Measurement of the top quark mass at CDF using the “neutrino <em>ϕ</em> weighting” template method on a lepton plus isolated track sample

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Reference

Measurement of the top quark mass at CDF using the “neutrino ϕ weighting” template method on a lepton plus isolated track sample

CDF Collaboration

CLARK, Allan Geoffrey (Collab.), et al.

Abstract

We present a measurement of the top quark mass with tt dilepton events produced in pp collisions at the Fermilab Tevatron (s√=1.96  TeV) and collected by the CDF II detector. A sample of 328 events with a charged electron or muon and an isolated track, corresponding to an integrated luminosity of 2.9  fb−1, are selected as tt candidates. To account for the unconstrained event kinematics, we scan over the phase space of the azimuthal angles (ϕν1,ϕν2) of neutrinos and reconstruct the top quark mass for each ϕν1, ϕν2 pair by minimizing a χ2 function in the tt dilepton hypothesis. We assign χ2-dependent weights to the solutions in order to build a preferred mass for each event. Preferred mass distributions (templates) are built from simulated tt and background events, and parametrized in order to provide continuous probability density functions. A likelihood fit to the mass distribution in data as a weighted sum of signal and background probability density functions gives a top quark mass of 165.5+3.4−3.3(stat)±3.1(syst)  GeV/c2.

CDF Collaboration, CLARK, Allan Geoffrey (Collab.), et al . Measurement of the top quark mass at CDF using the “neutrino ϕ weighting” template method on a lepton plus isolated track sample.

Physical Review. D , 2009, vol. 79, no. 07, p. 072005

DOI : 10.1103/PhysRevD.79.072005

Available at:

http://archive-ouverte.unige.ch/unige:38612

Disclaimer: layout of this document may differ from the published version.

Measurement of the top quark mass at CDF using the ‘‘neutrino weighting’’ template method on a lepton plus isolated track sample

T. Aaltonen,²⁴J. Adelman,¹⁴T. Akimoto,⁵⁶B. A´ lvarez Gonza´lez,^12,tS. Amerio,^44b,44aD. Amidei,³⁵A. Anastassov,³⁹ A. Annovi,²⁰J. Antos,¹⁵G. Apollinari,¹⁸A. Apresyan,⁴⁹T. Arisawa,⁵⁸A. Artikov,¹⁶W. Ashmanskas,¹⁸A. Attal,⁴

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X. Zhang,²⁵Y. Zheng,^9,eand S. Zucchelli^6b,6a (CDF Collaboration)

1Institute of Physics, Academia Sinica, Taipei, Taiwan 11529, Republic of China

2Argonne National Laboratory, Argonne, Illinois 60439

3University of Athens, 157 71 Athens, Greece

4Institut de Fisica d’Altes Energies, Universitat Autonoma de Barcelona, E-08193, Bellaterra (Barcelona), Spain

5Baylor University, Waco, Texas 76798

6aIstituto Nazionale di Fisica Nucleare Bologna, I-40127 Bologna, Italy

6bUniversity of Bologna, I-40127 Bologna, Italy

7Brandeis University, Waltham, Massachusetts 02254

8University of California, Davis, Davis, California 95616

9University of California, Los Angeles, Los Angeles, California 90024

10University of California, San Diego, La Jolla, California 92093

11University of California, Santa Barbara, Santa Barbara, California 93106

12Instituto de Fisica de Cantabria, CSIC-University of Cantabria, 39005 Santander, Spain

13Carnegie Mellon University, Pittsburgh, Pennsylvania 15213

14Enrico Fermi Institute, University of Chicago, Chicago, Illinois 60637

15Comenius University, 842 48 Bratislava, Slovakia; Institute of Experimental Physics, 040 01 Kosice, Slovakia

16Joint Institute for Nuclear Research, RU-141980 Dubna, Russia

17Duke University, Durham, North Carolina 27708

18Fermi National Accelerator Laboratory, Batavia, Illinois 60510

19University of Florida, Gainesville, Florida 32611

20Laboratori Nazionali di Frascati, Istituto Nazionale di Fisica Nucleare, I-00044 Frascati, Italy

