Relative systematic uncertainties in the averaged cross-section for various differential distributions in the (a, b) inclusive and (c, d) collinear phase spaces. The upper solid line shows the total uncertainty in the measured cross-section in data, and includes correlations between the systematic components. The 'Others' category contains sub-dominant uncertainties arising from missing transverse momentum reconstruction and the jet-to-vertex fraction uncertainties.

Differential cross-section measurement in the inclusive phase space as function of (a) the minimum angular separation between the lepton and any jet with transverse momentum greater than 100 GeV (ΔR _min(ℓ,jet¹⁰⁰_i)), and (b) the ratio of W p_T to the closest-jet p_T (p_T^ℓν / p_T^{closest jet}). The measured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The bins around p_T^ℓν / p_T^{closest jet} equal to 1 are merged to be insensitive to the singularity that exists in the fixed-order MCFM calculation. Additionally, in (b), the central two bins from the MCFM prediction are merged due to a singularity in fixed-order calculations, which requires p_T resummation of the W + jets system. The two lower panels show the effect of NLO EW_virt as computed from Sherpa 2.2.11.

Differential cross-section measurement in the inclusive phase space as function of (a) the minimum angular separation between the lepton and any jet with transverse momentum greater than 100 GeV (ΔR _min(ℓ,jet¹⁰⁰_i)), and (b) the ratio of W p_T to the closest-jet p_T (p_T^ℓν / p_T^{closest jet}). The measured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The bins around p_T^ℓν / p_T^{closest jet} equal to 1 are merged to be insensitive to the singularity that exists in the fixed-order MCFM calculation. Additionally, in (b), the central two bins from the MCFM prediction are merged due to a singularity in fixed-order calculations, which requires p_T resummation of the W + jets system. The two lower panels show the effect of NLO EW_virt as computed from Sherpa 2.2.11.

Differential cross-section as a function of the invariant mass of the leading two jets (m_jj) in the inclusive, 2-jet phase space. The measured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The two lower panels show the effect of NLO EW_virt as computed from Sherpa 2.2.11.

Differential distributions at reconstruction level in the (a, c) electron or (b, d) muon channel for (a, b) inclusive and (c, d) collinear signal regions after the application of the background normalisation factors. The signal process is stacked above all background predictions. The bottom panel shows the ratio of the data to the total signal plus background prediction. The shaded band includes statistical and systematic uncertainties from signal and background processes added in quadrature.

Differential distributions at reconstruction level in the (a, c) electron or (b, d) muon channel for (a, b) inclusive and (c, d) collinear signal regions after the application of the background normalisation factors. The signal process is stacked above all background predictions. The bottom panel shows the ratio of the data to the total signal plus background prediction. The shaded band includes statistical and systematic uncertainties from signal and background processes added in quadrature.

Relative systematic uncertainties in the averaged cross-section for various differential distributions in the (a, b) inclusive and (c, d) collinear phase spaces. The upper solid line shows the total uncertainty in the measured cross-section in data, and includes correlations between the systematic components. The 'Others' category contains sub-dominant uncertainties arising from missing transverse momentum reconstruction and the jet-to-vertex fraction uncertainties.

Relative systematic uncertainties in the averaged cross-section for various differential distributions in the (a, b) inclusive and (c, d) collinear phase spaces. The upper solid line shows the total uncertainty in the measured cross-section in data, and includes correlations between the systematic components. The 'Others' category contains sub-dominant uncertainties arising from missing transverse momentum reconstruction and the jet-to-vertex fraction uncertainties.

Differential cross-section as a function of (a) the leading p_T ^jet, (b) the inclusive jet multiplicity, (c) S_T, and (d) p^ℓν_T in the collinear phase-space. The measured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The two lower panels show the effect of NLO EW_virt as computed from Sherpa 2.2.11.

Differential cross-section as a function of (a) the leading p_T ^jet, (b) the inclusive jet multiplicity, (c) S_T, and (d) p^ℓν_T in the collinear phase-space. The measured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The two lower panels show the effect of NLO EW_virt as computed from Sherpa 2.2.11.

