Article
Reference
Top quark mass measurement from dilepton events at CDF II with the matrix-element method
CDF Collaboration
CAMPANELLI, Mario (Collab.), et al.
Abstract
We describe a measurement of the top quark mass using events with two charged leptons collected by the CDF II detector from pp collisions with s√=1.96 TeV at the Fermilab Tevatron.
The likelihood in top quark mass is calculated for each event by convoluting the leading order matrix element describing qq→tt→bℓνℓbℓ′νℓ′ with detector resolution functions. The presence of background events in the data sample is modeled using similar calculations involving the matrix elements for major background processes. In a data sample with integrated luminosity of 340 pb−1, we observe 33 candidate events and measure Mtop=165.2±6.1(stat.)±3.4(syst.) GeV/c2. This measurement represents the first application of this method to events with two charged leptons and is the most precise single measurement of the top quark mass in this channel.
CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Top quark mass measurement from dilepton events at CDF II with the matrix-element method. Physical Review. D , 2006, vol. 74, no. 03, p. 032009
DOI : 10.1103/PhysRevD.74.032009
Available at:
http://archive-ouverte.unige.ch/unige:38357
Disclaimer: layout of this document may differ from the published version.
Top quark mass measurement from dilepton events at CDF II with the matrix-element method
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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J. C. Yun,16L. Zanello,51A. 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, USA
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, Helsinki, Finland 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, Korea, Seoul National University, Seoul 151-742, Korea,
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 Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France
45University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
46Istituto Nazionale di Fisica Nucleare Pisa, Universities of Pisa, Siena, Italy 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 1 June 2006; published 28 August 2006)
We describe a measurement of the top quark mass using events with two charged leptons collected by the CDF II detector frompp collisions withps
1:96 TeVat the Fermilab Tevatron. The likelihood in top quark mass is calculated for each event by convoluting the leading order matrix element describing qq!tt!b‘‘b‘ 0‘0with detector resolution functions. The presence of background events in the data sample is modeled using similar calculations involving the matrix elements for major background processes. In a data sample with integrated luminosity of 340 pb1, we observe 33 candidate events and measure Mtop165:26:1stat: 3:4syst:GeV=c2:This measurement represents the first ap- plication of this method to events with two charged leptons and is the most precise single measurement of the top quark mass in this channel.
DOI:10.1103/PhysRevD.74.032009 PACS numbers: 14.65.Ha, 12.15.Ff, 13.85.Ni, 13.85.Qk
I. INTRODUCTION
The standard model accommodates quark masses through Yukawa couplings to the Higgs boson, but does not predict the size of these couplings and contains no explanation for the observed quark masses. A striking feature is the large mass of the top quark, the heaviest of
the observed fundamental particles. Its large mass suggests that it may play a unique role in electroweak symmetry breaking [1,2]. Precise measurements of the mass of the top quark constrain the mass of the yet unobserved Higgs boson through radiative corrections [3], and can restrict possible extensions to the standard model [4].
. . .
In collisions of protons and antiprotons at ps 1:96 TeV, top quark pairs are produced primarily through the annihilation of quarks and antiquarks. In the standard model, the top quark decays to abquark and aW boson nearly 100% of the time; theW boson decays to a pair of quarks or a charged lepton and neutrino. Quarks fragment and hadronize and are reconstructed as jets (clusters of particles). The dilepton channel, consisting of decaystt! b‘‘b‘ 0‘0, has a small branching fraction, but measure- ments of the mass in this channel have the advantage that they are less reliant on the calibration of the jet energy scale than channels with hadronicW boson decay. A top quark mass measurement in this channel is an important verification that the observed top quark candidates are consistent with standard model production and decay. A discrepancy from measurements in other channels could indicate the presence of physics beyond the standard model that makes contributions to the dilepton sample [5].
Reconstruction of the top quark mass in the dilepton channel is particularly challenging due to the two unde- tected neutrinos from theW boson decays. Previous mea- surements [6,7] in this channel using Tevatron run I data calculated a mass in each event by making several kine- matic assumptions and integrating over the remaining un- measured quantities; the distribution of event masses was then compared to simulation at varying top quark masses.