21University of Geneva, CH-1211 Geneva 4, Switzerland

22Glasgow University, Glasgow G12 8QQ, United Kingdom

23Harvard University, Cambridge, Massachusetts 02138

24Division of High Energy Physics, Department of Physics, University of Helsinki and Helsinki Institute of Physics, FIN-00014, Helsinki, Finland

25University of Illinois, Urbana, Illinois 61801

26The Johns Hopkins University, Baltimore, Maryland 21218

27Institut fu¨r Experimentelle Kernphysik, Universita¨t Karlsruhe, 76128 Karlsruhe, Germany

28Center for High Energy Physics: Kyungpook National University, Daegu 702-701, Korea;

Seoul National University, Seoul 151-742, Korea; Sungkyunkwan University, Suwon 440-746, Korea;

Korea Institute of Science and Technology Information, Daejeon, 305-806, Korea;

Chonnam National University, Gwangju, 500-757, Korea

29Ernest Orlando Lawrence Berkeley National Laboratory, Berkeley, California 94720

30University of Liverpool, Liverpool L69 7ZE, United Kingdom

31University College London, London WC1E 6BT, United Kingdom

32Centro de Investigaciones Energeticas Medioambientales y Tecnologicas, E-28040 Madrid, Spain

33Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

34Institute of Particle Physics: McGill University, Montre´al, Que´bec, Canada H3A 2T8;

Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6;

University of Toronto, Toronto, Ontario, Canada M5S 1A7;

and TRIUMF, Vancouver, British Columbia, Canada V6T 2A3

35University of Michigan, Ann Arbor, Michigan 48109

36Michigan State University, East Lansing, Michigan 48824

37Institution for Theoretical and Experimental Physics, ITEP, Moscow 117259, Russia

38University of New Mexico, Albuquerque, New Mexico 87131

39Northwestern University, Evanston, Illinois 60208

40The Ohio State University, Columbus, Ohio 43210

41Okayama University, Okayama 700-8530, Japan

42Osaka City University, Osaka 588, Japan

43University of Oxford, Oxford OX1 3RH, United Kingdom

44aIstituto Nazionale di Fisica Nucleare, Sezione di Padova-Trento, I-35131 Padova, Italy

44bUniversity of Padova, I-35131 Padova, Italy

45LPNHE, Universite Pierre et Marie Curie/IN2P3-CNRS, UMR7585, Paris, F-75252 France

46University of Pennsylvania, Philadelphia, Pennsylvania 19104

47aIstituto Nazionale di Fisica Nucleare Pisa, I-56127 Pisa, Italy

47bUniversity of Pisa, I-56127 Pisa, Italy

47cUniversity of Siena, I-56127 Pisa, Italy

47dScuola Normale Superiore, I-56127 Pisa, Italy

48University of Pittsburgh, Pittsburgh, Pennsylvania 15260

49Purdue University, West Lafayette, Indiana 47907

50University of Rochester, Rochester, New York 14627

51The Rockefeller University, New York, New York 10021

kVisitor from University College Dublin, Dublin 4, Ireland.

yOn leave from J. Stefan Institute, Ljubljana, Slovenia.

wVisitor from University of Virginia, Charlottesville, Virginia 22904.

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California 95064. ^uVisitor from Texas Tech University, Lubbock, Texas 79609.

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52aIstituto Nazionale di Fisica Nucleare, Sezione di Roma 1, I-00185 Roma, Italy

52bSapienza Universita` di Roma, I-00185 Roma, Italy

53Rutgers University, Piscataway, New Jersey 08855

54Texas A&M University, College Station, Texas 77843

55aIstituto Nazionale di Fisica Nucleare Trieste/Udine, I-34100 Trieste, Italy

55bUniversity of Trieste/Udine, I-33100 Udine, Italy

56University of Tsukuba, Tsukuba, Ibaraki 305, Japan

57Tufts University, Medford, Massachusetts 02155

58Waseda University, Tokyo 169, Japan

59Wayne State University, Detroit, Michigan 48201

60University of Wisconsin, Madison, Wisconsin 53706

61Yale University, New Haven, Connecticut 06520 (Received 4 February 2009; published 16 April 2009)

