Measurement of the Top Quark Mass in the All-Hadronic Mode at CDF

We present a measurement of the top quark mass (Mtop) in the all-hadronic decay channel using 5.8 fb^{-1} of proton-antiproton data collected with the CDF II detector at the Fermilab Tevatron Collider. Events with 6 to 8 jets are selected by a neural network algorithm and by the requirement that at least one of the jets is tagged as a b quark jet. The measurement is performed by a likelihood fit technique, which determines simultaneously Mtop and the jet energy scale (JES) calibration. The fit yields a value of 172.5 +- 1.4(stat) +-1.0(JES) +-1.1(syst) GeV/c^2.

The mass of the top quark (M top ) is a fundamental parameter of the standard model (SM) and its large value makes the top quark contribution dominant in loop corrections to many observables, like the W boson mass M W . Precise measurements of M W and M top allow one to set indirect constraints on the mass of the, as yet unobserved, Higgs boson [1].
In this Letter we present a measurement of M top using proton-antiproton collision events at a centerof-mass energy of 1.96 TeV.Top quarks are produced at the largest rate in pairs (t t), with each top quark decaying immediately into a W boson and a b quark nearly 100% of the time [2].In this analysis events where both the W 's decay to a quark-antiquark pair y University of Notre Dame, Notre Dame, IN 46556, USA, z Universidad de Oviedo, E-33007 Oviedo, Spain, aa CNRS-IN2P3, Paris, F-75205 France, bb Texas Tech University, Lubbock, TX 79609, USA, cc Universidad Tecnica Federico Santa Maria, 110v Valparaiso, Chile, dd Yarmouk University, Irbid 211-63, Jordan.
(t t → W + b W −b → q 1 q2 b q 3 q4 b) are considered.This all-hadronic final state has the largest branching ratio among the possible decay channels (46%), but it is overwhelmed by the QCD multijet background processes, which surpass t t production by three orders of magnitude even after a dedicated trigger requirement.Nevertheless, it will be shown how this difficult background can be successfully controlled and significantly suppressed with a properly optimized event selection.The fundamental analysis technique is the same exploited to obtain the previous result from CDF, and is described in details in [3].However, improvements in the event selection and a larger dataset allow us to decrease the total uncertainty on M top by 21%.The additional dataset has been acquired at higher instantaneous luminosity, which results in a higher number of background events in the data sample.Despite this fact, the introduction of significant improvements to the analysis results in the world best measurement of M top in the all-hadronic channel so far, also entering with the third largest weight in the M top world average calculation [4,5].
The data correspond to an integrated luminosity of 5.8 fb −1 .They have been collected between March 2002 and February 2010 by the CDF detector, a general-purpose apparatus designed to study pp collisions at the Tevatron and described in detail in [6].Events used in this measurement are selected by a multijet trigger [3], and retained only if they are well contained in the detector acceptance, have no well identified energetic electron or muon, and have a missing transverse energy E T [7] satisfying , where E T is the sum of the transverse energy E T of all jets.Candidate events are also required to have from six to eight "tight" (E T ≥ 15 GeV and |η| ≤ 2.0) jets.After this preselection, a total of about 5.7 M events is observed in the data, with less than 9 thousand expected from t t events.To improve the signal-to-background ratio (S/B) a b-tagging algorithm [8] is used to identify ("btag" or simply "tag") jets that most likely resulted from the fragmentation of a b quark.Only events with one to three tagged jets are then retained, improving the S/B by a factor of 6.In order to further increase the signal purity, a multivariate algorithm is implemented.An artificial neural network, based on a set of kinematic and jet shape variables [3], is used to take advantage of the distinctive features of signal and background events.The neural network was trained using simulated t t events generated by Pythia [9] and propagated through the CDF detector simulation.At this level of selection the fraction of signal events is still negligible so that the data can be used to represent the background.The value of the output node, N out , is used as a discriminant between signal and background, providing a gain in S/B by an additional factor of about 30.
The background for the t t multijet final state comes mainly from QCD production of heavy-quark pairs (b b and cc) and events with false tags from lightquark and gluon jets.Given the large theoretical uncertainties on the QCD multijet production cross section, the background prediction is obtained from the data themselves.The probability of tagging a jet in a background event (P + ) is evaluated using data with five tight jets and passing the preselection (S/B ≈ 1/2000).This "tag rate" is parametrized in terms of a few relevant jet variables and is then used to estimate the probability that a candidate event belongs to the background and contains a given number of tagged jets.As described in detail in [3] this allows to predict the expected amount of background events in the selected samples as well as their distributions.For example, the average number of background 1-tag events is estimated by where the outer sum runs over all events selected just before the b-tagging requirement, and the inner one over the jets of the event.The factor C 1 tag represents a correction to take into account correlations among jets within the same event [3], and it is parametrized as a function of the same variables used for the tag rate.
