CMS-TOP-21-008

CMS-TOP-21-008 ; CERN-EP-2022-112
Measurement of the top quark pole mass using $\mathrm{t\bar{t}}$ +jet events in the dilepton final state in proton-proton collisions at $\sqrt{s} =$ 13 TeV
CMS Collaboration
5 July 2022
JHEP 07 (2023) 077
Abstract: A measurement of the top quark pole mass ${{m_{\mathrm{t}}} ^{\text{pole}}}$ in events where a top quark-antiquark pair ( $\mathrm{t\bar{t}}$ ) is produced in association with at least one additional jet ( $\mathrm{t\bar{t}}$ +jet) is presented. This analysis is performed using proton-proton collision data at $\sqrt{s} =$ 13 TeV collected by the CMS experiment at the CERN LHC, corresponding to a total integrated luminosity of 36.3 fb $^{-1}$ . Events with two opposite-sign leptons in the final state (e $^{+}$ e $^{-}$ , $\mu^{+}\mu^{-}$ , e $^{\pm}\mu^{\mp}$ ) are analyzed. The reconstruction of the main observable and the event classification are optimized using multivariate analysis techniques based on machine learning. The production cross section is measured as a function of the inverse of the invariant mass of the $\mathrm{t\bar{t}}$ +jet system at the parton level using a maximum likelihood unfolding. Given a reference parton distribution function (PDF), the top quark pole mass is extracted using the theoretical predictions at next-to-leading order. For the ABMP16NLO PDF, this results in ${{m_{\mathrm{t}}} ^{\text{pole}}} =$ 172.94 $\pm$ 1.37 GeV.
Links: e-print arXiv:2207.02270 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; HepData record ; CADI line (restricted) ;