This article describes in detail the first application to the dilepton channel of a technique pioneered for analysis of single lepton tt!b‘‘bqq 0 decays [8–12]. This tech- nique convolutes the matrix element for tt decays with detector resolution functions and integrates over unmeas- ured quantities to construct per-event likelihoods in top quark mass. We relax many of the kinematic assumptions of previous methods and integrate over six unmeasured quantities. The event likelihoods are directly multiplied to obtain the joint likelihood from whichMtis extracted. This weights events according to the relative amount of infor- mation they carry. The data used in this measurement correspond to an integrated luminosity of 340 pb1 col- lected between March 2002 and August 2004 by the CDF II detector in collisions at
ps
1:96 TeVat the Fermilab Tevatron; this measurement and a brief description were first reported in Ref. [13].
Sections II and III describe the CDF detector and the selection of the data sample. Section IV gives an overview of the analysis method. Sections V, VI, and VII describe in detail the major pieces of the likelihood calculation.
Section VIII describes the reconstruction and calibration of the top quark mass. Section IX covers the systematic uncertainties and Sec. X presents the measurement.
II. THE CDF DETECTOR
The CDF II detector is an azimuthally and forward- backward symmetric detector designed to studypp colli- sions at the Fermilab Tevatron. The CDF coordinate sys-
tem is right-handed, with the z axis pointing along a tangent to the Tevatron ring along the proton direction.
The remaining rectangular coordinatesxandyare defined pointing outward and upward from the Tevatron ring, respectively, and the azimuthal angle is measured rela- tive to thexaxis in thexyplane. Transverse quantities such as transverse momentum, pT, and transverse energy, ET, are projections onto this plane. The polar angle is mea- sured from the proton direction and is typically expressed as pseudorapidity lntan2. Subdetectors which are particularly relevant to this analysis are described below. A more complete description of the CDF II detector can be found elsewhere [14].
The CDF tracking system consists of an inner silicon microstrip detector and a large outer open-cell drift cham- ber. These subsystems are immersed in a superconducting solenoid producing a 1.4 T magnetic field parallel to thep and p beams. The silicon detector, which provides high- resolution position measurements of charged particles close to the interaction region, consists of three subdetec- tors. The innermost detector, Layer 00 (L00) [15], is a single-sided layer of silicon wafers mounted directly on the beampipe at a radius of 1.6 cm. The SVXII [16]
detector is a five layer, double-sided silicon detector that covers the radial region between 2.5 cm and 10.6 cm. The Intermediate Silicon Layers (ISL) [17] comprise one or two additional layers of double-sided silicon, depending on the polar angle, at radii from 20 cm to 28 cm. The Central Outer Tracker (COT) [18], a large open-cell drift chamber, is positioned outside the silicon detector from radii of 0.43 m to 1.32 m. The COT contains 8 superlayers (alter- nating between axial and2stereo angle) each contain- ing 12 wire layers for a total of 96 layers. In combination the Silicon and COT detectors provide excellent tracking up tojj 1:1with decreasing coverage tojj 2:0.
Sampling calorimeters segmented inandsurround- ing the tracking system measure particle energies. In the central region ofjj<1:1, the calorimeter is divided into projective towers subtending 15 in and 0.1 in. The central electromagnetic calorimeter (CEM) [19] consti- tutes the front of the wedges in the central region. The CEM consists of alternating layers of lead and scintillator, amounting to 18 radiation lengths of material. Embedded in the CEM is the shower maximum detector (CES). The CES provides position measurements of the electromag- netic showers at a depth of 5 radiation lengths and is used in electron identification. Behind the CEM is the central hadronic calorimeter (CHA) [20], which provides energy measurements of hadronic jets. The CHA consists of 4.7 interaction lengths of alternating steel and scintillator. In addition to the central calorimeters, end plug calorimeters cover1:1<jj<3:6. The plug electromagnetic calorime- ter (PEM) [21] consists of alternating lead absorber and scintillating tile readout with wavelength shifting fibers;
the total thickness is 23.2 radiation lengths of material. A
plug shower maximum detector (PES) [22] provides posi- tion measurement of electron and photon showers. The plug hadronic calorimeter (PHA) has alternating layers of iron and scintillating tile for a total of 6.8 interaction lengths.
