A Measurement of Top Quark Mass
Using MET + Jets Events with 5.7 fb-1 of CDF Data

Jian Tang 1, Hyun Su Lee 1, Young-Kee Kim1,2, and Gabriele Compostella3
1 The University of Chicago
2 Fermilab
3INFN-CNAF &University of Padova

Contact the authors

Measurement: Mtop = 172.3 +/- 2.4 (stat.+JES) +/- 1.0 (syst.) GeV/c2 = 172.3 +/- 2.6 GeV/c2
   = 172.3 +/- 1.8 (stat.) +/- 1.5 (JES) +/- 1.0 (syst.) GeV/c2  

Public Note

Analysis in Combined Lepton+Jets and Dilepton Channels with 5.6 fb-1: Public Webpage, Public Note
Analysis of top Xsection measurement using METJets events with 2.2 fb-1: Public Webpage, Public Note
Anslysis in Combined Lepton+Jets and Dilepton Channels with 1.9 fb-1: public Webpage, Public Note

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We present a measurement of top-quark mass using 5.7 fb-1 collected by the CDF II detector at Fermilab. We use a neural network to select the events after a series of event clean up, which have a signature of MET + Jets in the final state. A total of 1432 data events are found after all cuts. The background is modeled from data set, and a few corrections are applied to improve the background modeling.

We use a three-dimensional template method to build the probability density functions of both signal and background, where the three observables are the M3 top mass of the underconstrained system, a second reconstructed M3 top mass called M3', and the invariant mass Mjj of two jets from the hadronic W decays, which provides an in situ improvement in the determination of jet energy scale.

Kernel density estimation (KDE) is used to estimate three-dimentional probability density functions for both backgrounds and signals, and data are then compared to these templates to make a likelihood fit to extract top mass. We measure Mtop=172.3 +/- 2.4 (stat.+JES) +/- 1.0 (syst.) GeV/c2.

Event Selection

The data set used in this analysis corresponding to a total integrated luminosity of 5.7 fb-1 were collected by a multijet trigger. A series of cuts are first applied to clean up the events. Events with tight or loose leptons are rejected. A requirement of MET significance > 3 GeV1/3 is also applied. The number of jets in one event is constrained to be within [4,6]( 4 ≤ njets ≤ 6).

The Monte-Carlo samples used in this analysis are generated by PYTHIA, with "true" top masses ranging from 150 GeV/c2 to 240 GeV/c2.

Background Estimation

We use a data driven background estimation in this analysis. Because the probability for a jet to be identified as a b-quark jet is different for the jets in the ttbar events and in the background processes, we can use this to distinguish the two of them in the data set. We build a b-tag rate matrix from a ttbar-signal-negligible data sample, which consist of events with exactly three jets, and parameterize the b-tag probability as a function of jet characteristics such as jet transverse energy, jet number of tracks, and the MET projection along the jet direction.

At higher jet multipliticies, the signal contamination is not negligible, we use an iterative correction method to remove the sizable ttbar events in each jet bin in order to improve our background prediction. We validate our background estimation by comparing the expected and observed number of b-tagged events at different jet-multiplicities at the background dominant region NNoutput < 0.4, as shown in the following table.
Num of Jets3 jets4 jets5 jets6 jets≥ 7 jets
We further divide our sample in to events with 1 btagged jet(1tag) and events with two or more btagged jets(2tag). Our calculation of number of 1tag and 2tag events involves a btagging correction factor that takes into account the fact that in QCD events heavy flavor quark tend to come in pairs, which enhances the 2tag probability of an event.
After the corrections, the output of neural network for both 1tag and 2tag events is shown below, and we apply a cut on NNoutput > 0.8 to increase the signal-to-background ration.

After applying all cuts, we get the number of observed and expected events in the signal region( 4 ≤ njets ≤ 6 ), which is shown in the following table:
b-taggingSignalBackgroundTotal ExpectedObserved

Event Reconstruction:

The event signature after event selection has a large missing transverse energy and big jet-multiplicities, and based on the HEPG(real information from the MC samples) study we found that most of the selected events come from the ttbar lepton + jets decay channel, in which one of the W bosons from the top quark decay decays into two jets and the other into a lepton and a neutrino. We reconstruct the W boson mass from its hadronically decay jets to constrain in situ the jet energy scale(JES). For each possible jet-to-quark assignment of an event we calculate the invariant mass of two non-btagged jets, then we choose the one that has the value closest to the world average W mass mesurement, 80.40 GeV/c2, to be the reconstructed W mass Mjj. The fact that this analysis does not identify leptons makes it hard to fully reconstruct the event, thus hard to reconstruct the top quark mass. However, we can reconstruct a variable called M3, which is defined as the invariant mass of three jets that give the largest summation of jet ET. To enhance the chance that these three jets come from the same top quark decay, we take two of the three jets from the Mjj reconstruction.
We also reconstruct a third variable called M3', similar to the M3 mentioned above, except that the third jet of M3', also one of the leading four jets, is different from any of the three jets that construct M3. The following figures show the distribution of Mjj from MC samples with different input JES values and the same input top mass(Mt = 172.5 GeV/c2), the distributions of reconstructed M3 and M3' from samples with different input top quark masses but the same input JES(JES=0).

Kernel Density Estimation:

We use a non-parametric Kernel Density Estimate-based approach to forming probability density functions from fully simulated Pythia MC. The probability for an event with an observable x is given by the linear sum of contributions from all entries in the MC:
KDE 2 image

Here, f(x) is the probability to observe x given some MC sample with known mass and JES (or the background). The kernel function K is a normalized function that adds varying probability to a measurement at x depending on its distance from xi. The smoothing parameter h is a number that determines the width of the kernel. Larger values of h smooth out the density estimate, and smaller values of h keep most of the probability weight near xi. We use an adaptive method in which the value of h = h(f(x_i)). The peak of the distribution, we use smaller smoothing. In the tails of the distribution, where statistics are poor and we are sensitive to statistiacl fluctuation, we use a larger amount of smoothing. KDE can be expanded to three (two) dimensions by multiplying together three (two) kernels:
KDE 4 image

We apply this technique to obtain pdf for each Mtop, JES Monte Carlo sample that was generated as well as the background samples generated at a range of JES values.

Likelihood Fit

We minimize the extended likelihood with respect to the top mass, JES and signal and background expectation to obtain the measurement as well as statistical uncertainty. The form of the likelihood for subsample k is shown below.
where ns and nb are signal and background expectations and N is the number of events in the subsample, Ps is the signal probability density function and Pb is the background probability density function. nb0 is the a-priori background estimate and σnb0 is the uncertainty on that estimate.

Method validation

To get a calibration of the method on the estimate of bias and the estimate of statistical uncertainty we perform ensamble tests. We repeatedly draw events from the signal and background model mimicking possible variations of signal and background numbers that may occur in data. A mass measurement is performed on each of these pseudo-datasets. Knowing the Mtop and JES of the dataset from which the signal events were drawn we can calculate residuals (M_top_fitted-M_top_MC) and pulls ((M_top_fitted-M_top_MC)/returned uncertainty) as well as similar quantities for the JES calibration. Ideal performance would yield 0 residual and pull distributions centered at 0 and with width 1. The residual distribution of the ensamble tests are shown below:
Residual before calibration

residuals residuals
Residual and Pull width after calibration

Residual of JES are shown below. Here we had similar calibration with linear fit:
Bias and Pull width of measured top mass vs different JES, after calibration

Residual and Pull width of measured JES vs "true" JES, after calibration

Systematic Uncertainties

The contributions to the systematic effects are shown below. The dominant effect comes from the residual jet energy scale and generator systematics. We model the jet energy scale as a single parameter, which is an over-simplification resulting in the Residual JES uncertainty. The generator systematic is comming from comparing pseudoexperiments generated with Herwig and Pythia.
Systematic(GeV/c2) ΔMtop
Residual JES 0.50
Geberator 0.65
PDFs 0.20
b jet energy 0.29
Background shape 0.12
gg fraction <0.01
Radiation 0.21
Trigger simulation 0.14
Multiple Hadron Interaction 0.16
Color Reconnection 0.20
Total Effect 0.98

Fit and Results

We perform fit to the data and measure Mtop = 172.3 +/- 2.4 (stat.+JES) +/- 1.0 GeV/c2 (syst) = 172.3 +/- 2.6 GeV/c2. The likelihood contour is shown below:
We perform pseudoexperiments using observed number of events to evaluate the probability of obtaining the uncertainty found in data. Results are shown below.

The reconstructed top mass distribution from the data with overlayed background and signal template fitted is depicted below.
residuals residuals
residuals residuals

Jian Tang for the TMT Group

Last modified Feb 28th, 2011