Figures & Tables	Summary	References	CMS Publications

Figures
png pdf	Figure 1: The observed (points) and predicted (stacked histograms) signal and background yields as a function of the leading (upper left) and subleading (upper right) lepton ${p_{\mathrm {T}}}$ and leading (lower left) and third-highest (lower right) jet ${p_{\mathrm {T}}}$ after applying the signal selection. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panels show the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 1-a: The observed (points) and predicted (stacked histograms) signal and background yields as a function of the leading lepton ${p_{\mathrm {T}}}$ after applying the signal selection. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 1-b: The observed (points) and predicted (stacked histograms) signal and background yields as a function of the subleading lepton ${p_{\mathrm {T}}}$ after applying the signal selection. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 1-c: The observed (points) and predicted (stacked histograms) signal and background yields as a function of the leading jet ${p_{\mathrm {T}}}$ after applying the signal selection. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 1-d: The observed (points) and predicted (stacked histograms) signal and background yields as a function of the third-highest jet ${p_{\mathrm {T}}}$ after applying the signal selection. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 2: The observed (points) and predicted (stacked histograms) signal and background yields as a function of the jet (left), and b jet (right) multiplicities, after applying the signal selection. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panels show the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 2-a: The observed (points) and predicted (stacked histograms) signal and background yields as a function of the jet multiplicity, after applying the signal selection. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 2-b: The observed (points) and predicted (stacked histograms) signal and background yields as a function of the b jet multiplicity, after applying the signal selection. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 3: The correlation between ${\rho _{\text {true}}}$ and ${\rho _{\text {reco}}}$ is shown for the regression NN reconstruction method (left). The ${\rho _{\text {reco}}}$ resolution, defined in the text, as a function of ${\rho _{\text {true}}}$ (right) for the full (blue line) and loose (orange line) kinematic reconstructions and the regression NN (red line) methods. The number of events per bin in the left plot is shown by the color scale.
png pdf	Figure 3-a: The correlation between ${\rho _{\text {true}}}$ and ${\rho _{\text {reco}}}$ is shown for the regression NN reconstruction method. The number of events per bin is shown by the color scale.
png pdf	Figure 3-b: The ${\rho _{\text {reco}}}$ resolution, defined in the text, as a function of ${\rho _{\text {true}}}$ for the full (blue line) and loose (orange line) kinematic reconstructions and the regression NN (red line) methods.
png pdf	Figure 4: The observed (points) and MC predicted (stacked histograms) signal and background yields as a function of ${\rho _{\text {reco}}}$ as determined by the NN reconstruction method for the e $^{\pm} \mu^{\mp}$ (left) and same-flavor dilepton channels (right). The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panels show the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 4-a: The observed (points) and MC predicted (stacked histograms) signal and background yields as a function of ${\rho _{\text {reco}}}$ as determined by the NN reconstruction method for the e $^{\pm} \mu^{\mp}$ channel. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 4-b: The observed (points) and MC predicted (stacked histograms) signal and background yields as a function of ${\rho _{\text {reco}}}$ as determined by the NN reconstruction method for the same-flavor dilepton channel. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 5: The observed (points) and MC predicted (stacked histograms) signal and background yields as a function of the signal (left) and ${\mathrm{t} {}\mathrm{\bar{t}}}$ +0 jet background (right) output node score of the classifier NN. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panels show the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 5-a: The observed (points) and MC predicted (stacked histograms) signal and background yields as a function of the signal output node score of the classifier NN. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 5-b: The observed (points) and MC predicted (stacked histograms) signal and background yields as a function of the ${\mathrm{t} {}\mathrm{\bar{t}}}$ +0 jet background output node score of the classifier NN. The vertical bars on the points represent the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel shows the ratio of the data to the sum of the signal and background predictions.
png pdf	Figure 6: The distributions from data (points) and simulated signal and background (colored histograms) used in the maximum likelihood fits before the fit to the data. The distributions are shown for each dilepton type and each event category, where the x-axis label "mjnb'' refers to events with m jets and n b jets. The vertical bars on the points show the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel gives the ratio of the data to the sum of the simulated predictions.
png pdf	Figure 7: The distributions from data (points) and simulated signal and background (colored histograms) used in the maximum likelihood fits after the fit to the data. The distributions are shown for each dilepton type and each event category, where the x-axis label " $m$ j $n$ b'' refers to events with $m$ jets and $n$ b jets. The vertical bars on the points show the statistical uncertainty in the data. The hatched band represents the total uncertainty in the sum of the simulated signal and background predictions. The lower panel gives the ratio of the data to the sum of the simulated predictions.
png pdf	Figure 8: The absolute (left) and normalized (right) ${\mathrm{t} \mathrm{\bar{t}}}$ +jet differential cross section as a function of $\rho$ for the data (points) and theoretical predictions described in the text using the AMBP16NLO PDF set from the NLO MC with three different ${m_{\mathrm{t}}}$ values and from the POWHEG (POW) + PYTHIA 8 (PYT) calculations (lines). The vertical bars on the points show the statistical uncertainty in the data and the shaded region represents the total uncertainty in the measurement. The lower panels give the ratio of the predictions to the data.
png pdf	Figure 8-a: The absolute ${\mathrm{t} \mathrm{\bar{t}}}$ +jet differential cross section as a function of $\rho$ for the data (points) and theoretical predictions described in the text using the AMBP16NLO PDF set from the NLO MC with three different ${m_{\mathrm{t}}}$ values and from the POWHEG (POW) + PYTHIA 8 (PYT) calculations (lines). The vertical bars on the points show the statistical uncertainty in the data and the shaded region represents the total uncertainty in the measurement. The lower panel gives the ratio of the predictions to the data.
png pdf	Figure 8-b: The normalized ${\mathrm{t} \mathrm{\bar{t}}}$ +jet differential cross section as a function of $\rho$ for the data (points) and theoretical predictions described in the text using the AMBP16NLO PDF set from the NLO MC with three different ${m_{\mathrm{t}}}$ values and from the POWHEG (POW) + PYTHIA 8 (PYT) calculations (lines). The vertical bars on the points show the statistical uncertainty in the data and the shaded region represents the total uncertainty in the measurement. The lower panel gives the ratio of the predictions to the data.
png pdf	Figure 9: The fitted nuisance-parameter values and their impacts ${\Delta {\hat{r}_k}}$ on the signal strengths ${\hat{r}_k}$ from the fit to the data, ordered by their relative summed impact. Only the 30 highest ranked parameters are shown. The resulting fitted values of ${\hat{r}_k}$ and their total uncertainties are also given. The nuisance-parameter values ( ${\hat{\theta}}$ , black lines) are shown in comparison to their input values ${\theta _0}$ before the fit and relative to their uncertainty ${\Delta \theta}$ . The impact ${\Delta {\hat{r}_k}}$ for each nuisance parameter is the difference between the nominal best fit value of ${r_k}$ and the best fit value when only that nuisance parameter is set to its best fit value ${\hat{\theta}}$ while all others are left free. The red and blue lines correspond to the variation in ${\Delta {\hat{r}_k}}$ when the nuisance parameter is varied up and down by its fitted uncertainty ( ${\Delta \theta}$ ), respectively. The corresponding gray, red, and blue regions show the expected values from fits to pseudo-data. For the nuisance parameters associated with the ${\mathrm{t} \mathrm{\bar{t}}}$ +0-jet normalization and ${{m_{\mathrm{t}}} ^{\text {MC}}}$ , the values after the fit to the data are given, because no prior pdf is assigned.
png pdf	Figure 10: Left: The ${\chi ^2}$ values versus ${{m_{\mathrm{t}}} ^{\text {pole}}}$ from the fit of the measured normalized ${\mathrm{t} \mathrm{\bar{t}}}$ +jet differential cross sections to the theoretical predictions using the ABMP16NLO (blue points) and CT18NLO (red points) PDF sets. The minimum ${\chi ^2}$ value and the number of degrees of freedom (ndof) are given for each fit. Right: The measured normalized ${\mathrm{t} \mathrm{\bar{t}}}$ +jet differential cross section (points) as a function of $\rho$ , compared to the predictions using the two PDF sets and the corresponding best fit values for ${{m_{\mathrm{t}}} ^{\text {pole}}}$ (hatched bands). The lower panel gives the ratio of the theoretical predictions to the measured values. For both panels, the vertical bars on the points show the statistical uncertainty in the data, the height of the hatched bands represent the theoretical uncertainties in the predictions, and the gray band gives the total uncertainty in the measured cross section.
png pdf	Figure 10-a: The ${\chi ^2}$ values versus ${{m_{\mathrm{t}}} ^{\text {pole}}}$ from the fit of the measured normalized ${\mathrm{t} \mathrm{\bar{t}}}$ +jet differential cross sections to the theoretical predictions using the ABMP16NLO (blue points) and CT18NLO (red points) PDF sets. The minimum ${\chi ^2}$ value and the number of degrees of freedom (ndof) are given for each fit.
png pdf	Figure 10-b: The measured normalized ${\mathrm{t} \mathrm{\bar{t}}}$ +jet differential cross section (points) as a function of $\rho$ , compared to the predictions using the two PDF sets and the corresponding best fit values for ${{m_{\mathrm{t}}} ^{\text {pole}}}$ (hatched bands). The lower panel gives the ratio of the theoretical predictions to the measured values. For both panels, the vertical bars on the points show the statistical uncertainty in the data, the height of the hatched bands represent the theoretical uncertainties in the predictions, and the gray band gives the total uncertainty in the measured cross section.

