Evidence for the charge asymmetry in $pp \rightarrow t\bar{t}$ production at $\sqrt{s}= 13$ TeV with the ATLAS detector

The ATLAS collaboration Aad, G. ; Abbott, B. ; Abbott, D.C. ; et al.
JHEP 08 (2023) 077, 2023.
Inspire Record 2141752 DOI 10.17182/hepdata.132116

Inclusive and differential measurements of the top-antitop ($t\bar{t}$) charge asymmetry $A_\text{C}^{t\bar{t}}$ and the leptonic asymmetry $A_\text{C}^{\ell\bar{\ell}}$ are presented in proton-proton collisions at $\sqrt{s} = 13$ TeV recorded by the ATLAS experiment at the CERN Large Hadron Collider. The measurement uses the complete Run 2 dataset, corresponding to an integrated luminosity of 139 fb$^{-1}$, combines data in the single-lepton and dilepton channels, and employs reconstruction techniques adapted to both the resolved and boosted topologies. A Bayesian unfolding procedure is performed to correct for detector resolution and acceptance effects. The combined inclusive $t\bar{t}$ charge asymmetry is measured to be $A_\text{C}^{t\bar{t}} = 0.0068 \pm 0.0015$, which differs from zero by 4.7 standard deviations. Differential measurements are performed as a function of the invariant mass, transverse momentum and longitudinal boost of the $t\bar{t}$ system. Both the inclusive and differential measurements are found to be compatible with the Standard Model predictions, at next-to-next-to-leading order in quantum chromodynamics perturbation theory with next-to-leading-order electroweak corrections. The measurements are interpreted in the framework of the Standard Model effective field theory, placing competitive bounds on several Wilson coefficients.

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The unfolded inclusive charge asymmetry. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed, and the impact of the linear term of the Wilson coefficient on the $A_C^{t\bar{t}}$ prediction is shown for two different values. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.

The unfolded differential charge asymmetry as a function of the invariant mass of the top pair system. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed, and the impact of the linear term of the Wilson coefficient on the $A_C^{t\bar{t}}$ prediction is shown for two different values. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.

The unfolded differential charge asymmetry as a function of the transverse momentum of the top pair system. The measured values are given with statistical and systematic uncertainties. The SM theory predictions calculated at NNLO in QCD and NLO in EW theory are listed. The scale uncertainty is obtained by varying renormalisation and factorisation scales independently by a factor of 2 or 0.5 around $\mu_0$ to calculate the maximum and minimum value of the asymmetry, respectively. The nominal value $\mu_0$ is chosen as $H_T/4$. The variations in which one scale is multiplied by 2 while the other scale is divided by 2 are excluded. Finally, the scale and MC integration uncertainties are added in quadrature.

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A search for resonant and non-resonant Higgs boson pair production in the ${b\bar{b}\tau^+\tau^-}$ decay channel in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

The ATLAS collaboration Aaboud, Morad ; Aad, Georges ; Abbott, Brad ; et al.
Phys.Rev.Lett. 121 (2018) 191801, 2018.
Inspire Record 1684645 DOI 10.17182/hepdata.83539

A search for resonant and non-resonant pair production of Higgs bosons in the $b\bar{b}\tau^+\tau^-$ final state is presented. The search uses 36.1 fb$^{-1}$ of $pp$ collision data with $\sqrt{s}= 13$ TeV recorded by the ATLAS experiment at the LHC in 2015 and 2016. The semileptonic and fully hadronic decays of the $\tau$-lepton pair are considered. No significant excess above the expected background is observed in the data. The cross-section times branching ratio for non-resonant Higgs boson pair production is constrained to be less than 30.9 fb, 12.7 times the Standard Model expectation, at 95% confidence level. The data are also analyzed to probe resonant Higgs boson pair production, constraining a model with an extended Higgs sector based on two doublets and a Randall-Sundrum bulk graviton model. Upper limits are placed on the resonant Higgs boson pair production cross-section times branching ratio, excluding resonances $X$ in the mass range $305~{\rm GeV} < m_X < 402~{\rm GeV}$ in the simplified hMSSM minimal supersymmetric model for $\tan\beta=2$ and excluding bulk Randall-Sundrum gravitons $G_{\mathrm{KK}}$ in the mass range $325~{\rm GeV} < m_{G_{\mathrm{KK}}} < 885~{\rm GeV}$ for $k/\overline{M}_{\mathrm{Pl}} = 1$.