The analysis employs the template method to measure M top with simultaneous calibration of the jet energy scale (JES) [3,10], allowing a strong reduction of the associated systematic uncertainty.Distributions of variables sensitive to the "true" values of M top and JES, obtained by Monte Carlo (MC) events, are used as a reference ("template") in the measurement.A maximum likelihood fit is performed to define the values that best reproduce the same distributions as observed in the data.An usual choice is to consider the distributions of the event-by-event reconstructed top quark mass, m rec t , and W boson mass, m rec W as the reference templates.The JES is a multiplicative factor representing a correction applied to the raw energy of a reconstructed jet (E raw T ), so that its corrected energy T , is a better estimate of the energy of the underlying parton [11].Discrepancies between data and simulation result in an uncertainty on the JES value to be applied in MC events to reproduce the data, and, as a consequence, on the measurements of M top .Nevertheless, this value can be calibrated "in situ", using m rec W as a template.This represents a well tested technique, first applied in [10] and now used to obtain the most precise top quark mass measurements at the Tevatron [4,5].
The templates are built as follows [3].For each selected event, each of the six highest-E T jets is assigned in turn to one of the six quarks of a t t all-hadronic final state.Then, for each combination the jets are arranged in two triplets (the top quarks), each including a doublet (corresponding to the W boson) and a b quark.To reduce the possible number of permutations, b-tagged jets are assigned to b quarks only, resulting in 30, 6 or 18 permutations for events with one, two or three tagged jets, respectively [12].
For each permutation m rec t is obtained through a constrained fit based on the minimization of the following χ 2 -like function: where m (1,2) jj are the invariant masses of the two pairs of jets assigned to light flavor quarks, m jjb are the invariant masses of the triplets including one pair and one jet assigned to a b quark, M W = 80.4 GeV/c 2 and Γ W = 2.1 GeV are the measured mass and natural width of the W boson [2], and Γ t = 1.5 GeV is the assumed natural width of the top quark [13].The jet transverse momenta are constrained in the fit to the measured values, p meas T,i , within their known resolutions, σ i .The fit is performed with respect to m rec t and the transverse momenta of the jets p fit T,i , and, among all the permutations, the one which gives the lowest value for the minimized χ 2 t is selected.The variable m rec W is reconstructed by the same procedure considered for m rec t , but with a χ 2 function, χ 2 W , where also the W mass is left free to vary in the fit.The selected values of m rec t and m rec W enter the respective distributions, built separately for events with exactly one or ≥ 2 tags.
Signal templates are built using MC events with M top values from 160 to 185 GeV/c 2 , with steps of 1.0 GeV/c 2 , and, for each value, moving the JES by ∆JES•σ JES from the default.Here σ JES is the absolute uncertainty on the JES [11] and ∆JES is a dimensionless number.Values of ∆JES between −2 and +2, in steps of 0.5, have been used, and in the following we refer to this parameter to denote variations of the JES.To construct the background templates we apply the fitting technique to the data events passing the neural network selection cut, omitting the b-tagging requirement ("pretag" sample) [3].The weight of each value of m rec t and m rec W is given by the probability of the event to belong to the background and to contain tagged jets, evaluated by the tag rates of jets, as outlined above.
Sets of simulated experiments ("pseudoexperiments", PEs) have been performed to optimize the requirements on the values of N out , χ 2 t and χ 2 W in order to minimize the statistical uncertainty on the M top measurement.As an improvement with respect to [3], two different sets of events, denoted by S JES and S Mtop , are used to build the m rec W and m rec t tem-plates, respectively.The set S JES is selected by using cuts on N out and χ 2 W , while S Mtop is selected by a further requirement on χ 2 t , so that S Mtop corresponds to a subset of S JES .This new procedure contributes in reducing the final total uncertainty on M top with respect to [3] by about 12%.Tables I and II report the flow of the event selection for 1-tag and ≥ 2-tag events, respectively.As the final requirements are optimized separately for the two tagging categories, the b-tag requirement is included in the flow just after the preselection.

