Article
Reference
Measurement of the tt production cross section in pp collisions at s√=1.96 TeV using kinematic fitting of b -tagged lepton+jet events
CDF Collaboration
CAMPANELLI, Mario (Collab.), et al.
Abstract
We report a measurement of the tt production cross section using the CDF II detector at the Fermilab Tevatron. The data consist of events with an energetic electron or muon, missing transverse energy, and three or more hadronic jets, at least one of which is identified as a b-quark jet by reconstructing a secondary vertex. The background fraction is determined from a fit of the transverse energy of the leading jet. Using 162±10 pb−1 of data, the total cross section is found to be 6.0±1.6(stat.)±1.2(syst.) pb, which is consistent with the standard model prediction.
CDF Collaboration, CAMPANELLI, Mario (Collab.), et al . Measurement of the tt production cross section in pp collisions at s√=1.96 TeV using kinematic fitting of b -tagged lepton+jet events. Physical Review. D , 2005, vol. 71, no. 17, p. 172005
DOI : 10.1103/PhysRevD.71.072005
Available at:
http://archive-ouverte.unige.ch/unige:38301
Disclaimer: layout of this document may differ from the published version.
Measurement of the t t production cross section in p p collisions at p s
1:96 TeV using kinematic
fitting of b-tagged leptonjet events
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Z. Yu,59J. C. Yun,15L. Zanello,49A. Zanetti,53I. Zaw,20F. Zetti,44J. Zhou,50A. Zsenei,18and S. Zucchelli4 (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
4Istituto Nazionale di Fisica Nucleare, University of Bologna, I-40127 Bologna, Italy
5Brandeis University, Waltham, Massachusetts 02254, USA
6University of California at Davis, Davis, California 95616, USA
7University of California at Los Angeles, Los Angeles, California 90024, USA
8University of California at San Diego, La Jolla, California 92093, USA
9University of California at Santa Barbara, Santa Barbara, California 93106, USA
10Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain
11Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
12Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637, USA
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
21The Helsinki Group: Helsinki Institute of Physics; and Division of High Energy Physics, Department of Physical Sciences, University of Helsinki, FIN-00044, Helsinki, Finland
22Hiroshima University, Higashi-Hiroshima 724, Japan
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
31Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
32Institute of Particle Physics: McGill University, Montre´al, Canada H3A 2T8; and University of Toronto, Toronto, Canada M5S 1A7
33University of Michigan, Ann Arbor, Michigan 48109, USA
34Michigan State University, East Lansing, Michigan 48824, USA
35Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia
36University of New Mexico, Albuquerque, New Mexico 87131, USA
37Northwestern University, Evanston, Illinois 60208, USA
38The Ohio State University, Columbus, Ohio 43210, USA
39Okayama University, Okayama 700-8530, Japan
40Osaka City University, Osaka 588, Japan
41University of Oxford, Oxford OX1 3RH, United Kingdom
42University of Padova, Istituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy
43University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA
44Istituto Nazionale di Fisica Nucleare, University and Scuola Normale Superiore of Pisa, I-56100 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 10021, USA
49Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, University di Roma ‘‘La Sapienza,’’ 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 79409, USA
53Istituto Nazionale di Fisica Nucleare, University of Trieste/ Udine, Italy
54University of Tsukuba, Tsukuba, Ibaraki 305, Japan
55Tufts University, Medford, Massachusetts 02155, USA
56Waseda University, Tokyo 169, Japan
57Wayne State University, Detroit, Michigan 48201, USA
58University of Wisconsin, Madison, Wisconsin 53706, USA
59Yale University, New Haven, Connecticut 06520, USA (Received 9 September 2004; published 14 April 2005)
We report a measurement of thettproduction cross section using the CDF II detector at the Fermilab Tevatron. The data consist of events with an energetic electron or muon, missing transverse energy, and three or more hadronic jets, at least one of which is identified as a b-quark jet by reconstructing a secondary vertex. The background fraction is determined from a fit of the transverse energy of the leading jet. Using16210 pb1 of data, the total cross section is found to be6:01:6stat: 1:2syst:pb, which is consistent with the standard model prediction.