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Observed and expected limits at 95% CL on the cross-sections of RS Graviton to HH for k/MPl = 1 process

Observed and expected limits at 95% CL on the cross-sections of RS Graviton to HH for k/MPl = 2 process

Observed and expected limits at 95% CL on the cross-sections of hMSSM scalar X to HH process

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Search for a heavy Higgs boson decaying into a $Z$ boson and another heavy Higgs boson in the $\ell\ell bb$ final state in $pp$ collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

The ATLAS collaboration Aaboud, Morad ; Aad, Georges ; Abbott, Brad ; et al.
Phys.Lett.B 783 (2018) 392-414, 2018.
Inspire Record 1665828 DOI 10.17182/hepdata.82527

A search for a heavy neutral Higgs boson, $A$, decaying into a $Z$ boson and another heavy Higgs boson, $H$, is performed using a data sample corresponding to an integrated luminosity of 36.1 fb$^{-1}$ from proton-proton collisions at $\sqrt{s} = 13$ TeV recorded in 2015 and 2016 by the ATLAS detector at the Large Hadron Collider. The search considers the $Z$ boson decaying to electrons or muons and the $H$ boson into a pair of $b$-quarks. No evidence for the production of an $A$ boson is found. Considering each production process separately, the 95% confidence-level upper limits on the $pp\rightarrow A\rightarrow ZH$ production cross-section times the branching ratio $H\rightarrow bb$ are in the range of 14-830 fb for the gluon-gluon fusion process and 26-570 fb for the $b$-associated process for the mass ranges 130-700 GeV of the $H$ boson and process for the mass ranges 130-700 GeV of the $H$ boson and 230-800 GeV of the $A$ boson. The results are interpreted in the context of the two-Higgs-doublet model.

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The signal efficiency for the production modes (gluon-gluon fusion and b-associated production) and the signal regions used in the analysis. The efficiency denominator has the total number of generated MC events. The numerator includes the events passing the full signal region selection, including the mbb window cuts. The table shows for each signal mass pair (mA, mH) 3 efficiencies corresponding to the two production modes in the two categories, 2tag and 3tag. These corresponds to "nb = 2 category" and "nb >= 3 category", respectively, of the preprint. No numbers for gluon-gluon fusion in the 3tag category are provided since those are not used in the analysis. The efficiencies are given in fractions.

The cross section times BR(A->ZH) times BR(H->bb) limits for a narrow width A boson produced via gluon-gluon fusion. For each signal point, characterised by the mass pair (mA, mH), two limits are provided, the observed and the expected. The result refers to the nb=2 category only.

The cross section times BR(A->ZH) times BR(H->bb) limits for a narrow width A boson produced in association with b-quarks. For each signal point, characterised by the mass pair (mA, mH), two limits are provided, the observed and the expected. The result refers to the combination of the nb=2 and nb>=3 categories.

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Search for squarks and gluinos in events with hadronically decaying tau leptons, jets and missing transverse momentum in proton-proton collisions at $\sqrt{s}=13$ TeV recorded with the ATLAS detector

The ATLAS collaboration Aaboud, Morad ; Aad, Georges ; Abbott, Brad ; et al.
Eur.Phys.J.C 76 (2016) 683, 2016.
Inspire Record 1477209 DOI 10.17182/hepdata.75330

A search for supersymmetry in events with large missing transverse momentum, jets, and at least one hadronically decaying tau lepton has been performed using 3.2 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV recorded by the ATLAS detector at the Large Hadron Collider in 2015. Two exclusive final states are considered, with either exactly one or at least two tau leptons. No excess over the Standard Model prediction is observed in the data. Results are interpreted in the context of gauge-mediated supersymmetry breaking and a simplified model of gluino pair production with tau-rich cascade decays, substantially improving on previous limits. In the GMSB model considered, supersymmetry-breaking scale ($\Lambda$) values below 92 TeV are excluded at the 95% confidence level, corresponding to gluino masses below 2000 GeV. For large values of $\tan\beta$, values of $\Lambda$ up to 107 TeV and gluino masses up to 2300 GeV are excluded. In the simplified model, gluino masses are excluded up to 1570 GeV for neutralino masses around 100 GeV. Neutralino masses up to 700 GeV are excluded for all gluino masses between 800 GeV and 1500 GeV, while the strongest exclusion of 750 GeV is achieved for gluino masses around 1400 GeV.