TABLE I:
Selection flow for 1-tag events samples.For each requirement the number of events observed in the data, the expected number of t t signal events, the absolute efficiency on the signal (ε) and the signal-tobackground ratio (S/B) are shown.For the signal Mtop = 172.5 GeV/c 2 and ∆JES = 0 are used.The expectations are normalized to the integrated luminosity of the data sample (5.8 fb −1 ) using the theoretical cross section (7.46 pb), while the background is evaluated as the difference between the data and the expected signal.).The notation points out that the shapes of the signal p.d.f.'s are functions of the fit parameters M top and ∆JES.This dependence is obtained by fitting the whole set of templates, initially built as histograms.Figure 1 shows examples of signal and background templates for the ≥ 2-tag sample, with the corresponding p.d.f.'s superimposed.The presence of the different sets S JES and S Mtop requires the generalizations of some of the terms of the likelihood with respect to [3].The function can be divided into three parts: where L ∆JESconstr is a Gaussian term constraining the JES to the nominal value (i.e.∆JES to 0) within its uncertainty : Terms L 1 tag and L ≥2 tags are in turn defined as: where, omitting the dependences on M top and ∆ JES , and In the first term the probability to observe the set m W, i , (i = 1, ..., N SJES obs ) of m rec W values reconstructed in the data is calculated by the signal and background expected distributions, P ), and the m rec t probability density functions.The factors A s (M top , ∆JES) and A b represent the acceptance of S Mtop with respect to S JES for signal and background, respectively (i.e., the fraction of events selected by the requirements on χ 2 t only).For the signal this acceptance is parametrized as a function of the fit parameters M top and ∆JES.The third term, L evts , gives the probability to observe simultaneously the number of events selected in the data in the S JES and the S Mtop samples, given the assumed values for the average number of signal (n s ) and background (n b ) events to be expected in S JES and the acceptances A s (M top , ∆JES) and A b .It depends on the Poisson (P ) and Binomial (B) probabilities In the last term, L N bkg constr , the parameter n b is constrained by a Gaussian to the a priori background estimate i.e. n (b, exp) = 3652 ± 181 for 1-tag events and n (b, exp) = 718 ± 14 for ≥ 2-tag events.
The possible presence of biases in the values returned by the likelihood fit has been investigated.
Pseudo-experiments are performed assuming specific values for M top and ∆JES and "pseudo-data" are therefore extracted from the corresponding signal and background templates.The results of these PEs have been compared to the input values, and calibration functions to be applied to the output from the fit have been defined in order to obtain, on average, a more reliable estimate of the true values and uncertainties.
Finally, the likelihood fit is applied to data.After the event selection described above, we are left with 4368 and 1196 events with one and ≥ 2 tags (147 have 3 tags), respectively, in the S JES sample.The corresponding expected backgrounds amount to 3652 ± 181 and 718 ± 14 events, respectively.The tighter requirements used for the S Mtop samples select 2256 with one tag and 600 with ≥ 2 tags (76 have 3 tags), with average background estimates of 1712 ± 77 and 305 ± 22 events, respectively.
For these events the variables m rec W and m rec t have been reconstructed and used as the data inputs to the likelihood fit.Once the calibration procedure has been applied, the measurements of M top and ∆JES are    Various sources of systematic uncertainties affect the M top and ∆JES measurements, as described in [3].They are evaluated by performing PEs using templates built by signal samples where effects due to systematic uncertainties have been included.The differences in the average values of M top and ∆JES with respect to the PEs performed with default templates are then taken into account.Possible residual biases existing after the calibration, and uncertainties on the parameters of the calibration functions are also taken into account.The largest contributions come from uncertainties on the modeling of the background, on the simulation of t t events, and on the individual corrections which JES depends on [11].Table III shows a summary of all the systematic uncertainties.
In summary, we have presented a measurement of the top quark mass in the all-hadronic channel, using pp collision data corresponding to an integrated luminosity of 5.8 fb −1 .An optimized event selection, based mainly on a neural network and a b-tagging algorithm, allows us to select candidate event samples with S/B close to 1 in spite of the huge background still existing at trigger level.The simultaneous calibration of the jet energy scale, following a well established technique, allows to reduce down to 1 GeV/c 2 the systematic uncertainty due to this source.The value obtained for the JES is in agreement both with the default value [11] and with the results obtained by other measurements of the top quark mass performed by the CDF Collaboration using the in situ calibration technique [4,5].The measured value of the top quark mass is M top = 172.5 ± 1.4 (stat) ± 1.0 (JES) ± 1.1 (syst) GeV/c 2 , with a total uncertainty of 2.0 GeV/c 2 .This result complements and is consistent with the most recent measurements obtained in other channels by the CDF and D0 Collaborations, and also represents the most accurate all-hadronic measurement at the Tevatron so far.