DOI: 10.1103/PhysRevD.71.072005 PACS numbers: 14.65.Ha, 13.85.Ni, 13.85.Qk
I. INTRODUCTION
The top quark is the most massive of nature’s building blocks yet discovered. Because new physics associated with electroweak symmetry breaking will likely couple to an elementary particle in proportion to its mass, it is important to measure the top quark couplings as accurately as possible. In the strong interaction sector, the couplings are reflected in the ttproduction cross section in hadron collisions. Previous measurements were made inpp colli- sions at a center-of-mass energy of 1.8 TeV [1]. We re- cently reported a result [2], using data taken at 1.96 TeV
with the CDF II detector at the Tevatron collider, using the double leptonic decay mode of the top quark. Here we report a measurement of the tt production cross section using a different decay mode and a new method.
In order to measure the cross section, one first has to obtain a sample rich in top quarks and then determine the amount of background in the sample. We select events consistent with the decay chain tt!WbWb!lbqq0b, where the charged lepton lis either an electron or muon.
We start with events containing an energetic electron or muon, significant transverse momentum imbalance indica- tive of a noninteracting neutrino, and at least three had-
MEASUREMENT OF THEttPRODUCTION CROSS. . . PHYSICAL REVIEW D71,072005 (2005)
ronic jets. To enrich the sample in top quarks, we require that at least one jet contain a secondary vertex consistent with the decay of aBhadron.
Measurements in the past have relied on the ability of theoretical calculations to determine, for the background, the fraction of events that contain b-quark jets. In this paper, we instead measure the background fraction directly in the signal data sample. The transverse energy of the highest ET jet [3] or the second highest ET jet is a good discriminator between signal and background. Typically in attevent, these jets are the primary decay products (b-jets) of the very heavy top quarks and thus have a hard ET spectrum. For most of the background sources, however, they are produced as QCD radiation, resulting in a much softer bremsstrahlunglikeETdistribution. We use the lead- ing jet ET spectrum for the primary measurement of the signal fraction. The second leading jet distribution is used to check the result.
In order to obtain the background spectrum, we need data that are kinematically similar to our final sample, but which do not have significant ttcontamination. We show that the leading jetETspectra for the background processes are similar whether or not the events containb-quark jets.
Then the nonheavy flavor spectrum becomes the back- ground template for measuring thettfraction in the signal sample.
We use the HERWIG [4] and PYTHIA [5] Monte Carlo calculations followed by a simulation of the CDF II detec- tor to obtain thettsignal behavior. The softETspectrum of the parton showers in these Monte Carlo models is not relevant for the signal shape. To test that our method is plausible, we study the background shape using the ALPGENHERWIG Monte Carlo [6]. ALPGEN pro- vides a harder and more realistic jetET spectrum. For the study of b-jet identification, the PYTHIA calculation is used.
II. DETECTOR
The CDF II detector [7] is an azimuthally and forward- backward symmetric apparatus designed to studypp col- lisions at the Fermilab Tevatron. It consists of a magnetic spectrometer surrounded by calorimeters and muon cham- bers. The charged particle tracking system is immersed in a 1.4 T magnetic field parallel to the p and p beams. A 700 000-channel silicon microstrip detector (SVXISL) provides tracking over the radial range from 1.5 to 28 cm.
A 3.1 m long open-cell drift chamber, the Central Outer Tracker (COT), covers the radial range from 40 to 137 cm.
The COT provides up to 96 measurements of the track position with alternating axial and2 stereo superlayers of 12 wires each. The fiducial region of the silicon detector extends to jj 2, while the COT provides coverage for jj 1.