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mTtau distributions for "extended SR selections" of the 1 tau channel, for the Compressed SR selection without the mTtau > 80 GeV requirement. The last bin includes overflow events. Uncertainties are statistical only. Signal predictions are overlaid for several benchmark models, normalised to their predicted cross sections. For the simplified model, "LM" refers to a low mass splitting, or compressed scenario, with m(gluino)=665 GeV and m(neutralino)=585 GeV; "MM" stands for a medium mass splitting, with m(gluino)=1145 GeV and m(neutralino)=265 GeV; "HM" denotes a high mass splitting scenario, with m(gluino)=1305 GeV and m(neutralino)=105 GeV.

mTtau distributions for "extended SR selections" of the 1 tau channel, for the Medium Mass SR selection without the mTtau > 200 GeV requirement. The last bin includes overflow events. Uncertainties are statistical only. Signal predictions are overlaid for several benchmark models, normalised to their predicted cross sections. For the simplified model, "LM" refers to a low mass splitting, or compressed scenario, with m(gluino)=665 GeV and m(neutralino)=585 GeV; "MM" stands for a medium mass splitting, with m(gluino)=1145 GeV and m(neutralino)=265 GeV; "HM" denotes a high mass splitting scenario, with m(gluino)=1305 GeV and m(neutralino)=105 GeV.

mTtau distributions for "extended SR selections" of the 1 tau channel, for the High Mass SR selection without the mTtau > 200 GeV requirement. The last bin includes overflow events. Uncertainties are statistical only. Signal predictions are overlaid for several benchmark models, normalised to their predicted cross sections. For the simplified model, "LM" refers to a low mass splitting, or compressed scenario, with m(gluino)=665 GeV and m(neutralino)=585 GeV; "MM" stands for a medium mass splitting, with m(gluino)=1145 GeV and m(neutralino)=265 GeV; "HM" denotes a high mass splitting scenario, with m(gluino)=1305 GeV and m(neutralino)=105 GeV.

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Search for charged Higgs bosons decaying via $H^{\pm} \to \tau^{\pm}\nu_{\tau}$ in the $\tau$+jets and $\tau$+lepton final states with 36 fb$^{-1}$ of $pp$ collision data recorded at $\sqrt{s} = 13$ TeV with the ATLAS experiment

The ATLAS collaboration Aaboud, Morad ; Aad, Georges ; Abbott, Brad ; et al.
JHEP 09 (2018) 139, 2018.
Inspire Record 1683331 DOI 10.17182/hepdata.83355

Charged Higgs bosons produced either in top-quark decays or in association with a top-quark, subsequently decaying via $H^{\pm} \to \tau^{\pm}\nu_{\tau}$, are searched for in 36.1 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV recorded with the ATLAS detector. Depending on whether the top-quark produced together with $H^{\pm}$ decays hadronically or leptonically, the search targets $\tau$+jets and $\tau$+lepton final states, in both cases with a hadronically decaying $\tau$-lepton. No evidence of a charged Higgs boson is found. For the mass range of $m_{H^{\pm}}$ = 90-2000 GeV, upper limits at the 95% confidence level are set on the production cross-section of the charged Higgs boson times the branching fraction $\mathrm{B}(H^{\pm} \to \tau^{\pm}\nu_{\tau})$ in the range 4.2-0.0025 pb. In the mass range 90-160 GeV, assuming the Standard Model cross-section for $t\overline{t}$ production, this corresponds to upper limits between 0.25% and 0.031% for the branching fraction $\mathrm{B}(t\to bH^{\pm}) \times \mathrm{B}(H^{\pm} \to \tau^{\pm}\nu_{\tau})$.