The muon detection system consists of three sandwiched drift tube layers, each utilizing single wire drift cells four layers deep. Directly behind the central hadronic calorime- ter is the central muon detector (CMU) [23] which can detect muons withpT>1:4 GeV=cin the region ofjj<
0:6. Additional muon coverage in this region is provided by the central muon upgrade (CMP) which is separated from the CMU by 60 cm of steel. The CMP detects muons with pT>2:0 GeV=c. The central muon extension (CMX) pro- vides further coverage in the region of0:6<jj<1:0.
CDF’s three level trigger system reduces the event rate from 1.7 MHz to80 Hz. The first two levels are hard- ware triggers that partially reconstruct events using infor- mation from individual subdetectors while the third level is a software trigger that performs event reconstruction.
III. DATA SAMPLE
We selecttt!b‘‘b‘ 0‘0decays with a high-pTlepton trigger and the requirement that candidates have (i) two leptons each withpT>20 GeV=c, (ii) significant missing energy transverse to the beam direction (ET) [24], and (iii) two jets each with ET>15 GeV. The selection was designed for a cross section measurement and is described as ‘‘DIL’’ in Ref. [25]. A description of the trigger require- ments and selection used to obtain this data set follows.
A. Trigger
The trigger requires at least one high-pT lepton. For central electron candidates, the first two trigger levels require an electromagnetic calorimeter cluster with a con- firming COT track and without a large hadronic energy deposit. The third level trigger requires an electron candi- date withET 18 GeV. Events with electron candidates in the plug (jj>1:2) are required to have electronET >
20 GeVand missing transverse energy6ET>15 GeV. For muon candidates, the first two trigger levels require hits in the muon chambers and a confirming COT track. The third level trigger requires a muon stub with a matching track of pT 18 GeV=c.
B. Leptons
Final lepton requirements are tighter than those made in the last stage of the trigger. Electron candidates are re- quired to have an electromagnetic calorimeter cluster with ET>20 GeV and jj<2:0. Muon candidates are re- quired to have a track withpT>20 GeV=c, which limits them to the coverage of the COT. At least one of the leptons is required to be isolated. Electrons and muons are isolated if the energy deposited in the calorimeter in a cone
R
2 2
p 0:4 around the lepton is at
most 10% of the lepton transverse energy. In addition, electron candidates are required to have a well-measured track pointing at an energy deposition in the calorimeter.
For electron candidates withjj>1:2, this track associa- tion uses a calorimeter-seeded silicon tracking algorithm [26]. Muon candidates are required to have a well- measured track linked to hits in the muon chambers and energy deposition in the calorimeter consistent with that expected for muons. If the event contains two muons, only one is required to have hits in muon chambers used in the trigger decision. The other muon may have hits in cham- bers not used for the trigger decision if there is a matching COT track, or no hits in muon chambers if the COT track points in regions where there is no muon chamber coverage.
C. Jets
A jet is defined as a cluster of energy surrounding a calorimeter tower with ET>1 GeV, grouped within a
cone of R
2 2
p 0:4 by the JETCLUal-
gorithm [27]. Events are required to have at least two jets with jj<2:5 and ET >15 GeV after the corrections described below are applied.
The total jetET is corrected for nonuniformities in the response of the calorimeter as a function of, for effects from multiple pp collisions, and for the hadronic jet energy scale of the calorimeter [28]. The two highest ET jets for each event are assumed to stem from thebquarks;
this assumption is true for 70%of simulated ttevents.
The momentum components of each b quark are then calculated from the measured jetETand angle by assuming a bquark mass of 4:7 GeV=c2 [29]. No explicit identifi- cation ofbjets is used.