Segmented electromagnetic and hadronic calorimeters surround the tracking system and measure the energy of
interacting particles. The electromagnetic and hadronic calorimeters are lead-scintillator and iron-scintillator sam- pling devices, respectively, covering the pseudorapidity rangejj<3:6. The electromagnetic calorimeters are in- strumented with proportional and scintillating strip detec- tors that measure the transverse profile of electromagnetic shower candidates at a depth corresponding to the shower- maximum. Drift chambers located outside the central had- ron calorimeters and behind a 60 cm iron shield detect muons withjj<0:6. Additional drift chambers and scin- tillation counters detect muons in the region 0.6<jj<
1:0. Gas Cherenkov counters measure the average number of inelasticpp collisions and thereby determine the lumi- nosity with the coverage3:7<jj<4:7.
The results reported here are based on data taken in Fermilab Collider Run II between March, 2002 and September, 2003. The integrated luminosity is 162 pb1 for events selected with an electron or central muon. For muon events with jjbetween 0.6 and 1.0, the integrated luminosity is150 pb1.
III. EVENT SELECTION A. Lepton trigger
CDF employs a three level trigger system, the first two consisting of special purpose hardware and the third a farm of computers. For the electron top sample, the level-1 trigger requires a track of PT>8 GeV=c matched to an electromagnetic calorimeter cell containing ET>8 GeV with a small amount of energy in the hadronic cell behind it. Calorimeter energy clustering is done at level-2, and the 8 GeV=ctrack must be matched to an electromagnetic cluster withET above 16 GeV. At level-3, a reconstructed electron candidate with ET>18 GeV is required. The PT>18 GeV=c level-3 muon triggers come directly from two level-1 triggers: a track with PT>4 GeV=c is matched to a stub in the central muon chambers; or a track with PT>8 GeV=c is matched to a stub in the 0:6<
jj<1:0muon chambers.
B. Wjets selection
After full event reconstruction, we require lepton candi- dates to pass identification criteria and to be isolated from other energy deposits in the calorimeter. The event selec- tion criteria are the same as those in Ref. [8], where they are described in detail. Electron candidates must have a well-measured track pointing at a cluster of energy in the calorimeter withET>20 GeV. The lateral and transverse shower size in the calorimeters as well as the transverse profile in the shower-maximum detectors must be consis- tent with an electromagnetic cascade. Muon candidates withPT >20 GeV=cmust pass through calorimeter cells whose energy deposition is consistent with the ionization of a muon, and the reconstructed position of the track
segment in the muon chambers is required to be consistent with multiple Coulomb scattering of the extrapolated track from the COT. Lepton candidates must also be isolated.
Isolation (I) is defined as the ratio between calorimeter energy in a cone of radius 0.4 in the-plane around the lepton, but excluding the lepton, divided by the lepton energy. We require I0:1. In addition, all candidate events must haveE6 T>20 GeV. TheE6 T is corrected for both muon momentum and the position of theppcollision point. Jets are found using a fixed-cone algorithm with a cone radius of 0.4 in-space. To obtain the correct jet energy, this analysis applies three corrections after jet clustering. We correct for detector response variations in , detector stability, and a correction for multiple interac- tions in an event. For this analysis, jets are counted if they haveET >15 GeVandjj<2:0after all the corrections are applied. We select events with three or more jets to retain high acceptance forttevents, allowing one jet to fail ourET orrequirement.
C.b-jet identification
In this sample, the major background to ttis the elec- troweak production of a W boson with hadron jets pro- duced by QCD. These Wjets events usually contain only light quark and gluon jets, whereas signal events always contain two b-quark jets. Thus identification of b-jets (b-tag) provides a significant increase in the signal-to-background ratio.
We identifyb-quark jets through the metastableBhad- rons in the jet fragmentation. Their1ps lifetime trans- lates into a secondary vertex a few millimeters from the primary interaction. We use the excellent position resolu- tion of the SVXISL to find these secondary vertices.
