York 10065, USA
49aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy
49bSapienza Universita` di Roma, I-00185 Roma, Italy
50Rutgers University, Piscataway, New Jersey 08855, USA
51Texas A&M University, College Station, Texas 77843, USA
52Texas Tech University, Lubbock, Texas 79609, USA
53aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, I-33100 Udine, Italy
53bUniversity of Trieste/Udine, I-33100 Udine, Italy
54University of Tsukuba, Tsukuba, Ibaraki 305, Japan
55Tufts University, Medford, Massachusetts 02155, USA
56University of Virginia, Charlottesville, Virginia 22906, 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 22 October 2010; published 13 December 2010)
A precision measurement of the top quark massmt is obtained using a sample ofttevents from pp collisions at the Fermilab Tevatron with the CDF II detector. Selected events require an electron or muon, large missing transverse energy, and exactly four high-energy jets, at least one of which is tagged as coming from abquark. A likelihood is calculated using a matrix element method with quasi-Monte Carlo integration taking into account finite detector resolution and jet mass effects. The event likelihood is a function ofmtand a parameterJES used to calibrate the jet energy scalein situ. Using a total of 1087 events in5:6 fb1 of integrated luminosity, a value ofmt¼173:01:2 GeV=c2is measured.
DOI:10.1103/PhysRevLett.105.252001 PACS numbers: 14.65.Ha
The top quark is the heaviest known fundamental parti- cle in the standard model of particle physics. Since the 1995 discovery of the top quark at the Fermilab Tevatron [1], both the CDF and D0 experiments have been improv- ing the measurement of its massmt, which is a fundamen- tal parameter in the standard model [2]. Loop corrections in electroweak theory relatemt (along with theW boson massmW) to the mass of the predicted Higgs boson. Thus,
precision measurements ofmthelp to constrain the value of the Higgs boson mass [3].
This Letter describes the single most-precise measure- ment to date of the top quark mass. It is performed on data collected by the CDF II detector [4] during Run II of the Fermilab Tevatron pp collider operating at ffiffiffi
ps
¼ 1:96 TeV with a total integrated luminosity of 5:6 fb1. The measurement is performed on candidate tt events
containing a lepton and four jets [5]. For each event selected in this analysis, we calculate the probability of observing that event by integrating the matrix element for ttproduction and decay over phase-space variables. We use a neural network discriminant to distinguish between sig- nal and background events to correct for the contribution due to background, and employ a cut on the peak like- lihood for a given event for additional rejection of back- ground and poorly modeled signal events. This analysis offers a gain of nearly 20% in statistical precision over our previous measurement [5] given an equal number of events; there, in order to make the likelihood integration computationally tractable, we introduced kinematic as- sumptions to reduce the dimensionality of the integral. In the present analysis, we use a quasi-Monte Carlo integra- tion technique [6], which converges more rapidly than the typical OðN1=2Þ convergence of standard Monte Carlo integration. This allows us to integrate over a total of 19 dimensions in a computationally practical time, result- ing in a more accurate modeling of the event. Furthermore, in addition to the increased data sample available with more integrated luminosity delivered by the Tevatron, we have expanded our muon selection ability, which increases the size of our data sample by nearly 30%. In total, this measurement improves our statistical precision by a factor of 2 over our previous analysis with1:9 fb1[5].
In this measurement, the largest uncertainty is due to the uncertainty in the jet energy scale (JES) determina- tion. To reduce this uncertainty, we calculate the likelihood as a two-dimensional function ofmtand a second parame- ter, JES, which corrects the jet energies by a factor of 1þJESj, wherej is the fractional systematic un- certainty on the energy for a given jet [7,8]. The knownW boson mass is used to constrain theW !qq0decay, which yields information on the JES parameter. We can thus optimally combine events to reduce the total uncertainty onmtdue to JES.
Within the standard model, the top quark decays almost exclusively into a W boson and a b quark. We define a
‘‘leptonþjets’’ event as an event where one of the W bosons produced by thettpair decays into a charged lepton (in this analysis, an electron or a muon) and a neutrino, and the other into a qq0 pair. The two b quarks and two quarks from theW boson then produce jets in the detector [9]. We thus require candidate events to have an electron with ET>20 GeV or a muon with pT>20 GeV=c in the central detector (jj<1[10]), or a muon with pT >
20 GeV=c obtained with a trigger [4] on missing trans- verse energy, ET [10], instead of a central muon. As the neutrino energy is not detected, we requireET >20 GeV in the event. We also require exactly four jets with ET>20 GeVwithin the region jj<2:0, at least one of which must be tagged as abjet using a secondary vertex tagging algorithm [11]. To model tt events, we use Monte Carlo-simulated events generated with thePYTHIA
[12] generator for 15 differentmtvalues ranging from 162 to184 GeV=c2.