FIG. 1 :
FIG. 1: Templates of m rec t for events with ≥ 2 tags and corresponding probability density functions superimposed.Top plot: the signal p.d.f, Ps, for various values of Mtop and ∆JES = 0. Bottom plot: the background p.d.f., P b .
of the free parameters of the fit M top , ∆JES, n s , and n b .In the second the same is done for the distributions of the observed reconstructed top masses, m t, i , (i = 1, ..., N SM top obs

Figure 2
Figure2shows the measured values together with the negative log-likelihood contours whose projections correspond to one, two, and three σ uncertainties on the values of M top and ∆JES as obtained from the likelihood fit.

FIG. 2 :
FIG.2: Negative log-likelihood contours for the likelihood fit performed for the Mtop and ∆JES measurement.The minimum is shown along with the contours whose projections correspond to one, two, and three σ uncertainties on the Mtop and ∆JES measurements.

Figure 3
Figure 3 shows the m rec t and m rec W distributions for the data compared to the expected background and the signal for M top and ∆JES corresponding to the measured values.The signal and background distributions are normalized to the respective yields as fitted to the data, with the 1-tag and ≥ 2-tag contributions summed together.

FIG. 3 :
FIG. 3: Distributions of m rec t (top plot) and m rec W (bottom plot) as obtained in the selected data (black points) with ≥ 1 tags, compared to the distributions from signal and background corresponding to the measured values of Mtop and ∆JES.The expected distributions are normalized to the best fit yields.

TABLE II :
Selection flow for ≥ 2-tag events samples.The same notations of Table I are used.
t and m rec W expected for signal (s) and background (b), P s (m rec t | M top , ∆JES), P s (m rec W | M top , ∆JES), P b (m rec t ), and P b (m rec W

TABLE III :
Sources of systematic uncertainty affecting the Mtop and ∆JES measurements.The total uncertainty is obtained by the quadrature sum of each contribution.