Measurement of the top quark mass using charged particles in $pp$ collisions at $\sqrt{s}=8\mathrm{TeV}$

A novel technique for measuring the mass of the top quark that uses only the kinematic properties of its charged decay products is presented. Top quark pair events with final states with one or two charged leptons and hadronic jets are selected from the data set of 8 TeV proton-proton collisions, corresponding to an integrated luminosity of $19.7{\mathrm{fb}}^{-1}$. By reconstructing secondary vertices inside the selected jets and computing the invariant mass of the system formed by the secondary vertex and an isolated lepton, an observable is constructed that is sensitive to the top quark mass that is expected to be robust against the energy scale of hadronic jets. The main theoretical systematic uncertainties, concerning the modeling of the fragmentation and hadronization of $b$ quarks and the reconstruction of secondary vertices from the decays of $b$ hadrons, are studied. A top quark mass of $173.68\pm 0.20{(\mathrm{stat})}_{-0.97}^{+1.58}(\mathrm{syst})\mathrm{GeV}$ is measured. The overall systematic uncertainty is dominated by the uncertainty in the $b$ quark fragmentation and the modeling of kinematic properties of the top quark.

Figure 1

Distributions of the transverse decay length of secondary vertices with respect to the primary vertex in dilepton (top) and semileptonic channels (bottom). The expectations from simulation and estimates from the data for the multijet background are compared to the reconstructed data. The last bin contains the overflow events.

Figure 2

Distributions of the ratio of the transverse momentum of secondary vertices to the charged component of the jet with three, four, and five tracks (from left to right) in $Z+\text{jets}$ dilepton (top) and $t\overline{t}$ dilepton events (bottom), compared to the expected shape using the ${\mathrm{Z}2}^{*}$ LEP $r_b$ fragmentation tune. In each plot, the top panels compare the average of the distribution measured in data and its statistical uncertainty (shaded area) with that expected from different choices of the $b$ quark fragmentation function in pythia. For ${\mathrm{Z}2}^{*}$ LEP $r_b$, the error bar represents the $\pm$ variations of ${\mathrm{Z}2}^{*}$ LEP $r_b$.

Figure 3

Fits to the invariant mass peaks of the three considered charmed mesons in $t\overline{t}$ events in the data, as described in the text: $J/\psi$ (left), $D^0$ (middle), and $D^{*}{(2010)}^{+}$ (right).

Figure 4

Distribution of the relative transverse momentum of $J/\psi$ (left), $D^0$ (middle), and $D^{*}{(2010)}^{+}$ (right) meson candidates with respect to the charged components of the jet in $t\overline{t}$ events for the data and the nominal ${\mathrm{Z}2}^{*}$ LEP $r_b$ fragmentation function. The top panels show the average of the distributions observed in the data and its statistical uncertainty (shaded area), as well as expectations obtained with different $b$ quark fragmentation functions and with an alternative generator setup using herwig 6 with the AUET2 tune.

Figure 5

Lepton-SV invariant mass distribution for a combination of all five channels, for a simulation of three different top quark mass values (166.5, 172.5, and 178.5 GeV), and the observed data distribution. Note that all possible lepton-vertex combinations for each event enter the distribution.

Figure 6

Template fits to the observed $m_{\mathrm{svl}}$ distributions for the three dilepton channels ($e\mu$, $ee$, $\mu \mu$ from top to bottom row), and for exactly three, four, and five tracks assigned to the secondary vertex (from left to right column). The top panels show the bin-by-bin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative log-likelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category.

Figure 7

Template fits to the observed $m_{\mathrm{svl}}$ distributions for the semileptonic channels ($e$ and $\mu$ from top to bottom row), and for exactly three, four, and five tracks assigned to the secondary vertex (from left to right column). The top panels show the bin-by-bin difference between the observed data and the fit result, divided by the statistical uncertainty (pull). The inset shows the scan of the negative log-likelihood as a function of the calibrated top quark mass, accounting only for the statistical uncertainty, when performed exclusively in each event category.

Figure 8

Variation of the simulated $m_{\mathrm{svl}}$ shape with systematic effects: reweighting of the simulated top quark $p_{\mathrm{T}}$ shape to the observed distribution, separately for correct and wrong lepton-vertex pairings (top); and different $b$ quark fragmentation function shapes (bottom). The bottom panels in the two plots show the ratios between the top quark $p_{\mathrm{T}}$ reweighted and nominal shapes for the correct and wrong pairings (top), and between the various fragmentation models and the central ${\mathrm{Z}2}^{*}$ LEP $r_b$ tune (bottom).

Figure 9

Impact of the average $b$ quark fragmentation, $⟨p_{\mathrm{T}}(B)/p_{\mathrm{T}}(b)⟩$, on the extracted $m_t$ value, for various different fragmentation shapes. The horizontal band represents the contribution of the $b$ quark fragmentation model to the systematic uncertainty in the measurement of the top quark mass, which is estimated from the ${\mathrm{Z}2}^{*}$ LEP $r_b$ ${}^{\pm }$ variations. A linear fit to the effects on the different variations (the line in the figure) suggests a relative change in the measured top quark mass of 0.61 GeV for each percent change in average momentum transfer.

Figure 10

Results of the $m_t$ measurement in the individual channels and their combination. Smaller and thicker error bars show the statistical uncertainty, whereas the thinner bars show the combined statistical and systematic uncertainty. The right panel shows the extracted mass when performing the analysis in separate track multiplicity bins, combining the lepton channels.