{'fraction_non_alphanumeric': 0.035446627506582944, 'fraction_numerical': 0.017925865910471947, 'mean_word_length': 4.2387267904509285, 'pattern_counts': {'":': 0, '<': 2, '<?xml version=': 0, '>': 7, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Precision Top Quark Mass Measurement in the Lepton + Jets Topology in ppbar Collisions at sqrt(s) = 1.96 TeV

We report two measurements of the top quark mass M_top using the CDF II detector at the Fermilab Tevatron in a 318 pb^-1 data sample observed in the lepton + jets final state. One method uses an event-based likelihood technique resulting in M_top = 173.2 +2.6/-2.4 (stat.) +/- 3.2 (syst.) GeV/c^2 or 173.2 +4.1/-4.0 GeV/c^2. The second method reconstructs a top quark mass in each event using the measured invariant mass of the hadronically decaying W boson to constrain the jet energy scale to obtain a value for M_top of 173.5 +3.7/-3.6 (stat.) +/- 1.3 (syst.) GeV/c^2 or 173.5 +3.9/-3.8 GeV/c^2. We take the latter, which is more precise, as our result.


Abstract
We report two measurements of the top quark mass M top using the CDF II detector at the Fermilab Tevatron in a 318 pb −1 data sample observed in the lepton + jets final state. One method uses an event-based likelihood technique resulting in M top = 173.2 +2.6 −2.4 (stat.) ± 3.2 (syst.) GeV/c 2 or 173.2 +4. 1 −4.0 GeV/c 2 . The second method reconstructs a top quark mass in each event using the measured invariant mass of the hadronically decaying W boson to constrain the jet energy scale to obtain a value for M top of 173.5 +3.7 −3.6 (stat.) ± 1.3 (syst.) GeV/c 2 or 173.5 +3.9 −3.8 GeV/c 2 . We take the latter, which is more precise, as our result. PACS numbers: 14.65.Ha,12.15.Ff The top quark is the heaviest known elementary particle with a mass approximately 40 times that of the next-heaviest quark or lepton. Because of this comparatively large mass, top quark studies provide insight into our understanding of mass in general, and test theories that explain the large range of quark and lepton masses. Within the context of the Standard Model of particle physics, the top quark mass is related to the masses of the W boson and the Higgs boson, the latter object being the key to our understanding of the origin of mass [1].
Precision measurements of the top quark and W boson masses test the consistency of the Standard Model, and in particular the Higgs mechanism. A precision measurement of the top quark mass is therefore a main goal of the experiments at the Fermilab Tevatron collider.
In this Letter we present two measurements of the top quark mass in the lepton + jets decay channel. We use a sample of tt decays corresponding to 318 pb −1 of proton-antiproton collisions at √ s = 1.96 TeV and collected using the Collider Detector at Fermilab (CDF II) between February 2002 and August 2004. In the lepton + jets channel, tt pair production is followed by the decay of each top quark to a W boson and a b quark, the hadronic decay of one W boson, and the leptonic decay of the other. This decay channel has the largest branching fraction with good signal-to-background, allowing accurate top quark mass measurements.
Events in this channel contain an electron or muon and a neutrino from the leptonic W boson decay, two quark jets from the hadronic W boson decay, and two b-quark jets.
We select events consistent with this decay topology and analyze them using two complementary methods. The first method uses an event-by-event likelihood analysis employing the leading order matrix element for tt production and decay to extract a joint likelihood as a function of the top quark mass, M top . This technique, known as the "dynamical likelihood method" or DLM, was developed by the CDF collaboration [2] and is similar to that used by the DØ collaboration to make the previous most precise measurement of the top quark mass [3]. The CDF II detector [5] is a general-purpose charged and neutral particle detector located at the Tevatron collider. We employ cylindrical coordinates where θ and φ are the polar and azimuthal angles, respectively, with respect to the proton beam, and pseudorapidity is η = − ln tan(θ/2). Transverse energy and momentum are E T = E sin θ and p T = p sin θ, respectively, where E and p are energy and momentum. The detector comprises a solenoidal charged particle spectrometer, consisting of an eight-layer silicon microstrip detector array and a cylindrical drift chamber immersed in a 1.4 T magnetic field, a segmented sampling calorimeter with acceptance up to pseudorapidity |η| = 3.6, and a set of charged particle detectors outside the calorimeter used to identify muon candidates.