Tables
png pdf	Table 1: A list of the event categories and distributions used in the maximum likelihood fit.
png pdf	Table 2: The relative uncertainties $\Delta {{{\sigma _{{{\mathrm{t} {}\mathrm{\bar{t}}} \text {+jet}}}} ^k}}$ in the parton-level cross section values ${{\sigma _{{{\mathrm{t} {}\mathrm{\bar{t}}} \text {+jet}}}} ^k}$ and their sources in each bin $k$ of the $\rho$ distribution. The statistical uncertainty is evaluated by keeping all nuisance parameters fixed to their values after the fit to data. The breakdown of the uncertainty is obtained by repeating the fit after fixing all but the nuisance parameters related to the components under consideration to their fitted values. The partial uncertainty is then estimated by subtracting the statistical component from the total uncertainty obtained with this procedure. The quadratic sum of the contributions is different from the total uncertainty because of correlations between the nuisance parameters.

Summary

Measurements are presented of the normalized differential cross section of top quark-antiquark pair (

$\mathrm{t\bar{t}}$ ) production in association with at least one additional jet as a function of the inverse of the invariant mass of the

$\mathrm{t\bar{t}}$ +jet system

$\rho=2{m_0} /{m_{\mathrm{t\bar{t}}+\text{jet}}}$ , with the scaling constant

${m_0} =$ 170 GeV. Proton-proton collision data collected by the CMS experiment at the CERN LHC at a center-of-mass energy of 13 TeV are used, corresponding to an integrated luminosity of 36.3 fb

$^{-1}$ . Events in the dilepton decay channel are considered, and a novel multivariate analysis technique is applied to maximize the sensitivity to the signal process. The differential cross section is measured at the parton level using a maximum likelihood fit to final-state observables, where all systematic uncertainties are profiled. The value of the top quark pole mass

${{m_{\mathrm{t}}} ^{\text{pole}}}$ is extracted by comparing the measured

$\mathrm{t\bar{t}}$ +jet normalized differential cross section as a function of

$\rho$ to theoretical predictions at next-to-leading order in quantum chromodynamics, obtained with two sets of parton distribution functions. The

${{m_{\mathrm{t}}} ^{\text{pole}}}$ values is determined to be 172.94

$\pm$ 1.37 GeV and 172.16

$\pm$ 1.44 GeV using the ABMP16NLO and CT18NLO parton distribution functions, respectively. Here, the uncertainties shown include the total statistical and systematic uncertainties including extrapolation uncertainties, and the theoretical uncertainties from the parton distribution functions and the matrix-element scales. The results are in good agreement with previous measurements.

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