Measurements of jet observables sensitive to $b$-quark fragmentation in $t\overline{t}$ events at the LHC with the ATLAS detector

Several observables sensitive to the fragmentation of $b$ quarks into $b$ hadrons are measured using $36{\mathrm{fb}}^{-1}$ of $\sqrt{s}=13\mathrm{TeV}$ proton-proton collision data collected with the ATLAS detector at the LHC. Jets containing $b$ hadrons are obtained from a sample of dileptonic $t\overline{t}$ events, and the associated set of charged-particle tracks is separated into those from the primary $pp$ interaction vertex and those from the displaced $b$-decay secondary vertex. This division is used to construct observables that characterize the longitudinal and transverse momentum distributions of the $b$ hadron within the jet. The measurements have been corrected for detector effects and provide a test of heavy-quark-fragmentation modeling at the LHC in a system where the top-quark decay products are color connected to the proton beam remnants. The unfolded distributions are compared with the predictions of several modern Monte Carlo parton-shower generators and generator tunes, and a wide range of agreement with the data is observed, with $p$ values varying from $5\times {10}^{-4}$ to 0.98. These measurements complement similar measurements from $e^{+}{e}^{-}$ collider experiments in which the $b$ quarks originate from a color singlet $Z/{\gamma }^{*}$.

Figure 1

Comparison of detector-level probe-jet observable distributions between simulation and collision data: (a) probe-jet $\eta$ and (b) $p_{\mathrm{T}}$. The nominal non-$t\overline{t}$ background and fiducial $t\overline{t}\to e\mu bb$ predictions are shown in addition to the total prediction; the fiducial probe-jet histogram is not stacked on top of the non-$t\overline{t}$ background, in order to show the expected fraction of fiducial events. All systematic uncertainties are included in the uncertainty on the total prediction. The first and last histogram bins do not include the underflow and overflow entries.

Figure 2

Comparison of detector-level probe-jet observable distributions between simulation and collision data: (a) the probe-jet total charged $p_{\mathrm{T}}$ and (b) the number of tracks matched to the jet that originate from the primary vertex. The nominal non-$t\overline{t}$ background and fiducial $t\overline{t}\to e\mu bb$ predictions are shown in addition to the total prediction; the fiducial probe-jet histogram is not stacked on top of the non-$t\overline{t}$ background, in order to show the expected fraction of fiducial events. All systematic uncertainties are included in the uncertainty on the total prediction. The first and last histogram bins do not include the underflow and overflow entries.

Figure 3

Comparison of detector-level probe-jet observable distributions between simulation and collision data: (a) the invariant mass of all track constituents of the jet secondary vertex and (b) the relative momentum of the secondary vertex transverse to the jet charged momentum, $z_{\mathrm{rel},b}^{\mathrm{ch}}=|({\overrightarrow{p}}_b^{\mathrm{ch}}\times {\overrightarrow{p}}_{\text{jet}}^{\mathrm{ch}})|/|{\overrightarrow{p}}_{\text{jet}}^{\mathrm{ch}}{|}^2$. The nominal non-$t\overline{t}$ background and fiducial $t\overline{t}\to e\mu bb$ predictions are shown in addition to the total prediction; the fiducial probe-jet histogram is not stacked on top of the non-$t\overline{t}$ background, in order to show the expected fraction of fiducial events. All systematic uncertainties are included in the uncertainty on the total prediction. The first and last histogram bins do not include the underflow and overflow entries.

Figure 4

Comparison between simulation and collision data for detector-level observables of interest: (a) $z_{\mathrm{L},b}^{\mathrm{ch}}$, (b) $z_{\mathrm{T},b}^{\mathrm{ch}}$, (c) $\rho$, and (d) $n_b^{\mathrm{ch}}$. The “prior” curve corresponds to the nominal observable prediction before unfolding; only uncertainties due to background and detector modeling are included in the uncertainty band. The “posterior” curve corresponds to the posterior probability at detector-level given the observed data used to unfold to particle level. Good agreement is observed between the posterior distribution and the observed data, and the posterior bands reflect the data statistical uncertainty, indicating that the unfolding model is able to describe the detector-level data.

Figure 5

Comparison of particle-level observable distributions between MC and unfolded data: (a) $z_{\mathrm{L},b}^{\mathrm{ch}}$, (b) $z_{\mathrm{T},b}^{\mathrm{ch}}$, (c) $\rho$, and (d) $n_b^{\mathrm{ch}}$. The plotted data points correspond to the maximum likelihood for the particle-level cross section, and the gray uncertainty band in the lower panel of each figure shows the total uncertainty on the measured cross sections.

Figure 6

Sources of uncertainty in the $b$-jet fractions in each particle-level observable bin for (a) $z_{\mathrm{L},b}^{\mathrm{ch}}$, (b) $z_{\mathrm{T},b}^{\mathrm{ch}}$, (c) $\rho$, and (d) $n_b^{\mathrm{ch}}$.

Figure 7

Comparison of particle-level observables between powheg+pythia8 A14 variations and unfolded data for (a) $z_{\mathrm{L},b}^{\mathrm{ch}}$, (b) $z_{\mathrm{T},b}^{\mathrm{ch}}$, (c) $\rho$, and (d) $n_b^{\mathrm{ch}}$.

Figure 8

Comparison of particle-level observables between pythia8 tunes and unfolded data for (a) $z_{\mathrm{L},b}^{\mathrm{ch}}$, (b) $z_{\mathrm{T},b}^{\mathrm{ch}}$, (c) $\rho$, and (d) $n_b^{\mathrm{ch}}$.

Figure 9

Comparison of particle-level observables between powheg+herwig 7 versions and unfolded data for (a) $z_{\mathrm{L},b}^{\mathrm{ch}}$, (b) $z_{\mathrm{T},b}^{\mathrm{ch}}$, (c) $\rho$, and (d) $n_b^{\mathrm{ch}}$.

Figure 10

Comparison of particle-level observables between sherpa versions and unfolded data for (a) $z_{\mathrm{L},b}^{\mathrm{ch}}$, (b) $z_{\mathrm{T},b}^{\mathrm{ch}}$, (c) $\rho$, and (d) $n_b^{\mathrm{ch}}$.