We present a measurement of the top quark mass withttdilepton events produced inppcollisions at the Fermilab Tevatron ( ffiffiffi

ps

¼1:96 TeV) and collected by the CDF II detector. A sample of 328 events with a charged electron or muon and an isolated track, corresponding to an integrated luminosity of 2:9 fb¹, are selected asttcandidates. To account for the unconstrained event kinematics, we scan over the phase space of the azimuthal anglesð1; 2Þof neutrinos and reconstruct the top quark mass for each1,2 pair by minimizing a²function in thettdilepton hypothesis. We assign²-dependent weights to the solutions in order to build a preferred mass for each event. Preferred mass distributions (templates) are built from simulated ttand background events, and parametrized in order to provide continuous probability density functions. A likelihood fit to the mass distribution in data as a weighted sum of signal and background probability density functions gives a top quark mass of165:5^þ3:4_3:3ðstatÞ 3:1ðsystÞGeV=c².

DOI:10.1103/PhysRevD.79.072005 PACS numbers: 14.65.Ha, 12.15.Ff, 13.85.Qk

I. INTRODUCTION

The standard model (SM) explains the nonzero weak boson masses by spontaneous breaking of the electroweak (EW) symmetry induced by the Higgs field [1]. Also, nonzero quark masses are generated by the coupling of the Higgs doublet with the fundamental fermions.

However, their values are not predicted since they are proportional to the unknown Yukawa couplings of each quark. The enormous top quark mass, with a value com- parable to the EW scale, justifies the suspicion that this quark may play a special role in electroweak symmetry breaking. In addition, because of its large mass, the top quark gives the largest contribution to loop corrections in theW propagator. Within the SM, the correlation between the top mass and theW mass induced by these corrections allows setting limits on the mass of the yet unobserved Higgs boson, and favors a relatively light Higgs. A more accurate measurement of the top quark mass will tighten the SM predicted region for the Higgs boson mass.

According to the SM, at the Tevatron’s 1.96 TeV energy top quarks are dominantly produced in pairs, byqq anni- hilation in85%of the cases and by gluon fusion in the remaining15%[2]. Because of its extremely short life- time, which in the SM is expected to be about10²⁵ s, the top quark decays before hadronizing in100% of cases into aWboson andb-quark [3]. Subsequently theWboson can either decay into quarks as aqq⁰pair or into a charged lepton-neutrino pair. This allows classifying the ttcandi- date events into three final states: all-hadronic, leptonþ

jets, or dilepton, depending on the decay modes of the two W bosons in the event. The all-hadronic state, where both W’s decay hadronically (about 46% ofttevents), is char- acterized by six or more jets in the event. The leptonþjets final state contains one electron or muon (about 30% oftt events), four or more jets, and one neutrino. Analyses dealing with the leptonþjets final state have provided the most precise top quark mass measurements, due to an optimal compromise between statistics and backgrounds.

The dilepton final state, which is defined by the presence of two leptons (electrons or muons, about 5% of ttevents), two or more jets, and large missing transverse energy from the two neutrinos, is the cleanest one, but suffers from the poorest statistics.

It is important to perform measurements using indepen- dent data samples in all final states in order to improve the precision on the top quark mass and to be able to cross- check the results. Once the channel-specific SM back- grounds have been removed, discrepancies in the results across different samples could provide hints of new phys- ics. The present analysis is performed in the dilepton final state by means of leptonþtrack (‘‘LTRK’’) top-pair se- lection. This selection is chosen to collect a large portion of events (about 45%) not involved in the other CDF high- precision top mass analyses performed in the dilepton final state [4,5].

The paper reports a measurement of the top quark mass with data collected by CDF II before spring 2008, corre- sponding to2:9 fb¹of integrated luminosity. We selecttt

candidate events in the dilepton channel by requiring a well-identified electron or muon plus a second, more loosely defined lepton, which is an isolated track. The measurement of the top quark mass in this channel is particularly challenging because of the two neutrinos in the final state. The kinematics is under-constrained, and therefore assumptions on some missing final state observ- ables are needed in order to reconstruct the event. In order to constrain the kinematics, we scan over the space of possibilities for the azimuthal angles of the two neutrinos, and reconstruct the top quark mass by minimizing a ² function using thettdilepton hypothesis. A weighted av- erage over a grid of the azimuthal neutrino angles ð1; 2Þreturns a single top quark mass value per event.