D. Final Selection Cuts
After lepton and jet identification, further requirements are made to reduce the expected level of background in the sample. Events are required to have missing transverse energy of 6ET >25 GeV.6ET is corrected for the presence of isolated high-pT muons by subtracting the momentum lost by the muons in the calorimeter and adding the muon pT to the vector sum. In events with 6ET<50 GeV, the direction of the6ETvector is required to be separated by at least 20 in from any lepton or jet in the event. This reduces the background from Drell-Yan production of pairs as well as the number of events in which mismeas- ured jet or lepton energy contributes a large fraction of the 6ET.
To reduce the number of Z= !ee, events in which mismeasured jet energy leads to significant amounts of measured missing transverse energy,eeandevents with dilepton invariant mass between 76 and106 GeV=c2 . . .
are required to have their 6ET vector point away from any energetic jets in the event [30].
To further suppress background, events are required to haveHT, defined as the scalar sum of leptonET, theET of the two leading jets, andE6 T, greater than 200 GeV.
Events which are likely to be due to cosmic rays are removed by requiring a coincidence of the muon arrival times to the calorimeter. Electrons resulting from photon conversion to ee pairs are also removed. Conversions are identified by pairing the electron track to a track of opposite sign and requiring that the two tracks are consis- tent with originating from a common vertex and being parallel at that vertex. Events with three leptons are re- moved as well as events in which the leptons have the same sign.
E. Sample composition
TableIlists the number of expected background events of each type and the number ofttsignal events expected at various top quark masses [31] for the data sample used in this measurement. The signal estimate includesttevents in which aWboson decays to awhen thedecays to aneor a. Studies in Monte Carlo simulations show that 14% of the accepted signal events have at least one W boson decaying to a.
The largest source of expected background is Z= ! ee, events with associated jets. The expected contri- bution to the sample from this background is estimated using a combination of Z boson data and PYTHIA [32]
Monte Carlo events. The second largest source of expected backgrounds is events in which one or more jets are mis- identified as leptons. The probability for a jet to be mis- identified as a lepton is very small, so the majority of these events have one real lepton and one jet misidentified as a
lepton. The expected contribution to the sample from this background is estimated usingW !‘jets data. There are several smaller sources of expected background:WW, WZ, andZ= !with leptonicdecays. The expected contribution from these processes is estimated using
ALPGEN[33] andPYTHIA Monte Carlo events. Other pro- cesses make negligible contributions. A detailed descrip- tion of the method of background estimation used can be found in Ref. [25].
IV. ANALYSIS OVERVIEW
The probability density for tt decays is expressed as PsxjMt, where Mt is the top quark pole mass and x contains the lepton and jet momentum measurements.
We calculate PsxjMt using the theoretical description of the tt production and decay process expressed with respect tox,
PsxjMt 1 Mt
dMt
dx ; (1)
where ddx is the differential cross section evaluated with respect to event measurements contained inx.
To evaluate the differential cross section ddx, we con- volute the leading order matrix-elementMforqq !tt! bllbl0l0 with detector resolution functions and integrate over unmeasured quantities.
The matrix element depends on the momenta of the incoming partons (q1 andq2), and of the outgoing twob quarks (p1 and p2), two leptons (‘1 and ‘2), and two neutrinos (1 and2). Observed quantities consist of jets j1 andj2, measured leptonsL1 and L2, and two compo- nents of missing transverse energy. To express the differ- ential cross section with respect to these observed quantities x, transfer functions are introduced to connect the quantities which correspond to external legs of the matrix element (q1, q2, p1, p2, l1, l2, 1, 2) to the observed quantities (j1,j2,L1,L2). Quantities which are well measured by the detector, lepton momenta, and jet angles, are described by delta functions which directly reduce the number of unknown parton-level quantities.
Integrations are performed over quantities which are not directly measured, i.e. quark and neutrino energies. While quark energies are not directly measured, they can be estimated from the observed energies of the corresponding jets. The transfer function between quark and jet energies parametrizes this relationship, and is expressed as WEp; Ej, the probability of measuring jet energy Ej given parton energyEp.