Background events contributing to the selected sample are: (a) events in which aWboson is produced in conjunc- tion with heavy-flavor quarks (bb, cc, or c); (b) events in which aW boson is produced along with light quarks, at least one of which is mistagged as heavy flavor; (c) QCD events that do not contain a trueWboson; (d) diboson (WW, WZ, orZZ) orZþjets events; (e) single top events. We model the contribution fromWþjets events usingALPGEN
[13], single top events usingMADGRAPH[14], and diboson events with PYTHIA. The Zþjets contributions are not modeled separately, but are included in theWþlight flavor contribution. All Monte Carlo samples are processed with the CDF II detector response simulation package [15]. The non-W QCD background is modeled using a sideband of data events selected to have a small contribution from heavy boson decay. The numbers of background events are esti- mated with the method used for the ttcross section mea- surement [16], and are shown in TableI.
For each event, we construct a likelihood as a function of mtandJES using the following integral:
Lðy~jmt;JESÞ ¼ 1 NðmtÞ
1 Aðmt;JESÞ X24
i¼1
wiLiðy~jmt;JESÞLiðy~jmt;JESÞ
¼Z fðz1Þfðz2Þ
FF TFðy~jx;~ JESÞ
jMðmt; ~xÞj2dðxÞ;~ (1) where y~ are the quantities measured in the detector (the momenta of the jets and charged lepton),x~are the parton- level quantities that define the kinematics of the event, NðmtÞis a global normalization factor, Aðmt;JESÞis the event acceptance as a function of mt andJES,fðz1Þand fðz2Þ are the parton distribution functions (PDFs) for incoming parton momentum fractions z1 and z2, FF is the relativistic flux factor, TFðy~jx;~ JESÞ are the transfer TABLE I. Expected sample composition for an integrated luminosity of 5:6 fb1. The ttcontribution is estimated using a cross section of 7.4 pb [17] andmt¼172:5 GeV=c2.
Event Type 1bTag 2bTags
WþHeavy Flavor 129:542:1 15:75:5
Non-WQCD 50:125:5 5:53:8
WþLight Flavor Mistag 48:517:1 1:00:4 Diboson (WW,WZ,ZZ) 10:51:1 1:00:1
Single Top 13.30.9 4.00.4
Z!‘‘þjets 9:91:2 0:80:1
Total Background 261:860:6 28:09:6
ttSignal 767:397:2 276:543:0
Total Expected 1029:1114:5 304:544:1
Events Observed 1016 247
252001-4
functions that describe the measured jet-momentum dis- tributions given the quark kinematics,dðxÞ~ is the phase space for the eight particles in thettproduction and decay process, andMðmt; ~xÞis the matrix element for the process.
The integral is calculated for each of the 24 possible permutations of jet-parton assignment and then summed with weightswidetermined by the probability that abor light parton will result in ab-tagged or untagged jet.
We use the Kleiss-Stirling matrix element [18], which is a leading-order matrix element including bothqq!ttand gg!ttproduction processes, as well as all spin correla- tions. For the PDFs, we use the CTEQ5L functions [19] for the incoming qq and gluons. The normalization factor NðmtÞis obtained by integrating the Kleiss-Stirling matrix element with the PDFs and the flux factor over the phase space formed by the two initial and the six final-state particles. The acceptance Aðmt;JESÞ is obtained from simulated events where the parton directions and momenta are smeared to simulate final-state jets. The transfer functions connect the measured jets to the partons. We construct the transfer functions by taking simulatedtt! leptonþjets events in a wide range of masses and match- ing the simulated jets to their parent partons. The transfer functions are separated into momentum and angular terms;
both are constructed with dependence on the true jet pT and mass from the Monte Carlo simulation. The transfer functions are constructed separately forband light quarks, as well as for each of four bins of jet. There are 32 phase space integration variables in Eq. (1) (for the two initial partons and six final partons). Four of these are eliminated by energy and momentum conservation, and four more by taking the charged lepton, neutrino, and initial parton masses as known. In addition, we assume that the lepton momentum is perfectly measured, and we neglect the effects of the individual transverse momenta of the initial partons so that we model only the transverse momentum of the totalttsystem, for which we use a prior derived from Monte Carlo simulation. This leaves a total of 19 dimen- sions over which the integral must be evaluated, which we perform using a quasi-Monte Carlo technique.