The algorithm [9] proceeds as follows: (i) select at least two good tracks in a jet with both COT and SVXISL information, (ii) search for a high quality secondary vertex using the selected tracks, (iii) measure the distance in the transverse plane (LT) between the primary and the second- ary vertices, and (iv) accept the secondary vertex if LT=LT>3, whereLTis theLT resolution.
Based on simulation of the b-tagging algorithm, we determined that requiring at least one of the jets in an event to be tagged as ab-jet is expected to retain53%of the top quark events while removing more than95%of the back- ground events [9]. The measured cross section depends on the value of theb-tagging efficiency used to extract it. The difference between the efficiency in the simulation and that in data has been measured with a b-enriched sample of dijet events in which an electron is found in one jet (e-jet) and a secondary vertex is found in the other jet. From the fraction of e-jets that have an observed secondary vertex, we find that the simulation has a b-tag efficiency higher than the data by21%, a factor that is independent of jetET [9]. This difference is corrected for in Sec. VI A and the uncertainty is discussed in Sec. VI B.
IV. BACKGROUND DETERMINATION There are several background sources in the b-tagged lE6 T 3jets sample. We give their approximate con- tributions to the total background, obtained from both data and theoretical calculations, although the precise compo- sition is not needed for this analysis because the spectra are very similar to each other. The sources are the production of a W boson accompanied by the QCD production of heavy flavor quarks (WHF:40%of the total number of the background events in W 3jets), misidentifica- tion inb-jet tagging mainly due to track and vertex reso- lution (mistag:30%), a fakeW boson associated with a real or fake lepton (non-W: 20%), diboson production (WW=WZ=ZZ) and electroweaktbproduction (diboson single top:10%) [9].
A. Method
We find that the leading jetET is the best discriminant between the signal and background among single jet ET variables after considering both statistical and systematic effects, including the difference between Leading-Order (LO) and a Next-to-Leading-Order (NLO) simulation [10].
Consequently we use the shape of the leading jet ET spectrum to determine the signal and background fractions.
For the background, we extract from data the shape for all of the sources except for the small diboson and single-top components. We assume that the WHF and mistag shapes are the same, so that we can extract that distribution from the background-rich sample of events in which no jet isb-tagged. To avoid subtle kinematic differences based on jet rapidity, we still require that at least one jet is taggable, i.e., has at least two good tracks that pass through the SVXISL detector. The assumption that the leading jet ET in W multijet events is independent of the flavor content of the jets is first studied in Monte Carlo simula- tions and then tested using events containing a W boson and either1or2jets (see Sec. IV B).
Figure 1 shows the shape comparison of the highest jet ET betweenW three light flavor jets (WLF) and the various heavy flavor contributions as predicted by ALPGENHERWIG Monte Carlo calculation followed by a simulation of the CDF II detector. InWHFcases, at least one jet is required to beb-tagged, while forWLF, we require that at least one jet is taggable. We then correct the WLF shape for the slight ET dependence in the b-tag efficiency, which is taken from simulation (Fig. 2).
The effect of theb-tagging algorithm could be different for WHF, where a real b-jet is tagged, and WLF, where a fake tag is found. However theET dependences of the tagging efficiency and mistag probability are similar.
Figure 3 comparesWHFevents with ab-tag toWLF after applying the mistag probability measured in jet data.
The agreement is good.
The other large background comes from events that do not contain a W boson. The lepton candidate is either
MEASUREMENT OF THEttPRODUCTION CROSS. . . PHYSICAL REVIEW D71,072005 (2005)
misidentified or due to semileptonic decay in ab- orc-jet.
Such leptons are typically not isolated in the calorimeter.
Consequently the shape of the leading jetETspectrum for non-W events is determined from events that still have large missing transverse energy (E6 T>20 GeV), but whose lepton is not isolated. We assume that the leading jetET shape of this sample is the same as for the non-W background events in the signal region since lepton iso- lation is not correlated with theET of other jets in an event.
The non-W background distribution is added to the other backgrounds with a relative normalization taken from ab- solute estimates of the various background sources.
