Top quark mass measurement in the lepton plus jets channel using a modified matrix element method

We report a measurement of the top quark mass, $m_t$, obtained from $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ at the Fermilab Tevatron using the CDF II detector. We analyze a sample corresponding to an integrated luminosity of $1.9{\mathrm{fb}}^{-1}$. We select events with an electron or muon, large missing transverse energy, and exactly four high-energy jets in the central region of the detector, at least one of which is tagged as coming from a $b$ quark. We calculate a signal likelihood using a matrix element integration method, where the matrix element is modified by using effective propagators to take into account assumptions on event kinematics. Our event likelihood is a function of $m_t$ and a parameter JES (jet energy scale) that determines in situ the calibration of the jet energies. We use a neural network discriminant to distinguish signal from background events. We also apply a cut on the peak value of each event likelihood curve to reduce the contribution of background and badly reconstructed events. Using the 318 events that pass all selection criteria, we find $m_t=172.7\pm 1.8(\mathrm{stat}+\mathrm{JES})\pm 1.2(\mathrm{syst})\mathrm{GeV}/c^2$.

Figure 1

A view of a $b$-jet in the $x\mathrm{\text{−}}y$ plane. $L_{2\mathrm{D}}$, the distance between the primary and secondary vertices projected onto the jet axis, along with its uncertainty, is used to determine whether a jet originates from a heavy flavor quark.

Figure 2

Comparison of data and MC predictions for the selected events. The confidence level obtained from a K-S test on the two distributions is indicated on the histogram. The plots show, in order, the corrected $E_T$ of the leading jet, 2nd jet, 3rd jet, and 4th jet in our events.

Figure 3

Comparison of data and MC predictions for the selected events. The confidence level obtained from a K-S test on the two distributions is indicated on the histogram. The plots show, in order, the event ${\mathrm{E̸}}_T$, the total number of jets with $E_T>12\mathrm{GeV}$ and $|\eta |<2.4$ in the event, the $E_T$ for all jets with a $b$-tag, and the lepton $p_T$.

Figure 4

Efficiency for the secvtx algorithm with systematic uncertainties. The top two plots show the tag efficiency for tagging $b$-jets as a function of the jet $E_T$ (left) and $|\eta |$ (right), and the bottom two plots show the tag rate for light jets (mistags), also as a function of jet $E_T$ (left) and $|\eta |$ (right). The fits used as a parametrization in our analysis are also shown.

Figure 5

Angular resolution in $\eta$ (left) and $\varphi$ (right) as a function of parton $p_T$. The dashed line indicates the resolution for light quarks, and the solid line for $b$ quarks.

Figure 6

Contour plots of the propagators in $M_W^2$ and $\Delta M_t$. Left: Breit-Wigner propagator, for comparison. Center: Sample effective propagator on the hadronic side of the event. Right: Sample effective propagator on the leptonic side of the event.

Figure 7

Sample fitted transfer functions for light and $b$ quarks in $\eta$ bins. Transfer functions are shown for light quarks with parton $P_T=40$ and $70\mathrm{GeV}/c$ (top left and right, respectively), and for $b$ quarks with parton $P_T=40$ and $70\mathrm{GeV}/c$ (bottom left and right, respectively).

Figure 8

Left: Cross section obtained from our normalization calculation as a function of $m_t$ compared with the cross section used in herwig. Right: Normalization correction factor due to effective propagators as a function of $m_t$.

Figure 9

Acceptance used in Eq. (2) as a function of $m_t$ and JES.

Figure 10

The distributions of our neural network discriminant variable for signal and background MC events. The peaks on the right are from $t\overline{t}$ signal events at three top masses. The peaks on the left are from various types of backgrounds.

Figure 11

Distributions of the peak value of the log-likelihood for MC events, divided into “good signal,” “bad signal,” and background events. Left: 1-tag events, right: multiple-tag events. The vertical lines indicate where the likelihood cut is applied.

Figure 12

Pseudoexperiment results using fully simulated signal and background events after applying a likelihood cut, with a mean of 303 events for each PE. For these samples, JES is fixed at its nominal value of 1. Top left: reconstructed vs input top quark mass; top right: bias vs input top quark mass; bottom: pull width vs input top quark mass.

Figure 13

JES pseudoexperiment results using fully simulated signal and background events after applying a likelihood cut, with a mean of 303 events for each PE. The top quark mass here is fixed at $m_t=170\mathrm{GeV}/c^2$. Top left: reconstructed vs input JES; top right: JES bias vs input JES; bottom: JES pull width vs input JES.

Figure 14

Results of studying samples with shifted JES values. Top left: Mass bias vs input top quark mass at the five different JES points; top right: JES bias vs input JES at the three different mass points; bottom: reconstructed top quark mass vs input JES for the three different top quark masses.

Figure 15

Left: Measured 2-D likelihood on the data events. The plot shows the contours corresponding to a $1\mathrm{\text{−}}\sigma$, $2\mathrm{\text{−}}\sigma$, and $3\mathrm{\text{−}}\sigma$ uncertainty (assuming Gaussian behavior) in our measurement. The calibration derived from MC events has been applied to both axes. The marker shows the point of maximum likelihood. Right: Likelihood peak position of the individual likelihood curves for data and MC events. The dashed line indicates the likelihood cut of 6 employed.

Figure 16

Expected statistical uncertainty (including uncertainty due to JES) on the top mass from the 2-D profile likelihood method, derived from MC events with $m_t=172\mathrm{GeV}/c^2$. The black arrow indicates the uncertainty in the data measurement. All uncertainties have been scaled by the average pull width of 1.198. They are also corrected by $1/0.995$ to account for a measured response slope slightly different from 1.