At the Tevatron, top quarks are mainly pair produced in ppar collisions via qqbar annihilation (85%) and gluon-gluon fusion (15%). According to the Standard Model, the top quarks decay into W bosons and b quarks with BR~1. In this analysis we search for events in which both W bosons decay into quark pairs, leading to an all-hadronic final state. This channel has the advantage of the largest branching ratio, about 44%, and of the fully reconstructed kinematics. The major downside is the huge background from QCD multijet production which dominates the signal by three orders of magnitude even after the application of the specific top multijet trigger. A sophisticated event selection based on kinematical and topological variables, followed by the request of identified b-jets is thus needed in order to further improve the signal to background ratio (S:B). In this document we present the TMT2D technique which we use for the measurement of the top quark mass using about 2.9fb^-1 of data. We use simulated events to build distributions (templates) of variables sensitive to the observables we want to measure : the top mass (Mtop) and JES. The shapes of these distributions can be used to discriminate the signal from the background and the measurement is obtained maximizing a likelihood fit of the data to the signal and background templates. Before applying the method to real data, we run simulated experiments (pseudo-experiments) to check for possible biases, to derive the expected statistical accuracy of the measurement and to evaluate the main sources of systematic uncertainties.

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To study the event selection, to build the signal templates and to check the performances of the method we use tt Monte Carlo events generated by PYTHIA v 6.216 with M_top values ranging from 160 to 190 GeV/c² in 1 GeV/c² steps. As for the background, we use a data-driven modeling based on the tag rate parametrization of jets. All data/MC events have to pass some prerequisites which require the run to be a good one, a well centered primary vertex and no tight lepton identified in the event. The events satisfying this selection are then required to have a number of detected tight jets (Et>15 GeV, |eta|<2) between 6 and 8 with a minimum distance between jets (DeltaRmin) larger than 0.5. Moreover we require the absence of significant missing transverse energy. A number of kinematic variables are then reconstructed using tight jets and serve as inputs to a neural network, deployed to obtain a good S/B ratio and high efficiency on the signal. The neural network chosen here is the Multilayer perceptron (MLP), a simple feed-forward network. As said above, in this new analysis the number of input nodes has been increased to 13, with inclusion of jet shape variables. The 13 inputs are:

1) Sum of the jet Et;

2) Sum of the three subleading jet Et;

3) Aplanarity

4) Centrality;

5) Minimum of the invariant mass of dijet system;

6) Maximum of the invariant mass of dijet system;

7) Minimum of the invariant mass of trijet system;

8) Maximum of the invariant mass of trijet system;

9) Et1Star = leading jet Et*sin²(theta^*);

10) Et2Star;

11) <EtStar>3N(geometric average over the 3rd-4th...Nth jets);

12) geometric average of the light quark jet eta momenta in the calorimeter

13) geometric average of the light quark jet phi momenta in the calorimeter

Finally we require the presence of tagged jets among the six leading jets, and subdivide our sample in events with exactly one tagged jet and two or three tagged jets. Events are selected if the output value from the neural network, Nout, is larger than a given value. This is chosen for events with 1 b-tag or with >=2 b-tags separately in a way to maximize the statistical signicance of the mass measurement.

Event Selection NN Output for events with exactly 1 b-tag(left) and with at least 2 b-tags (right).

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To reconstruct the top invariant mass, we consider only the 6 leading jets (highest in Et) and define a chi² containing 2 dijet masses (set to be equal to the W mass), 2 triplet masses (set to be equal one to the other) and 6 terms representing the jet energy resolution. For each event with at least one b-tagged jet we consider all possible combinations where the tagged jets are assigned to b partons and keep the mass corresponding to the combination with the smallest chi². The same procedure is applied to build W mass templates, the only difference being in the absence of the W mass constraint in the fitter.

We use a contol region of events with exactly 4 jets to build a probability for a jet to be tagged. This probability is parametrized in terms of:

1) number of primary vertices in the event

2) number of good tracks inside the jets (with silicon hits)

3) jet Et

We then apply this probability to events in the signal region to estimate the background kinematics and normalizetion due to QCD multijet production. A specific procedure is applied to account, on average, for correlations among tags. The agreement between expected and observed tagged events in control regions is quite good, as can be seen in the following two different control regions. Only variables crucial to the analysis are shown here.