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Observed and expected 95% CL exclusion limits on $\sigma(pp\to tbH^+)\times \mathrm{\cal{B}}(H^+\to\tau\nu)$ as a function of the charged Higgs boson mass in 36.1 fb$^{-1}$ of $pp$ collision data at $\sqrt{s} = 13$ TeV, after combination of the $\tau_{\rm had-vis}$+jets and $\tau_{\rm had-vis}$+lepton final states.

Observed and expected 95% CL exclusion limits on $\mathrm{\cal{B}}(t\to bH^+)\times\mathrm{\cal{B}}(H^+\to\tau\nu)$ as a function of the charged Higgs boson mass in 36.1 fb$^{-1}$ of $pp$ collision data at $\sqrt{s} = 13$ TeV, after combination of the $\tau_{\rm had-vis}$+jets and $\tau_{\rm had-vis}$+lepton final states.

Observed 95% CL exclusion contour in the tan$\beta$ - $m_H$ plane shown in the context of the hMSSM, for the regions in which theoretical predictions are available (0.5$\leq\text{tan}\beta\leq60$).

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Search for new phenomena in final states with large jet multiplicities and missing transverse momentum with ATLAS using $\sqrt{s} =13$ TeV proton--proton collisions

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abdallah, Jalal ; et al.
Phys.Lett.B 757 (2016) 334-355, 2016.
Inspire Record 1422615 DOI 10.17182/hepdata.71987

Results are reported of a search for new phenomena, such as supersymmetric particle production, that could be observed in high-energy proton--proton collisions. Events with large numbers of jets, together with missing transverse momentum from unobserved particles, are selected. The data analysed were recorded by the ATLAS experiment during 2015 using the 13 TeV centre-of-mass proton--proton collisions at the Large Hadron Collider, and correspond to an integrated luminosity of 3.2 fb$^{-1}$. The search selected events with various jet multiplicities from $\ge 7$ to $\ge 10$ jets, and with various $b$-jet multiplicity requirements to enhance sensitivity. No excess above Standard Model expectations is observed. The results are interpreted within two supersymmetry models, where gluino masses up to 1400 GeV are excluded at 95% confidence level, significantly extending previous limits.

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$E_{\mathrm{T}}^{\mathrm{miss}} / \sqrt{H_{\mathrm{T}}}$ distribution in validation region 7ej50 0b. Two benchmark signal models are overlaid on the plot for comparison. Labelled `pMSSM' and `2-step', they show signal distributions from the example SUSY models (as described in the paper): a pMSSM slice model with ($m \tilde{g}$, $m \tilde{\chi_{1}^{\pm}}$) = (1300, 200) GeV and a cascade decay model with ($m \tilde{g}$, $m \tilde{\chi_{1}^{0}}$) = (1300, 200) GeV.

$E_{\mathrm{T}}^{\mathrm{miss}} / \sqrt{H_{\mathrm{T}}}$ distribution in validation region 6ej80 0b. Two benchmark signal models are overlaid on the plot for comparison. Labelled `pMSSM' and `2-step', they show signal distributions from the example SUSY models (as described in the paper): a pMSSM slice model with ($m \tilde{g}$, $m \tilde{\chi_{1}^{\pm}}$) = (1300, 200) GeV and a cascade decay model with ($m \tilde{g}$, $m \tilde{\chi_{1}^{0}}$) = (1300, 200) GeV.

$E_{\mathrm{T}}^{\mathrm{miss}} / \sqrt{H_{\mathrm{T}}}$ distribution in signal region 10j50 0b. Two benchmark signal models are overlaid on the plot for comparison. Labelled `pMSSM' and `2-step', they show signal distributions from the example SUSY models (as described in the paper): a pMSSM slice model with ($m \tilde{g}$, $m \tilde{\chi_{1}^{\pm}}$) = (1300, 200) GeV and a cascade decay model with ($m \tilde{g}$, $m \tilde{\chi_{1}^{0}}$) = (1300, 200) GeV.