However, since the non-W jetET spectrum is very similar to those in theWHFand mistag backgrounds, the final result is insensitive to the non-W fraction. A systematic uncertainty is taken based on a large variation in this background fraction.
The spectra from diboson and single top production are estimated from ALPGENHERWIG Monte Carlo calcu- lations. The leading jet ET spectrum from single top pro- duction is added to the total background shape using the theoretical cross section, which is 6% of the total back- ground, while the diboson spectra are neglected because these spectra are similar to the other dominant background sources, and their contribution is expected to be small, 3:0%[11].
B. Test usingW1-jet andW2-jet data The performance of the background modeling is tested using events containing a high PT lepton, large E6 T, and either 1or 2jets (recall the signal sample has3or more jets). This sample contains all of the signal region back-
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FIG. 3 (color online). The leading jetET spectrum for mis- taggedWplus three light flavor jets (solid histogram in all plots) compared toWbbplus one light quark (left),Wcplus two light quarks (center), andWccplus one light quark (right) inW3or more jets sample. ForWHFsample, we require at least one taggedb-jet. Note that the mistag prediction is realistic since it is obtained from jet data.
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estimated non−W
Jet E (GeV)T
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Data (W+1,2 jet, b−tagged) Prediction from data
FIG. 4 (color online). The jetET distribution for the 309 jets in the W1and2jet data sample. The open histogram is the total background prediction, with the dark shaded region the non-Wcomponent. The data points are theb-tagged events with statistical error bars.
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FIG. 2. The efficiency ofb-jet identification as a function of the leading jetETderived from ALPGENWbbMonte Carlo in the W 3-jet sample. The curve is a fourth-degree polyno- mial fit below 140 GeV.
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FIG. 1 (color online). The leading jetETspectrum forWplus three light flavor jets (solid histogram in all plots) compared to Wbb plus one light quark (left), Wc plus two light quarks (center), and Wcc plus one light quark (right). These are ALPGENHERWIG Monte Carlo calculations followed by a simulation of the CDF II detector. (normalized by area)
ground sources, but thettcontribution is small, only4%.
A similar procedure is applied here as in theW 3-jet sample. The dominant background shape is taken from events without a b-tag, but with at least one taggable jet, and then a non-Wcontribution is added with a fraction (15:2%) determined from absolute background esti- mates [9]. A correction is made for theET dependence of the b-tagging efficiency. The resulting spectrum should agree well with that of theb-tagged events if our method is valid. Figure 4 shows the results using 309 jets in the W1 and2jet samples. The agreement is good, with a Kolmogorov-Smirnov (KS) test probability of18%. This value is not the KS probability itself but the p-value based on pseudoexperiments using the maximum difference of the accumulating distributions.
C. Background shape in theW3-jet sample The ET spectra of the four main backgrounds in the signal sample, W 3 jets, are shown in Fig. 5. The dominant contribution is taken from the non-b-tagged events (WHF, mistag). These spectra have been cor- rected for the shape of theb-tag efficiency, which has been determined from simulation, and is shown in Fig. 2 as a function of the jetET. The smallttcontamination,6%, in the non-b-tagged sample is subtracted iteratively, as de- scribed below, so that the amount of this contamination is consistent with the finalttcross section. The non-Wcom- ponent is 21% of the total and is shown as the shaded portion. The small contribution from single-top production is then added, and the diboson components (WW=WZ=ZZ) are neglected as noted above.
As indicated above, the shape change due to the appli- cation of the b-tagging algorithm is applied to the back- ground spectra. The efficiency of the algorithm is defined as the number of events that have at least oneb-tagged jet divided by the number having at least one taggable jet. This
function, which drops at very low ET, is fit to a fourth- degree polynomial below 140 GeV and a flat line above 140 GeV. Possible variations in this shape are considered as a systematic uncertainty on the cross section measurement.
Note that only the shape, not the absolute efficiency, is used here.