We make the following assumptions regarding the trans- fer between parton-level quantities and the observables:
(i) Leptons are measured perfectly. We express the lepton transfer functions as a three-dimensional -function,
TABLE I. Expected numbers of signal and background events for a data sample ofR
Ldt340 pb1. The signal cross section is obtained from [31]. The total expected background is the sum of the indented background contributions.
Source Events
tt(Mt165 GeV=c2,9:1 pb) 21:71:4 tt(Mt175 GeV=c2,6:7 pb) 17:21:4 tt(Mt185 GeV=c2,4:9 pb) 13:31:4 Total Expected Background Rate 10:51:9
WW 1:20:2
WZ 0:40:1
Z=!ee, 4:71:2
Z=! 0:80:2
Lepton misID 3:51:4
Total Expected Rate (Mt165 GeV=c2) 32:22:3 Total Expected Rate (Mt175 GeV=c2) 27:72:3 Total Expected Rate (Mt185 GeV=c2) 23:82:3 Run II Data (R
Ldt340 pb1) 33
3‘1L1 3‘2L2:
(ii) Jet angles are measured perfectly, and jet energy can be described as a parametric function of parton energy. We express the b quark to jet transfer function as
j1p1 j1p1WEp1; Ej1: (iii) The two most energetic jets in the event are due to
the fragmentation and hadronization of the two b quarks from top quark decay. All other jets in the event, if present, are disregarded.
(iv) Incoming partons are massless and have no trans- verse momentum.
(v) Masses of the final-state leptons are zero, masses of thebquarks are set to4:7 GeV=c2.
The probability density in x for qq !tt! b‘ ‘b‘00‘ for a fixedMtcan be written as
PsxjMt 1 Mt
Z dX
a;b
jMttqi; pi;Mtj2 Y
jets
WEp; EjfPDFa q1fbPDFq2: (2)
In this expression, the integral is over the phase spaced forqq !tt!bllbl0l0, the sum runs over the flavorsa, bof the incoming partons, andfPDFa are parton distribution functions for flavora. Constraints such as conservation of momentum which appear as delta functions and modify the integration are here implicitly included in the phase-space integration and are discussed in detail in the following sections. The term, 1=Mt, in front of the integral en- sures the normalization condition for the probability,
Z dxPsxjMt 1; (3)
where the integration is performed over all accepted xto account for mass-dependent effects of the selection.
A. Signal and background processes
We calculate the probability for the dominant back- ground processes, Pbgx and form the generalized per- event probability density inx,
PxjMt PsxjMtpsMt Pbg1xpbg1Pbg2xpbg2 ; (4) as a weighted sum of the probabilities for each process,
where the weightspsMtandpbgiare determined from the expected fractions of signal and background events (see Table I). We evaluate probabilities for the three largest expected backgrounds: Z= boson production with 2 associated jets, W boson production with 3 associated jets in which one jet is incorrectly identified as a lepton, andW boson pair production with 2 associated jets.
B. Calibration
The probability Px is an approximation of the true probability and balances precision with computational tractability. To account for the approximations made in the construction of Px, we derive a calibration in fully realistic Monte Carlo events. This strategy accounts for the
differences between the model used in constructing Px and the fully realistic simulation. Uncertainties in the model used to produce the simulated events contribute to systematic errors on the final measurement described in Sec. VIII.
V. TRANSFER FUNCTIONS
The transfer function between quark and jet energies, WEp; Ej, expresses the probability of measuring jet en- ergyEjfrom a given parton with energyEpsuch that
nEj; EpdEjdEpnEpdEpWEp; Ej; (5) where nEj; EpdEjdEp is the number of events with jet energy between Ej and EjdEj and parton energy be- tween Ep and EpdEp, and nEp is the number of partons with energy betweenEpandEpdEp.