In this analysis the Breit-Wigner probability distribution function with a top quark mass-dependent decay width is applied in the kinematical event reconstruction, which helps to decrease the statistical uncertainty by 20% com- pared to the method described in [6]. The top quark mass distribution in the data is fitted to the parametrized signal and background templates, and the mass is extracted as the one corresponding to the best fit.

SectionsIIandIIIdescribe the detector and the selection of the data sample. Section IV gives an overview of the method used to reconstruct the events and to derive a single value of the top quark mass for each event. Section V defines the parametrization of signal and background mass distributions and the likelihood function used to fit the data to these distributions. Section VI describes the studies performed to calibrate the method, Secs. VIIand VIII present the results and the systematic uncertainties, and Sec.IXgives the conclusions.

II. THE CDF II DETECTOR

The Collider Detector at Fermilab was upgraded in the year 2000 (CDF II, Fig.1) in order to be able to handle the higher collision rate from the increased Tevatron luminos- ity. CDF II is a cylindrically and forward-backward sym- metric apparatus detecting the products of the pp collisions over almost the full solid angle. A cylindrical ðr; ; zÞcoordinate system is used to describe the detector geometry. The origin of the reference system is the geo- metric center of the detector, with thezaxis pointing along the proton beam. The pseudorapidityis defined by lnðtanð=2ÞÞ, whereis the polar angle relative to thez axis. The detector elements which are most relevant for this analysis are described below. A more complete description of the detector can be found elsewhere [7].

The tracking system consists of an inner silicon system and an outer gas drift chamber, the Central Outer Tracker (COT). The entire tracker is enclosed in a superconducting solenoid which generates a nearly uniform 1.4 T magnetic field in thezdirection and provides precision tracking and momentum measurement of charged particles withinjj 1. The silicon tracker, which covers thejj<2region, is

composed of the innermost detector (L00) [8], the Silicon Vertex Detector (SVXII) [9], and the Intermediate Silicon Layers (ISL) [10]. L00 is a layer of single-sided radiation- hardened silicon strips mounted directly on the beam pipe at a radius ranging from 1.35 cm to 1.62 cm. SVXII is an approximately 95 cm long cylinder of five layers of double-sided silicon microstrips covering a radial region between 2.5 cm and 10.7 cm. The ISL employs the same sensors as SVXII and covers the radial region between 20 cm and 28 cm, with one layer in the central region and two layers at larger angles. The COT [11], which spans 310 cm in length at a radial distance ranging between 43 and 132 cm, contains four axial and four2stereo super- layers of azimuthal drift cells. Axial and stereo superlayers alternate radially with one another. The COT provides full coverage in thejj 1region, with reduced coverage in the region1<jj 2.

Sampling calorimeters, divided into an inner electro- magnetic and an outer hadronic compartment, surround the solenoid. Except for limited areas of noninstrumented regions (‘‘cracks’’), the calorimeters provide full azimuthal coverage withinjj 3:6. All calorimeters are split into towers with projective geometry pointing at the nominal interaction vertex [7]. Embedded in the electromagnetic compartment, a shower maximum detector provides good position measurements of the electromagnetic showers and is used in electron identification [12].

The muon detection system consists of stacks of drift chamber modules backed by plastic scintillator counters.

The stacks are four layers deep with laterally staggered cells from layer to layer to compensate for cell-edge in- efficiencies. Four separate systems are used to detect muons in thejj<1:5region. The central muon detector (CMU) [13] is located behind the central hadronic calo- rimeter at a radius of3:5 mfrom the beam axis, covering thejj<0:63region. The central muon upgrade detector (CMP) is arranged to enclose thejj<0:54region in an approximate four-sided box. It is separated from the CMU by the additional shielding provided by 60 cm of steel. The central muon extension (CMX) extends the muon identi- fication to the region 0:6<jj<1:0. The more forward region (1:0<jj<1:5) is covered by the intermediate muon detector (IMU). Table I summarizes the character- istics of the CDF subdetectors used in this analysis.