The final background shape is shown in Fig. 6. We fit this shape for use in the final unbinned log-likelihood fit using a Landau distribution plus a Gaussian function. The fitted parameters are summarized in Table I, and the fit result is shown in Fig. 6. The2=d:o:f:for the agreement between the fit function and the data points is11:4=10.
V. SIGNAL FRACTION
We use a HERWIG Monte Carlo calculation followed by a full detector simulation to obtain the tt signal shape.
Figure 7 shows the predicted leading jet ET distribution forttevents. It is significantly harder than the background spectrum, making it possible to separate the two contribu- tions using a fit to the data. The spectrum in Fig. 7 is fit to a
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Expected dominant background non−W
FIG. 5 (color online). The calculated dominant background shape (WHF, mistag, non-W) in W 3 jets sample. The shaded part is the non-W portion. Error bars are statistical only.
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FIG. 6. The calculated leading jet ET distribution for the background in the W 3-jet sample. The fitted curve shows the Landau plus Gaussian function that is employed in the final unbinned likelihood fit.
TABLE I. Presented in this table are the fit parameters used to describe the background probability density function shown in Fig. 6. (L) and (G) refer to the Landau function and Gaussian parameters, respectively. The variable MPV represents the most probable value of Landau function. The means and sigmas are expressed in GeV.
Parameters Values
height(G) 30:8010:27
mean(G) 66:717:4
sigma(G) 32:775:6
height(L) 512:879:2
MPV(L) 37:03:6
sigma(L) 7:671:5
MEASUREMENT OF THEttPRODUCTION CROSS. . . PHYSICAL REVIEW D71,072005 (2005)
Landau distribution plus two Gaussians (2=d:o:f:
19:9=28). The fitted parameters are shown in Table II.
To fit the data to a sum of the signal and background templates, we use an unbinned likelihood fit with the following form.
L YN
i1
PETi;R
YN
i1
RPsignalETi 1RPbackgroundETi where the signal fractionRN Nsignal
signalNbackgroundis the one free parameter in the fit, PsignalETi is the signal probability density as a function ofET, andPbackgroundETiis that of the background. We tested the ability of this fit procedure to report correct values of the signal fraction and its uncertainty using a large number of Monte Carlo pseu- doexperiments. Each pseudoexperiment used the number of signal and background events in our data sample and
used a range of signal fractions (R) centered around the value found from our fit to the data.
As mentioned above, there is a smallttcontamination in the untagged data sample that is used to create the back- ground template. The amount ofttthat is subtracted when making the template is determined by an iterative process.
Initially the fit is done without removing a ttcomponent from the background template. The number of top events reported by the fit is used along with the b-tagging effi- ciency to calculate the number of top events in the un- tagged sample. Attsubtraction in the background template is then made, and the data are refit. Thisttcontamination is determined to be small, 6%, thus only one iteration is necessary. The final background template after the iteration is shown in Fig. 6.
The result of the fit of the W 3-jet data sample is shown in Fig. 8. The histogram contains the 57 data events in which at least one jet has been tagged as a b-jet. The solid curve is the best fit, with the individual components shown as dashed (tt) and dot-dashed (background) curves.
The insert contains lnL=Lmax) as a function of signal fraction. The signal fraction obtained isR0:680:140:16.
Although we selected the leading jet ET as the fit vari- ablea priori, we have studied other variables to check the robustness of the result. For the second leading jetET and the sum of the first and second leading jet ET’s, we find signal fractions of R0:750:110:13 (Fig. 9) and R 0:650:140:16 (Fig. 10), respectively. The agreement is good.
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FIG. 7. The simulated leading jetETspectrum forttevents for the top mass175 GeV=c2. The smooth curve is a fit to a Landau distribution plus two Gaussians.