Differential cross-section as a function of (a) the leading p_T ^jet, (b) the inclusive jet multiplicity, (c) S_T, and (d) p^ℓν_T in the collinear phase-space. The measured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The two lower panels show the effect of NLO EW_virt as computed from Sherpa 2.2.11.

Differential cross-section as a function of (a) the leading p_T ^jet, (b) the inclusive jet multiplicity, (c) S_T, and (d) p^ℓν_T in the collinear phase-space. The measured cross-sections in data and their statistical uncertainty are shown by the solid dots and error bars, while the shaded band shows the systematic and statistical uncertainties added in quadrature. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text. The two lower panels show the effect of NLO EW_virt as computed from Sherpa 2.2.11.

Measured fiducial cross-sections in each signal region. The measured cross-sections in data and their total uncertainty are shown by the solid dots and error band. Various theoretical predictions are overlaid and compared with the data in the lower panel. Uncertainties in predictions accurate to NLO precision include QCD scale and PDF uncertainties, while predictions that add NLO EW_virt (electroweak) corrections show uncertainties only due to different electroweak combination schemes. Uncertainties in predictions accurate at fixed-order NNLO precision are derived primarily from MCFM, do not include PDF variations, with an additional extrapolation from the Sherpa QCD with EW_virt prediction to assess the effects of higher-order electroweak corrections. On predictions with EW_virt corrections, the total uncertainty is shown as a shaded region, while the electroweak correction is overlaid with an error bar line.

Differential distributions at reconstructed-level comparing data with the background model in the (a) tt̄ muon, (b) Z + jets muon, and (c) multijet electron control selections. All backgrounds and signal samples are stacked to produce the figures. The data points are shown as solid dots with their corresponding statistical uncertainty, while the total background model uncertainty is shown by the shaded band. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text.

Differential distributions at reconstructed-level comparing data with the background model in the multijet electron validation region for (a) the transverse momentum of the leading jet and (b) the transverse momentum of the lepton–neutrino system. All backgrounds and signal samples are stacked to produce the figures. The data points are shown as solid dots with their corresponding statistical uncertainty, while the total background model uncertainty is shown by the shaded band. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text.

Differential distributions at reconstructed-level comparing data with the background model in the multijet electron validation region for (a) the transverse momentum of the leading jet and (b) the transverse momentum of the lepton–neutrino system. All backgrounds and signal samples are stacked to produce the figures. The data points are shown as solid dots with their corresponding statistical uncertainty, while the total background model uncertainty is shown by the shaded band. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text.

Differential distributions at reconstructed-level comparing data with the background model in the (a) tt̄ muon, (b) Z + jets muon, and (c) multijet electron control selections. All backgrounds and signal samples are stacked to produce the figures. The data points are shown as solid dots with their corresponding statistical uncertainty, while the total background model uncertainty is shown by the shaded band. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text.

Differential distributions at reconstructed-level comparing data with the background model in the (a) tt̄ muon, (b) Z + jets muon, and (c) multijet electron control selections. All backgrounds and signal samples are stacked to produce the figures. The data points are shown as solid dots with their corresponding statistical uncertainty, while the total background model uncertainty is shown by the shaded band. Errors bars on the theory prediction include theoretical uncertainties as discussed in the text.

Response matrices from the Sherpa 2.2.11 event generator for (a) ΔR _min(ℓ,jet¹⁰⁰_i) in the inclusive electron selection, and (b) transverse momentum of the leading jet in the collinear muon selection. The sum of the entries in each reconstructed bin (column) are normalised to unity.

Response matrices from the Sherpa 2.2.11 event generator for (a) ΔR _min(ℓ,jet¹⁰⁰_i) in the inclusive electron selection, and (b) transverse momentum of the leading jet in the collinear muon selection. The sum of the entries in each reconstructed bin (column) are normalised to unity.

Cross section of midrapidity charged-hadron production from $p$ + $p$ collisions at $\sqrt{s}$ = 62.4 GeV as a function of $p_T$ for positive and negative hadrons.

Double-helicity asymmetries and the statistical uncertainties as a function of $p_T$ for positive and negative inclusive charged hadrons from $p$ + $p$ collisions at $\sqrt{s}$ = 62.4 GeV.