CDF uses a three-level trigger system to select events to be recorded on tape, filtering the interactions from a 1.7 MHz average bunch crossing rate to an output of 75–

100 Hz. This analysis uses data from triggers based on leptons with high-transverse-momentum PT, as expected from the leptonically decayingW’s in the event. The first two trigger levels perform limited reconstruction using dedicated hardware, which reconstructs tracks from the COT in the r-plane with a transverse momentum reso- lution better than 2%P²_T ½GeV=c [18]. The electron trigger requires a coincidence of a COT track with an

TABLE I. CDF II subdetectors, purposes, resolutions or acceptances.

Component Purpose Resolution/Acceptance Reference

Silicon System Hit position 11m(L00) [8]

9m(SVXII) [9]

16 23m(ISL) [7]

Impact parameter 40m

Interaction Vertex Position 70m

COT Hit position 140m [11]

Momentum measurement _P^PT

T ¼0:15P_T ½GeV=c Central Calorimeters

Electromagnetic calorimeter Energy _E^E¼13:5%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E_T ½GeV

p 2% [14]

Shower Max Detector Position 2 mm [15]

Hadron Calorimeter Energy _E^E¼50:0%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

E½GeV

p 3% [16]

Wall Hadron Calorimeter Energy _E^E¼75:0%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E½GeV

p 4% [7]

Forward Calorimeters

Electro-magnetic calorimeter Energy _E^E¼16:0%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E½GeV

p 1% [17]

Shower Max Detector Position 1 mm [12]

Hadron Calorimeter Energy _E^E¼80:0%= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

E½GeV

p 5% [7]

Muon Systems Muon Detection

CMU P_T>1:4 GeV=c [7,13]

CMP PT>2:2 GeV=c [7]

CMX PT>1:4 GeV=c [7]

FIG. 1. Elevation view of half of the CDF II detector, showing the inner microstrip detector, the Central Outer Tracker drift chamber, the electromagnetic and hadronic calorimeters, the muon drift chambers and scintillation counters.

electromagnetic cluster in the central calorimeter, while the muon trigger requires that a COT track points toward a set of hits in the muon chambers. The third level is a software trigger which runs offline algorithms optimized for speed.

III. DATA SAMPLE

The signature ofttdilepton events consists of two large transverse momentum leptons (e or ), large missing transverse energy (E6 _T), two jets originating frombquarks, and possible additional jets from initial and final state radiation. We select dilepton events from inclusive high-PT electron and muon triggers using the standard CDF leptonþtrack algorithm, as described in the next sections.

The main expected background processes in the dilepton sample are Wþjets with a jet misidentified as a lepton (‘‘fakes’’), Drell-Yan (Z=!e^þe,^þ, ^þ ), and diboson eventsðWW; WZ; ZZÞwith additional jets. In the case of Drell-Yan, nonphysicalE6 _T can be faked by mis- measured jets or leptons. The contribution of these pro- cesses to the selected data sample is reduced by optimized selection cuts.

A. Trigger

A high-transverse-momentum lepton is required by the trigger. For a central electron candidate, an electromag- netic calorimeter cluster with ET Esin18 GeV, accompanied by a matched COT track with PT Psin9 GeV=c, is required. For an electron in the plug region (1:1<jj<2:0), the trigger requires an elec- tromagnetic cluster in the calorimeter withET 20 GeV andE6 _T 15 GeV. For muon candidates two or more hits in the outer muon chambers matching a track of P_T 18 GeV=cin the central tracker are required.

B. Leptons

The LTRK selection aims at selecting two charged leptons of opposite charge with a greater acceptance than if tight lepton selection cuts were applied on both leptons.

One lepton (‘‘tight lepton’’) must have a well-measured track reconstructed from the interaction point with associ- ated hits in the COT and SVX. For muons, the track is required to be compatible with hits in the muon chambers and to have PT>20 GeV=c and jj<1. For forward electrons a calorimetry-seeded tracking algorithm is used to identify tracks since the plug region is not well covered by the COT. In the case of electrons, the track is required to point to an electromagnetic cluster withE_T>20 GeVand jj<2. Tight leptons must also satisfy an isolation re- quirement, i.e. the additionalET in a cone of radiusR¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ²þ²

p ¼0:4 about the lepton trajectory must not exceed 10% of the leptonET.

