Top quark mass measurement in the $t\overline{t}$ all hadronic channel using a matrix element technique in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$

We present a measurement of the top quark mass in the all hadronic channel ($t\overline{t}\to b\overline{b}{q}_1{\overline{q}}_2{q}_3{\overline{q}}_4$) using $943{\mathrm{pb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ collected at the CDF II detector at Fermilab (CDF). We apply the standard model production and decay matrix element (ME) to $t\overline{t}$ candidate events. We calculate per-event probability densities according to the ME calculation and construct template models of signal and background. The scale of the jet energy is calibrated using additional templates formed with the invariant mass of pairs of jets. These templates form an overall likelihood function that depends on the top quark mass and on the jet energy scale (JES). We estimate both by maximizing this function. Given 72 observed events, we measure a top quark mass of $171.1\pm 3.7(\mathrm{stat}+\mathrm{JES})\pm 2.1(\mathrm{syst})\mathrm{GeV}/c^2$. The combined uncertainty on the top quark mass is $4.3\mathrm{GeV}/c^2$.

Figure 1

Distribution of $\min LKL$ (minimum of the negative log event probability) for simulated $t\overline{t}$ events with $M_{\mathrm{top}}=175\mathrm{GeV}/c^2$ (continuous line) and for background events (dashed line) modeled in Sec. 5. The events pass the kinematical and $b$-tagging requirements.

Figure 2

Magnitude of the transverse momentum of the $t\overline{t}$ system in simulated $t\overline{t}$ events. The fit is a sum of three Gaussians.

Figure 3

Cross section for $t\overline{t}$ production as a function of the top quark mass, as obtained from comphep [32].

Figure 4

Reconstructed top mass versus input top mass at parton level. The energies of the partons have been smeared using the transfer functions. The continuous line $y=x$ is added for visual reference.

Figure 5

Reconstructed top mass versus input top mass using jets that were uniquely matched to partons. The continuous line $y=x$ is added for visual reference.

Figure 6

Reconstructed top mass versus input top mass using realistic jets. The continuous line $y=x$ is added for visual reference.

Figure 7

Background validation in control region CR1 for single tagged events from the multijet data (dots) and from the background model (solid histogram). The distributions are normalized to the same area.

Figure 8

Background validation in control region CR1 for double tagged events from the multijet data (dots) and from the background model (solid histogram). The distributions are normalized to the same area.

Figure 9

Invariant mass of pairs of untagged jets in control region CR2 for alpgen $b\overline{b}+4$ light partons (cross), and for the background model (solid line): (a) for single tagged events (Kolmogorov-Smirnov probability is 25%) and (b) for double tagged events (Kolmogorov-Smirnov probability is 43%).

Figure 10

Invariant mass of pairs of untagged jets in signal region for alpgen $b\overline{b}+4$ light partons (cross), and for the background model (solid line): (a) for single tagged events (Kolmogorov-Smirnov probability is 90%), and (b) for double tagged events (Kolmogorov-Smirnov probability is 70%).

Figure 11

Event by event most probable top quark masses in the signal region for alpgen $b\overline{b}+4$ light partons (cross), and for the background model (solid line): (a) for single tagged events, and (b) for double tagged events.

Figure 12

The function fitting the top templates for $t\overline{t}$ events at nominal JES and for various hypotheses of the top quark mass in the case of events with one tagged jet. A similar parametrization is obtained for events with at least two tagged jets.

Figure 13

Top templates for (a) single tagged background events and for (b) double tagged background events.

Figure 14

The function fitting the dijet mass templates for $t\overline{t}$ events with $M_{\mathrm{top}}=170\mathrm{GeV}/c^2$ and various values of JES in the case of events with one tagged jet. A similar parametrization is obtained for events with at least two tagged jets.

Figure 15

Dijet mass templates for (a) single tagged background events and for (b) double tagged background events.

Figure 16

JES versus top quark mass plane. The points represent the reconstructed JES, ${\mathrm{JES}}_{\mathrm{out}}$, and top quark mass $M_t$ and have attached their corresponding statistical uncertainties, $\delta {\mathrm{JES}}_{\mathrm{out}}$ and $\delta M_t$. The vertical dashed lines correspond to the true values of the mass, while the horizontal lines correspond to the true values of JES. For a perfect reconstruction the points should sit right at the intersection of the dashed lines.

Figure 17

Distribution of parameter $C_m$ (Eq. (41)) as a function of JES.

Figure 18

Distribution of parameter $S_m$ (Eq. (41)) as a function of JES.

Figure 19

Distribution of parameter $C_j$ (Eq. (41)) as a function of $M_{\mathrm{top}}$.

Figure 20

Distribution of parameter $S_j$ (Eq. (41)) as a function of $M_{\mathrm{top}}$.

Figure 21

Pull means versus $M_{\mathrm{top}}$ in the case of the reconstruction of top quark mass in samples with ${\mathrm{JES}}_{\mathrm{true}}=0{\sigma }_c$. The continuous line represents the average pull mean and the dashed lines show the uncertainty on it.

Figure 22

Pull widths versus $M_{\mathrm{top}}$ in the case of the reconstruction of top quark mass in samples with ${\mathrm{JES}}_{\mathrm{true}}=0{\sigma }_c$. The continuous line represents the average pull width and the dashed lines show the uncertainty on it.

Figure 23

Pull means versus ${\mathrm{JES}}_{\mathrm{true}}$ in the case of the reconstruction of JES in samples with $M_{\mathrm{top}}=170\mathrm{GeV}/c^2$. The continuous line represents the average pull mean and the dashed lines show the uncertainty on it.

Figure 24

Pull widths versus ${\mathrm{JES}}_{\mathrm{true}}$ in the case of the reconstruction of JES in samples with $M_{\mathrm{top}}=170\mathrm{GeV}/c^2$. The continuous line represents the average pull width and the dashed lines show the uncertainty on it.

Figure 25

Expected uncertainty on top quark mass, $\delta M_t^{\mathrm{corr}}$, versus $M_{\mathrm{top}}$, for samples with ${\mathrm{JES}}_{\mathrm{true}}=0{\sigma }_c$. This uncertainty includes the uncertainty due to statistical effects and the systematic uncertainty due to jet energy scale.

Figure 26

Expected uncertainty on JES, $\delta {\mathrm{JES}}_{\mathrm{out}}$, versus ${\mathrm{JES}}_{\mathrm{true}}$, for samples with $M_{\mathrm{top}}=170\mathrm{GeV}/c^2$.

Figure 27

Reconstructed top mass for data (points), best $\mathrm{\text{signal}}+\mathrm{\text{background}}$ fit (light), and background shape from the best fit (dark): for (a) sample with only one secondary vertex tag, and (b) the sample with at least two secondary vertex tags.

Figure 28

Contours of the likelihood in the $M_{\mathrm{top}}$ and JES plane at a number of values of $\Delta \ln L$, the change in negative log-likelihood from its maximum.

Figure 29

Distribution of expected statistical uncertainty on $M_t$ (histogram) and the measured uncertainty (vertical line). In about 41% of simulated experiments a statistical uncertainty on the top quark mass smaller than in the experiment is found.