Measurement of the top quark mass using a profile likelihood approach with the lepton + jets final states in proton-proton collisions at s=13TeV

Abstract

The mass of the top quark is measured in 36.3${\text{fb}}^{-1}$ of LHC proton-proton collision data collected with the CMS detector at $\sqrt{s}=13\text{Te}\text{V}$. The measurement uses a sample of top quark pair candidate events containing one isolated electron or muon and at least four jets in the final state. For each event, the mass is reconstructed from a kinematic fit of the decay products to a top quark pair hypothesis. A profile likelihood method is applied using up to four observables per event to extract the top quark mass. The top quark mass is measured to be $171.77\pm 0.37\text{Ge}\text{V}$. This approach significantly improves the precision over previous measurements.

Fig. 1

The top quark mass distribution before (upper) and after (lower) the $P_{\text{gof}}>0.2$ selection and the kinematic fit. For the simulated $\text{t}\overline{\text{t}}$ events, the jet-parton assignments are classified as correct, wrong, and unmatched permutations, as described in the text. The uncertainty bands contain statistical uncertainties in the simulation, normalization uncertainties due to luminosity and cross section, jet energy correction uncertainties, and all uncertainties that are evaluated from event-based weights. A large part of the depicted uncertainties on the expected event yields are correlated. The lower panels show the ratio of data to the prediction. A value of $m_{\text{t}}^{\text{gen}}=172.5\text{Ge}\text{V}$ is used in the simulation

Fig. 2

The distributions of the reconstructed W boson mass for the $P_{\text{gof}}>0.2$ category (upper) and of the invariant mass of the lepton and the jet assigned to the semileptonic decaying top quark for the $P_{\text{gof}}<0.2$ category (lower). The uncertainty bands contain statistical uncertainties in the simulation, normalization uncertainties due to luminosity and cross section, jet energy correction uncertainties, and all uncertainties that are evaluated from event-based weights. A large part of the depicted uncertainties on the expected event yields are correlated. The lower panels show the ratio of data to the prediction. A value of $m_{\text{t}}^{\text{gen}}=172.5\text{Ge}\text{V}$ is used in the simulation

Fig. 3

The distributions of $m_{\ell \text{b}}^{\text{reco}}/m_{\text{t}}^{\text{fit}}$ (upper) and of $R_{\text{bq}}^{\text{reco}}$ (lower), both for the $P_{\text{gof}}>0.2$ category. The uncertainty bands contain statistical uncertainties in the simulation, normalization uncertainties due to luminosity and cross section, jet energy correction uncertainties, and all uncertainties that are evaluated from event-based weights. A large part of the depicted uncertainties on the expected event yields are correlated. The lower panels show the ratio of data to the prediction. A value of $m_{\text{t}}^{\text{gen}}=172.5\text{Ge}\text{V}$ is used in the simulation

Fig. 4

Upper: Comparison of the expected total uncertainty in $m_{\text{t}}$ in the combined lepton + jets channel and for the different observable-category sets defined in Table 1. Lower: The difference between the measured and generated $m_{\text{t}}$ values, divided by the uncertainty reported by the fit from pseudo-experiments without (red) or with (blue) the statistical nuisance parameters $\overrightarrow{\beta }$ and $\Omega$ in the 5D ML fit. Also included in the legend are the $\mu$ and $\sigma$ parameters of Gaussian functions (red and blue lines) fit to the histograms

Fig. 5

Measurement of $m_{\text{t}}$ in the three different channels for the different sets of observables and categories as defined in Table 1

Fig. 6

Distribution of $m_{\text{t}}^{\text{fit}}$ (upper) and the additional observables (lower) that are the input to the 5D ML fit and their post-fit probability density functions for the combined fit to the electron+jets (left) and muon+jets (right) channels. For the additional observables results, the events in each bin are divided by the bin width. The lower panels show the ratio of data and post-fit template values. The green and yellow bands represent the 68 and 95% confidence levels in the fit uncertainty

Fig. 7

Measurement of $m_{\text{t}}$ in the combined lepton + jets channel using the 5D set of observables and categories. The left plot shows the post-fit pulls on the most important nuisance parameters and the numbers quote the post-fit uncertainty in the nuisance parameter. The right plot shows their pre-fit (lighter colored bars) and post-fit impacts (darker colored bars) on $m_{\text{t}}$ for up (red) and down (blue) variations. The post-fit impacts of systematic effects that are affected by the limited size of simulation samples include the contribution from the additional statistical nuisance parameters accounting for the effect. The size of the additional contribution from the statistical nuisance parameters is called MC stat. and shown as gray-dotted areas. The average of the post-fit impacts in $\text{Ge}\text{V}$ for up and down variations is printed on the right. The rows are sorted by the size of the averaged post-fit impact. The statistical uncertainty in $m_{\text{t}}$ is depicted in the corresponding row

Fig. 8

Dependence of the 5D result on the assumed correlation ${\rho }_{\text{FSR}}$ between the FSR PS scales in the lepton + jets channel