The handling of background events is unchanged from our previous publication [5]. We identify events likely to be background using aJETNET 3.5artificial neural network [20] with 10 inputs. We construct distributions of the neural network output weightufor signal,SðuÞ, and back- ground,BðuÞ, events, normalized to their overall expected fractions, and calculate the expected background fraction for a given event asfbgðuÞ ¼BðuÞ=½BðuÞ þSðuÞ.
We calculate the likelihood for all candidate events under the assumption that they are signal, but the combined like- lihood contains contributions from both signal and back- ground events. However, only the signal events contain information about mt, so using Monte Carlo-simulated events we compute the average likelihood for background events and subtract it from the total likelihood
logLadjðmt;JESÞ ¼ X
ievents
½logLðy~ijmt;JESÞ
fbgðuiÞlog Lbgðmt;JESÞ; (2) whereLadjis the adjusted total likelihood for a given set of events, Lðy~ijmt;JESÞ is the likelihood for an individual event from Eq. (1), fbgðuiÞ is the background fraction for a given event with a neural network output ui, and Lbgðmt;JESÞ is the average likelihood for a background event.
Besides background events, the sample includes events which contain a realtt, but where one or more of the four jets or the lepton observed in the detector do not come directly from thettdecay, and are not well modeled by the signal likelihood or handled by the background subtraction above. These events, which we refer to as ‘‘bad signal,’’
have a variety of sources (extra jets from gluon radiation, tt events where both W bosons decay into leptons or hadrons, W ! decay, etc.) and make up 36% of the simulated ttevents formt¼172:5 GeV=c2. We suppress these events by requiring that the peak log-likelihood value for an event be at least 10. This cut retains 96.3% of the signal, while rejecting 30.8% of the bad signal and 37.3%
of the background.
We test and calibrate the method by constructing simu- lated experiments using the Monte Carlo samples of ttevents and background described earlier. For a given input mtandJES, we perform 2000 experiments using a Poisson distribution with mean of 1089 events (the number of events expected to pass the likelihood cut), and use these to calibrate the measurement as a function of the inputmt andJES. Figure1shows the output mass before calibra- tion and the calibrated expected uncertainty.
In the data we find a total of 1087 events which pass all of the selection requirements (including the likelihood peak cut), of which 854 have 1btag and 233 have >1b tag. Figure 2 shows the resulting 2D likelihood contours for1,2, and3after all calibration.
)2 (GeV/ctOutput m
160 165 170 175 180 185
0.06
± Value at 173 = 172.46
0.01
± Slope = 0.97
2) (GeV/c Input mt
155 160 165 170 175 180 185
)2 (GeV/cmσ 0.8
0.85 0.9 0.95
FIG. 1. Simulated experiment results using Monte Carlo signal and background events. Top: Output mt vs input mt, before calibration is applied. Bottom: Expected uncertaintymvs input mt, with calibration applied. The lines are linear best fits.
To obtain a 1D likelihood curve inmtonly, we treatJES as a nuisance parameter and eliminate it using the profile likelihood method [21], where we take the maximum value of the likelihood along theJESaxis for eachmtvalue. The top quark mass value extracted from the profile likelihood after calibration ismt¼173:00:9 GeV=c2. We can sep- arate this uncertainty into the statistical uncertainty onmt and the uncertainty due toJESby fixing theJESvalue to its maximum likelihood value. We find that the uncertainty from the resulting 1D likelihood is 0:7 GeV=c2, so we assign the remaining uncertainty of 0:6 GeV=c2 to JES and concludemt¼173:00:7ðstatÞ 0:6ðJESÞGeV=c2. To validate the likelihood cut procedure, we compare the peak values of the log-likelihood curves obtained with data to those obtained with Monte Carlo-simulated events at mt¼172:5 GeV=c2 (the nearest available mass value).
The results are shown in Fig.3.
The systematic uncertainties onmt, given in TableII, are derived using the methods described in Ref. [5]. In brief, we include uncertainties coming from: the calibration method, signal Monte Carlo modeling, evaluated by com- paring events simulated with thePYTHIAandHERWIG[22]
generators, variations of the parameters used for initial state radiation and final state radiation, a residual JES uncertainty because the JES uncertainty contains several components with different pT and dependence, addi- tional uncertainties on the energy scale for bjets, uncer- tainty on the leptonpT scale, multiple hadron interactions, to take into account uncertainty on the jet corrections as a function of the number of interactions in the event, uncer- tainties arising from the PDFs used in the integration, and the background modeling. This analysis includes a system- atic uncertainty due to color reconnection effects, not considered in our previous analysis. We usePYTHIAversion 6.4.20, which includes a color reconnection model [23], and measure the difference between two tunes, Tune A, which is the tune used in this analysis, and Tune ACR, which adds color reconnection effects to Tune A. The individual systematic uncertainties are added in quadrature to obtain the final total of0:9 GeV=c2.