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tt + BKG tt (HERWIG) BKG (from data)
Leading jet E (GeV)
T−ln (L / Lmax)
signal fraction
events / 10 GeV
FIG. 8 (color online). The fifty-seven candidate events (his- togram) with the best fit curve (solid). The best fit composition, tt (dashed) and background (dot-dashed), is also shown. The insert showslnL=Lmax) as a function of the signal fraction.
TABLE II. Fit parameters for thettleading jetETdistribution in Fig. 7 using two Gaussians and a Landau distribution. (L) and (G) refer to the Landau and Gaussian parameters, respectively.
The variable MPV represents the most probable value of Landau function. The means and sigmas are expressed in GeV.
Parameters Values
height(G1) 200:826:0
mean(G1) 60:05:0
sigma(G1) 35:61:1
height(G2) 109:98:3
mean(G2) 76:16:5
sigma(G2) 192:914:3
height(L) 3913:5192:8
MPV(L) 65:81:1
sigma(L) 13:90:6
VI.ttCROSS SECTION A. Acceptance and Efficiency Thettcross section is obtained from the formula,
tt NobsRfit Atttt
RLdt (1) whereNobsis the number of candidateW 3-jet events with at least oneb-tagged jet (57 events),Rfitis the signal fraction determined from the likelihood fit (0:680:140:16), and Attis the geometric acceptance forttevents in the CDF II detector [8]. Note that this acceptance includes the branch- ing ratios. The parameterttis the detector efficiency fortt events [9], which includes the trigger, event vertex posi- tion, eventb-tagging, and the lepton identification efficien- cies. It also includes the effects due to photon conversion, cosmic ray, dilepton, andZ0 boson removal. The quantity RLdt is the integrated luminosity. The term Atttt was determined from a PYTHIA Monte Carlo [5] calculation and detector simulation with a number of individual effi- ciency components determined from the data. The result for A is 4:020:03stat: 0:43syst:%. The electron (muon) channel contributes57%43%of the totalA.
All calculations have been done using a top quark mass of 175 GeV=c2 [12]. MultiplyingAby the integrated lumi- nosity gives the denominator for Eq. (1),6:420:8 pb1.
B. Systematic uncertainties
There are a number of sources of systematic uncertainty as summarized in Table III. Template shape uncertainties affect the signal fraction determination, while other effects mostly impact the acceptance. Systematic uncertainties in the signal fraction are determined by a series of pseudoex- periments in which the generated pseudodata are changed based on the systematics and then refit using the original templates. If the systematic uncertainty affects both the template shapes and the acceptance the uncertainty is taken to be100%correlated.
The largest uncertainty originates from the effect of the jet energy scale on the ttsimulation. This comes from a number of sources including modeling the relative calo- rimeter response as a function of , the absolute hadron energy scale, the underlying event contribution, and jet fragmentation [8]. The largest contributions are due to the correction of the jet energy and the energy scale uncertainty. The mean energy of the leading jet from top quark decay is varied by6:1%, or about 5 GeV, and this effect contributes 15:3% to the final top cross section uncertainty. The jet energy scale uncertainty does not contribute to the background template shape systematic uncertainty largely because it is determined from the data.
There are uncertainties in both the absolute value andET dependence of theb-tag efficiencies, which are determined from b-jet rich and generic-jet control samples [9]. The uncertainty of the absolute b-tagging efficiency is domi-
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FIG. 10 (color online). The fit result using the sum of the leading and the second leading jets. The fifty-seven candidate events (histogram) with the best fit curve (solid). The best fit composition, tt(dashed) and background (dot-dashed), is also shown. The insert shows lnL=Lmax) as a function of the signal fraction.
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−ln (L / Lmax)
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events / 10GeV
FIG. 9 (color online). The fit result using the second leading jet. The fifty-seven candidate events (histogram) with the best fit curve (solid). The best fit composition, tt(dashed) and back- ground (dot-dashed), is also shown. The insert shows lnL=Lmax) as a function of the signal fraction.
MEASUREMENT OF THEttPRODUCTION CROSS. . . PHYSICAL REVIEW D71,072005 (2005)