We parametrize the distribution of measured jet ener- gies, Ej, as a function of the quark energies,Ep, and the difference between the parton energy and the jet energy, W EpEj [12]. The parametrization is a sum of two Gaussians to account for both the peak of the distribution and its tails,
W 1
2
p p2p3p5
e p12=2p22p3e p42=2p25
;
(6) TABLE II. Parameters for WEp; Ej extracted using jets
matched in angle to b quarks (see text), from HERWIG tt Monte Carlo.
pi ai bi
p1 1:900:62 GeV 0:0230:008 p2 2:830:54 GeV 0:0750:005
p3 0:700:08 0:0000:001 GeV1
p4 1:790:79 GeV 0:1870:012 p5 8:040:67 GeV 0:0950:008
. . .
where eachpidepends linearly onEp:
piaibiEp: (7) The parameterspiare extracted with an unbinned maxi- mum likelihood fit over N jets in a sample of simulated
HERWIG[34]ttevents withMt178 GeV=c2which pass the event selection and contain jets whose axis is contained in a cone ofR0:4surrounding bquarks. Jets which arise from initial or final-state radiation are excluded. The
log likelihood is expressed as a sum over jets:
lnL XN
k1
lnnEpk XN
k1
lnWEpk; Ejk: (8) The first term does not depend on the parameterspiand can be dropped from the minimization. We extract the parameters shown in TableII.
To test the jet transfer function, we calculate the distri- bution of jet energies which result from simulated partons of known energy. The calculation for jet energies resulting from partons with energyE1< Ep< E2 is the integral of nEj; EpdEp:
ZE2
E1
nEpdEpWEp; Ej: (9) The calculation for the jet energy distribution and the difference in jet and parton energies resulting from all partons (0< Ep<1 TeV) in a simulated sample of tt with Mt178 GeV=c2 is shown in Fig. 1. Similar tests using slices of parton energies are shown in Fig.2.
The jet transfer function models the detector response to partons and should be independent of the production pro- cess. We confirm this by using WEp; Ej parametrized fromMt178 GeV=c2 events to calculate the jet energy distribution resulting from b quarks in Monte Carlo top quark decays of varied top quark masses. Figure3shows that the jet transfer function derived using partons from Mt178 GeV=c2 top quark decays satisfactorily de- scribes jet energies from top quark decays of Mt ranging from150 GeV=c2through200 GeV=c2. The performance of the transfer functions in fully realistic simulated events is included in the measurement calibrations discussed below.
VI. SIGNAL LIKELIHOOD
The probability density for qq !tt!b‘‘b‘ 0‘0 de- cays is constructed as the differential cross section, d,
Jet-Parton Pairs/2 GeV
0 100 200 300 400
(GeV) -Ej
Ep
-30 -20 -10 0 10 20 30 40 50 60 70
Jets/4 GeV
0 100 200 300
0 20 40 6 0 80 100 120 140 160 180 200 220 240 (GeV)
Ej
Partons/4 GeV
0 100 200 300
(GeV) Ep
0 20 40 60 80 100 120 140 160 180 200 220 240
FIG. 1 (color online). Top, difference of EpEj between parton and jet energy for reconstructed jets matched in angle tobquarks (see text). Center, distribution of Ej of jet energy.
Bottom, input distribution of parton energyEp. Histograms are simulated events forMt178 GeV=c2; curves in the upper two histograms show the distributions calculated usingWEp; Ej.
<60) [GeV]
(10<Ep Ej
0 50 100 150 200 250 300
Jets/10 GeV
0 50 100 150 200 250 300 350 400
<80) [GeV]
(60<Ep Ej
0 50 100 150 200 250 300
Jets/10 GeV
0 100 200 300 400 500
<100) [GeV]
(80<Ep Ej
0 50 100 150 200 250 300
Jets/10 GeV
0 50 100 150 200 250 300 350 400
<120) [GeV]
(100<Ep Ej
0 50 100 150 200 250 300
Jets/10 GeV
0 50 100 150 200 250
<150) [GeV]
(120<Ep Ej
0 50 100 150 200 250 300
Jets/10 GeV
0 20 40 60 80 100 120 140 160 180
<180) [GeV]
(150<Ep Ej
0 50 100 150 200 250 300
Jets/10 GeV
0 20 40 60 80 100
FIG. 2 (color online). Comparison of simulated Ej with calculations from WEp; Ej from six ranges of Ep. Histograms are simulated events; curves show the calculated distributions usingWEp; Ej.