The other lepton (‘‘track lepton’’) is required to be a well-measured track originating at the interaction point withjj<1andP_T >20 GeV=c. The track lepton must be isolated, which means that the ratio between the addi- tional transverse momentum of tracks in aR¼0:4cone around the track lepton and the overall PT in the cone is less than 10%. Compared to the dilepton selection (‘‘DIL’’

[19]) LTRK relaxes the calorimeter constraints on the track lepton in order to recover those events in which a lepton hits a detector crack. We refer to [6] for a more detailed comparison between LTRK and DIL.

C. Jets

Jets are the final products of quark hadronization. They are identified by looking for clusters of energy in the calorimeter using the JETCLU cone algorithm [20]. The jet search is seeded by towers withE_T>1 GeV. Starting from the most energetic seed, all seeds within a77bins wide area around the seed are grouped into a cluster and the centroid is calculated. Seeds cannot belong to more than one cluster. All towers withE_T>0:1 GeVwithin aR¼ 0:4cone about the cluster centroid are added to the cluster and the centroid is recalculated. The procedure is iterated and a final step of splitting and merging is performed in order not to include the same tower in more than one jet.

Jet transverse energy is corrected for nonuniformities in the calorimeter response as a function of jet, multiplepp interactions, and the hadronic jet energy scale of the calo- rimeter [21]. Events are required to have two or more jets withET>20 GeVandjj<2.

D. Missing transverse energy

The definition of the uncorrected missing transverse energy is

6~

ET ¼ X

i

Eⁱ_Tn^_i (1) where the sum is performed over all towers with a depos- ited energy of at least 0.1 GeV. n^i is the transverse unit vector pointing from the CDF geometrical center to theith tower.

6~

ET is corrected to compensate for the following effects:

(i) the interaction vertex displacement with respect to the CDF geometrical center:6E~_T is recalculated with n^_i (Eq. (1)) as having the origin in the interaction point.

(ii) potential jet mismeasurement: if a track within the jet cone has a transverse momentum larger than the jet transverse energy, the difference between thePT

of the highest-P_Ttrack and the jetE_Tis added toE6~_T. (iii) muons: to correct6E~_T for the identified muons and to account for their minimum ionization contribution in the calorimeters, the difference between muon calo- rimeterET and muonPT is added toE6~T.

(iv) jet corrections:E6~_T is updated according to the cor- rections applied to the jet transverse energies, as explained above.

After corrections are applied the magnitude of the miss- ing transverse energy is required to be larger than 25 GeV.

E. Final selection cuts

Several topological vetoes are implemented in order to reduce the impact of backgrounds in the sample.

Background contributions from Z boson decays yielding overestimatedE6~_T are removed by raising theE6~_T require- ment to 40 GeV and the invariant mass of the tight leptonþ track lepton pair to be inside the Z mass window (½76;106 GeV=c²). Large azimuthal separations between theE6~_T and jets ( >25), tight lepton ( >5), and track lepton ( >5, <175) are required. These requirements have been implemented in order to reduce the number of events where mismeasured leptons or jets lead to overestimatedE6 _T, mostly contributed by the Drell-Yan process. A lower cut on the angle between the tight lepton and 6E~T is applied to reduce the acceptance for Z= ! as electronþtrack, where high-P_T muons are mis- identified as electrons because of the emission of brems- strahlung photons. The requirement of a minimum azimuthal angle between jets andE6~T is dropped ifE6 _T >

50 GeV, since such large values of missing transverse energy are not expected to arise from jet mismeasurements.

Events with muons from cosmic rays or electrons orig- inating from the conversion of photons are removed.

Cosmic muons are identified by requiring a delayed coin- cidence of the particle hits in the calorimeter [22].

Conversions are identified by pairing the electron track to an opposite sign track originating from a common vertex [22].