Events for these analyses were selected by requiring an electron or muon candidate with transverse momentum p T > 20 GeV/c and |η| < 1 and missing transverse energy exceeding 20 GeV, corresponding to a high-energy neutrino candidate. The signal-to-background was improved by requiring in each event the presence of four or more jets with |η| < 2.0. To reduce backgrounds further we required either (a) at least four jets with transverse energy E T > 21 GeV or (b) at least three jets with E T > 15 GeV and a fourth jet with E T > 8 GeV with at least one jet with E T > 15 GeV identified as a b quark candidate through the presence of a displaced vertex within the jet arising from the decay of the long-lived bottom hadron (b tag). This selection resulted in 165 events that, based on our background estimates, are primarily tt events. The methods used to estimate the backgrounds are detailed in [6].
The DLM analysis uses a 63-event subset of those data defined by requiring exactly four jets with E T > 15 GeV where at least one of the jets has a b tag. We have estimated the various sources of background contamination in this sample, summarized in Table I, Table I. The background level in the 0-tag sample is determined in the subsequent fit. Both analyses use calibrated jet energies, based on a combination of instrumental calibration and analysis of data control samples [7]. The uncertainty σ c on the jet energy scale is the a major source of uncertainty on M top . For jets in the tt sample, σ c is approximately 3% of the measured jet energy, depending on the η and p T of the jet. The parameter JES is defined as the difference, averaged over all jets in the sample, between the true jet energy and our measured jet energy after calibration in units of σ c .
The DLM technique, described in detail in [8], defines a likelihood for each event based on the differential cross section per unit phase space volume of the final state partons, dσ tt /dΦ, as a function of M top . Detector resolution effects are accounted for using tt events generated by the HERWIG Monte Carlo program [9] and full detector simulation to derive a transfer function (TF). The TF relates the transverse energies of the quarks, denoted by x, and the observed jets. For a given event, a Monte Carlo integration is performed over the possible tt final state kinematics in the following way: we first generate a random value for the virtual mass squared of the W boson in the leptonic channel, s W , according to the Breit-Wigner form. We identify the momentum of the electron or muon daughter with the measured value, and the neutrino transverse momentum with the measured missing transverse energy.
We then generate random values for the momenta of final state quarks according to the TF probabilities. We determine the z component of the neutrino momentum, with a two-fold ambiguity, using s W as a constraint. Thus, for a given set of x and s W , we fully determine the event kinematics, and the event likelihood as a function of M top is given by where the normalization factor N is independent of M top for a given event, and the indices I j and I ν run over the parton-jet assignments and the two neutrino solutions, respectively.
The event likelihood is obtained by numerically integrating over x given by the TF and s W given by the Breit-Wigner distribution. The template method is described in detail in [10]. We perform a χ 2 minimization to fit the parton momenta from the tt daughters and determine m reco t for each event, assuming that the final state arises from the decay of a tt pair into W bosons and b quarks. We use only the four leading jets in the mass reconstruction. In the χ 2 fit, both sets of W decay daughters are constrained to have the invariant mass of the W boson, and both W b states are constrained to have the same mass. The ambiguity arising from the different ways of assigning the jets to the four quarks is resolved by selecting the assignment with the lowest χ 2 , taking into account the b-tagging information. We construct a histogram of m reco t for each subsample, discarding events with χ 2 > 9, corresponding to poorly reconstructed or background events.
The parameter JES is determined within this event sample by removing the W boson mass constraints, and identifying for each event all pairs of jets that would be consistent with the W boson final state. We form histograms of the invariant masses of these jet pairs for each of the four event subsamples and compare these with what we expect given the precisely known W boson mass [11].
We use these eight histograms to measure simultaneously M top and JES. An unbinned likelihood fit is performed to parameterized signal templates taken from simulated tt events M top = 173.5 +3.7 −3.6 (stat.) GeV/c 2 , where the uncertainty is statistical and incorporates the uncertainty due to JES, which we estimate contributes ∼ 2.5 GeV/c 2 . Figure  This also demonstrates that the JES constraint from the W boson decay has comparable precision to the jet energy calibration.
There are a number of additional systematic uncertainties that affect both analyses: initial state and final state radiation uncertainties (ISR/FSR), uncertainties arising from the parton distribution functions (PDFs), and uncertainties arising from modeling of the background processes, the choice of event generators and b-jet fragmentation, decays, and color connections (Modeling) [12,13]. Table II