In conclusion, the measured top quark mass in a sample with 5:6 fb1 of integrated luminosity, with 1087 events passing all cuts, is mt¼173:00:7ðstat:Þ 0:6ðJESÞ 0:9ðsyst:ÞGeV=c2, for a total uncertainty of1:2 GeV=c2. The improved integration techniques and increased data sample make this the best single measurement of the top quark mass to date, and it is comparable in precision to the most recent combination for the top quark mass at the Tevatron [2].
We thank the Fermilab staff and the technical staffs of the participating institutions for their vital contributions.
This work was supported by the U.S. Department of Energy and the National Science Foundation; the Italian Istituto Nazionale di Fisica Nucleare; the Ministry of Education, Culture, Sports, Science and Technology of Japan; the Natural Sciences and Engineering Research
2) (GeV/c mt
170 171 172 173 174 175
)σ (JES∆
-0.6 -0.4 -0.2 -0 0.2 0.4 0.6 0.8
(ln L) = -0.5
∆
(ln L) = -2.0
∆
(ln L) = -4.5
∆
FIG. 2. Measured 2D likelihood on the data events, with the contours corresponding to a1-,2-, and3-uncertainty in the final mt measurement from the profile method. The marker shows the point of maximum likelihood.
−2 0 2 4 6 8 10 12 14 16 18
0 50 100 150 200 250
Log−likelihood value at peak Number of events
Signal + background MC Background MC
Data events
FIG. 3. Comparison of the log-likelihood value of the peak of likelihood curves for data and Monte Carlo events. The vertical line at 10 indicates the likelihood cut used in this analysis. A Kolmogorov-Smirnov test gives a confidence level of 0.93, showing good agreement between the two.
TABLE II. List of systematic uncertainties onmt. Systematic Source Uncertainty (GeV=c2)
Calibration 0.10
Monte Carlo Generator 0.37
Initial State Radiation and Final State Radiation
0.15
Residual JES 0.49
b-JES 0.26
LeptonpT 0.14
Multiple Hadron Interactions 0.10
PDFs 0.14
Background Modeling 0.33
Color Reconnection 0.37
Total 0.88
252001-6
Council of Canada; the National Science Council of the Republic of China; the Swiss National Science Foundation; the A. P. Sloan Foundation; the Bundesministerium fu¨r Bildung und Forschung, Germany; the World Class University Program, the National Research Foundation of Korea; the Science and Technology Facilities Council and the Royal Society, United Kingdom; the Institut National de Physique Nucleaire et Physique des Particules/CNRS; the Russian Foundation for Basic Research; the Ministerio de Ciencia e Innovacio´n, and Programa Consolider-Ingenio 2010, Spain; the Slovak R&D Agency; and the Academy of Finland.
aDeceased
bWith visitors from University of Massachusetts Amherst, Amherst, MA 01003, USA
cWith visitors from Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, 09042 Monserrato (Cagliari), Italy
dWith visitors from University of California Irvine, Irvine, CA 92697, USA
eWith visitors from University of California Santa Barbara, Santa Barbara, CA 93106, USA
fWith visitors from University of California Santa Cruz, Santa Cruz, CA 95064, USA
gWith visitors from CERN,CH-1211 Geneva, Switzerland
hWith visitors from Cornell University, Ithaca, NY 14853, USA
iWith visitors from University of Cyprus, Nicosia CY- 1678, Cyprus
jWith visitors from University College Dublin, Dublin 4, Ireland
kWith visitors from University of Fukui, Fukui City, Fukui Prefecture, Japan 910-0017
lWith visitors from Universidad Iberoamericana, Mexico D.F., Mexico
mWith visitors from Iowa State University, Ames, IA 50011, USA
nWith visitors from University of Iowa, IA City, IA 52242, USA
oWith visitors from Kinki University, Higashi-Osaka City, Japan 577-8502
pWith visitors from Kansas State University, Manhattan, KS 66506, USA
qWith visitors from University of Manchester, Manchester M13 9PL, England
rWith visitors from Queen Mary, University of London, London, E1 4NS, England
sWith visitors from Muons, Inc., Batavia, IL 60510, USA
tWith visitors from Nagasaki Institute of Applied Science, Nagasaki, Japan
uWith visitors from National Research Nuclear University, Moscow, Russia
vWith visitors from University of Notre Dame, Notre Dame, IN 46556, USA
wWith visitors from Universidad de Oviedo, E-33007 Oviedo, Spain
xWith visitors from Texas Tech University, Lubbock, TX 79609, USA
yWith visitors from Universidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile
zWith visitors from Yarmouk University, Irbid 211-63, Jordan
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