F. Sample composition

TableIIsummarizes thettsignal and background rates expected for an LTRK sample corresponding to an inte- grated luminosity of2:9 fb¹. Depending on the process, background rates are estimated using simulated or data events. Simulated events are generated with the PYTHIA

[23] Monte Carlo program, which employs CTEQ5L [24]

parton distribution functions, leading-order QCD matrix elements for the hard process simulation, and parton show- ering to simulate fragmentation and gluon radiation. A full simulation of the CDF II detector [25] is applied. Diboson and Z= ! ^þ rates are estimated with simulated events, while Z= !e^þe, ^þ rates are estimated with a mixture of data and simulation. We use Z= ! e^þe, ^þ simulated events to predict the ratio of events in different kinematic regions, while we use data to normalize the overall rates. The expected fakes from Wþjets andttsingle lepton events with a jet misidentified as a lepton are estimated withWþjets data [26]. Signal

acceptance and expected rate are evaluated using simulated ttevents with a cross section of 6.7 pb [27] and a top quark mass of175 GeV=c².

IV. MASS RECONSTRUCTION

In this section we describe the procedure to reconstruct an event-by-event preferred top quark mass (m^recot ). In the next sections we will explain how them^recot distribution is used to extract the top quark mass.

A. Kinematics in the dilepton channel

To reconstruct thettevent one needs to get 4-momenta for six final state particles, 24 values in total. These final state particles are two leptons and two neutrinos fromW’s decays, as well as two jets originated from the top-decayb quarks. Out of the 24 final quantities, 16 ( jet and lepton 4- momenta) are measured, two (6E~_T components in the trans- verse plane) are obtained by assuming overall transverse momentum conservation, and five constraints are imposed on the involved particle masses (m_W¼m_W^þ ¼m_W, where mW ¼80:4 GeV=c² [3], mt¼mt,m ¼m ¼0).

The event kinematics is therefore under-constrained. One must assume that at least one more parameter is known in order to reconstruct the kinematics and solve for the top quark mass.

B. Neutrinoweighting method

The method implemented in this work for reconstructing the top quark mass event by event is called the ‘‘Neutrino Weighting Method.’’ This method was previously de- scribed in [6]. In order to constrain the kinematics a scan over the space of possibilities for the azimuthal angles of the neutrinos ð1; 2Þ is used. A top quark mass is reconstructed by minimizing a chi-squared function (²) in the dileptonttevent hypothesis. The²has two terms:

² ¼²resoþ²constr: (2)

TABLE II. Expected numbers of tt signal and background events with statistical uncertainties for the LTRK data sample.

Attcross section of 6.7 pb at a top quark mass of175 GeV=c²is assumed.

Process Expected number

Signal (tt) 162:65:1

WW 10:51:0

WZ 3:80:3

ZZ 0:90:1

Z=!e^þe 20:86:0

Z=!^þ 9:13:1

Z=! ^þ 19:62:4

Fakes 80:215:7

Total background 145:017:3

The first term takes into account the detector uncertain- ties, whereas the second one constrains the parameters to the known physical quantities within their uncertainties.

The first term is as follows:

²reso¼X²

l¼1

ðP^l_TP~^l_TÞ²

^l_PT² 2X²

j¼1

lnðPtfðP~^j_TjP^j_TÞÞ

þ X

i¼x;y

ðEⁱ_UE~ⁱ_UÞ²

_EU² : (3)

With the use of the tilde () we specify the parameters of the minimization procedure, whereas variables without a tilde represent the measured values. P_tf are the transfer functions between b quark and jets: they express the probability of measuring a jet transverse momentum P^j_T from a b quark with transverse momentum P~^j_T. We will comment onP_tf in Sec.IV C. The sum in the first term is over the two leptons in the event; the second sum loops over the two highest-ET (leading) jets, which are assumed to originate from thebquarks (this assumption is true in about 70% of simulatedttevents [6]).

The third sum in Eq. (3) runs over the transverse com- ponents of the unclustered energyðE^x_U; E^y_UÞ, which is de- fined as the sum of the energy vectors from the towers not associated with leptons or any leading jets. It also includes possible additional jets withE_T>8 GeVwithinjj<2.

The uncertainties (_PT) on the tight leptonP_T used for identified electrons (e) and muons () are calculated as [6]:

^e_PT P^e_T ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0:135²

P^e_T ½GeV=cþ0:02² s

(4)

_PT

P_T ¼0:0011P_T ½GeV=c: (5) The track-lepton momentum uncertainty is calculated as for the muons, since momentum is measured in the tracker for both electrons and muons. Uncertainty for the trans- verse components of the unclustered energy, EU, is de- fined as 0:4

ffiffiffiffiffiffiffiffiffiffi E^uncl_T

q ½GeV [28], where E^uncl_T is the scalar sum of the transverse energy excluding the two leptons and the two leading jets.