Low NN score Control Region, i.e 0.50 < Nout < 0.75

NN output, chi2 of the kinematic fit, reconstructed top invariant mass, reconstructed W invariant mass for events with exactly 1 b-tag. The control region is defined by the range of the Nout variables, 0.50 < Nout < 0.75

NN output, chi2 of the kinematic fit, reconstructed top invariant mass, reconstructed W invariant mass for events with at least 2 b-tags. The control region is defined by the range of the Nout variables, 0.50 < Nout < 0.75.

High NN score Control Region, i.e. 0.75 < Nout < 0.85

NN output, chi2 of the kinematic fit, reconstructed top invariant mass, reconstructed W invariant mass for events with exactly 1 b-tag. The control region is defined by the range of the Nout variables, 0.75 < Nout < 0.85.

NN output, chi2 of the kinematic fit, reconstructed top invariant mass, reconstructed W invariant mass for events with at least 2 b-tags. The control region is defined by the range of the Nout variables, 0.75 < Nout < 0.85.

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The signal and background templates are parametrized with combinations of one/two gaussian and one/two gamma functions. For the signal templates the parameters depend linearly on the input top mass and on the input JES. For the background, the expected contribution from tt events is accounted for.

Reconstructed signal Mtop distribution, as a function of the input top mass and JES and reconstructed signal Mw distribution, as a function of the input top mass and JES, for events with exactly 1 b-tag, and their respective parametrization.

Reconstructed signal Mtop distribution, as a function of the input top mass and JES and reconstructed signal Mw distribution, as a function of the input top mass and JES, for events with at least 2 b-tags, and their respective parametrization.

Reconstructed background Mtop distribution (left) and reconstructed background Mw distribution (right) for events with exactly 1 b-tag, and their respective parametrization.

Reconstructed background Mtop distribution (left) and reconstructed background Mw distribution (right) for events with at least 2 b-tags, and their respective parametrizations.

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We define a likelihood function which depends on the number of signal and background events and on the corresponding probability density functions (templates) We then find the input top mass and JES value which maximize the likelihood. Before applying this to the data we test the performance on a set of pseudo-experiments where we sum background and signal events (for different input top masses) extracted from the templates in the expected proportion. This procedure is used for the calibration of the response functions and to estimate possible biases in the measurement. We study the linearity of the values returned by the fit with respect to the input values, the residuals and pulls of these values, and we account for these small biases.

Linearity in Mtop and JES response after calibration

Pull widths for Mtop measurement as a function of input Mtop(left) or input JES(right)

Pull means and widths for JES measurements

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After the kinematic selection with Nout > 0.90 (Nout>0.88) and chi² <6 (chi² <5) for events with 1 tag (>= 2 tags), we are left with 3452 (441) events with 1 b-tag (>=2 b-tags). The expected background, corrected for the contribution due to ttbar events, amounts to 2785 ± 83 (201 ± 29) events with 1 tag (>= 2 tags). We apply our analysis to 2.9fb^-1 of CDF Run II data and measure the top quark mass in the all-hadronic channel to be

Mtop = 174.8 ± 2.4(stat.+JES) +1.2 -1.0(syst.) GeV/c2

or by separating the purely statistical uncertainty from the uncertainty due to the in situ JES measurement,

Mtop = 174.8 ± 1.7(stat) ± 1.6(JES) +1.2 -1.0(syst.) GeV/c2

or by separating the purely statistical uncertainty from all systematic uncertainties,

Mtop = 174.8 ± 1.7(stat.) ± 1.9(syst.) GeV/c2 = 174.8 ± 2.7 (total) GeV/c2

2D contour likelihood in the M_top and JES plane; on the right plot, only the contours corresponding to 1, 2 or 3&sigma are shown.

Expected and observed statistical precision of the Mtop measurement (on the left) and of the JES measurement (on the right). There is about 90% probability to measure a lower statistical uncertainty for both.

Top reconstructed invariant masses for signal events with exactly one b-tag (left) or at least 2 b-tags (right).

W reconstructed invariant masses for events with exactly 1 b-tag (left) or at least 2 b-tags (right).

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