The second term in Eq. (2), ²constr, constrains the pa- rameters of the minimization procedure through the invari- ant masses of the lepton-neutrino and of the lepton- neutrino–leading-jet systems. This term is as follows:

²constr¼ 2 lnðPBWðm^l_inv^1;1jmW;_m

WÞÞ 2 lnðPBWðm^l_inv^2;2jm_W;_m

WÞÞ 2 lnðPBWðm^l_inv^1;1;j1jm~t;_m~

tÞÞ 2 lnðPBWðm^l_inv^2;2;j2jm~_t;_m~

tÞÞ: (6)

m~_t is the parameter giving the reconstructed top quark mass.PBWðminv;m;Þ _ðm2 ^2m2

invm²Þ²þm²²indicates the rela- tivistic Breit-Wigner distribution function, which ex- presses the probability that an unstable particle of mass mand decay widthdecays into a system of particles with invariant massminv. We use the PDG [3] values formWand _mW. For the top width we use the function

_m

t ¼ G_F

8 ffiffiffi p2

m³t

1m²_W

m²t

₂

1þ2m²_W m²t

(7) according to Ref. [29]. This new formulation of the²constr

term helps to decrease the statistical error of the top mass reconstruction by 20%.

The longitudinal components of the neutrino momenta are free parameters of the minimization procedure, while the transverse components are related to E6~T and to the assumedð1; 2Þas follows:

Px¹ P_T¹cosð1Þ

¼E6 _Txsinð₂Þ E6 _Tycosð₂Þ

sinð₂₁Þ cosð1Þ Py¹ P_T¹sinð1Þ

¼E6 _Txsinð2Þ E6 _Tycosð2Þ

sinð21Þ sinð₁Þ Px² P_T²cosð₂Þ

¼E6 _Txsinð1Þ E6 _Tycosð1Þ

sinð₁₂Þ cosð₂Þ Py² P_T²sinð2Þ

¼E6 _Txsinð₁Þ E6 _Tycosð₁Þ

sinð12Þ sinð2Þ: (8)

The minimization procedure described above must be performed for all the allowed values of ₁, ₂ in the ð0;2Þ ð0;2Þregion. Based on simulation, we choose a ₁,₂ grid of2424values as inputs for the minimi- zation procedure. In building the grid we avoid the singular points at 1 ¼2þk, where k is an integer. For these points, which correspond to a configuration where the two neutrinos are collinear in the transverse plane, the kinematics of the event cannot be reconstructed using Eqs. (3)–(8). Avoiding these points in our procedure does not affect the reconstruction of the top mass central value, but rather affects the width of the mass distribution per event. Note from Eq. (8) that performing the transforma-

tion!þ leavesP_x andP_y unchanged, but re- verses the sign of P_T. We exclude unphysical solutions (P_T¹<0 and/or P_T²<0) and choose the solution which leads to positive transverse momenta for both neutrinos.

This decreases the number of grid points to 1212. At each point eight solutions can exist, because of the two- fold ambiguity in the longitudinal momentum for each neutrino and of the ambiguity on the lepton-jet association.

Therefore, for each event, we perform 1152 minimizations,

each of which returns a value of m^reco_ijk and ²_ijk (i; j¼ 1;. . .;12; k¼1;. . .;8). We define ⁰²_ij ¼²_ijþ4 lnð_m

tÞ, which is obtained by using Eq. (6) wherePBWis substituted with _ð ^m2

m²_invm²Þ²þm²², and select the lowest⁰² solution for each point of the ð₁; ₂Þ grid, thereby reducing the number of obtained masses to 144. Each mass is next weighted according to

FIG. 2. Examples of the transfer functions ofbquarks into jets used in the fit. These functions of jetandPTare defined as the parametrization ofðP^b-quark

T P^jet_TÞ=P^jet_T distributions. The points are from the simulatedttevents. The curves show the parametrization with Eq. (10).