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Search for pair production of vector-like top quarks in events with one lepton, jets, and missing transverse momentum in $\sqrt{s} = 13$ TeV pp collisions with the ATLAS detector

The ATLAS collaboration Aaboud, Morad ; Aad, Georges ; Abbott, Brad ; et al.
JHEP 08 (2017) 052, 2017.
Inspire Record 1601647 DOI 10.17182/hepdata.77266

The results of a search for vector-like top quarks using events with exactly one lepton, at least four jets, and large missing transverse momentum are reported. The search is optimised for pair production of vector-like top quarks in the $Z(\rightarrow \! \! \nu \nu) \, t + X$ decay channel. LHC pp collision data at a centre-of-mass energy of $\sqrt{s}=13$ TeV recorded by the ATLAS detector in 2015 and 2016 are used, corresponding to an integrated luminosity of 36.1 $\mathrm{fb}^{-1}$. No significant excess over the Standard Model expectation is seen and upper limits on the production cross-section of a vector-like $T$ quark pair as a function of the $T$ quark mass are derived. The observed (expected) 95% CL lower limits on the $T$ mass are 870 GeV (890 GeV) for the weak-isospin singlet model, 1.05 TeV (1.06 TeV) for the weak-isospin doublet model and 1.16 TeV (1.17 TeV) for the pure $Zt$ decay mode. Limits are also set on the mass as a function of the decay branching ratios, excluding large parts of the parameter space for masses below 1 TeV.

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Expected and observed 95% CL upper limit on the cross-section times branching ratio for VLQ $T$ pair production as a function of the $T$ mass for BR($T \rightarrow Zt$) = 100%.

Expected and observed 95% CL upper limit on the cross-section times branching ratio for VLQ $T$ pair production as a function of the $T$ mass for branching ratios according to the singlet model.

Expected and observed 95% CL upper limit on the cross-section times branching ratio for VLQ $T$ pair production as a function of the $T$ mass for branching ratios according to the doublet model. Contributions from the $X$ or $B$ quark in the $(X^{5/3}, T)$ or $(T, B)$ doublet models are neglected, leading to very conservative limits.

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Search for squarks and gluinos in final states with jets and missing transverse momentum at $\sqrt{s}=$ 13 TeV with the ATLAS detector

The ATLAS collaboration Aaboud, Morad ; Aad, Georges ; Abbott, Brad ; et al.
Eur.Phys.J.C 76 (2016) 392, 2016.
Inspire Record 1458270 DOI 10.17182/hepdata.74253

A search for squarks and gluinos in final states containing hadronic jets, missing transverse momentum but no electrons or muons is presented. The data were recorded in 2015 by the ATLAS experiment in $\sqrt{s}=$ 13 TeV proton--proton collisions at the Large Hadron Collider. No excess above the Standard Model background expectation was observed in 3.2 fb$^{-1}$ of analyzed data. Results are interpreted within simplified models that assume R-parity is conserved and the neutralino is the lightest supersymmetric particle. An exclusion limit at the 95% confidence level on the mass of the gluino is set at 1.51 TeV for a simplified model incorporating only a gluino octet and the lightest neutralino, assuming the lightest neutralino is massless. For a simplified model involving the strong production of mass-degenerate first- and second-generation squarks, squark masses below 1.03 TeV are excluded for a massless lightest neutralino. These limits substantially extend the region of supersymmetric parameter space excluded by previous measurements with the ATLAS detector.

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Observed and expected background effective mass distributions in control region CRgamma for SR4jt.

Observed and expected background effective mass distributions in control region CRW for SR4jt.

Observed and expected background effective mass distributions in control region CRT for SR4jt.

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Version 2
Search for squarks and gluinos in final states with one isolated lepton, jets, and missing transverse momentum at $\sqrt{s}=13$ TeV with the ATLAS detector

The ATLAS collaboration Aad, Georges ; Abbott, Brad ; Abbott, Dale Charles ; et al.
Eur.Phys.J.C 81 (2021) 600, 2021.
Inspire Record 1839446 DOI 10.17182/hepdata.97041

The results of a search for gluino and squark pair production with the pairs decaying via the lightest charginos into a final state consisting of two $W$ bosons, the lightest neutralinos ($\tilde\chi^0_1$), and quarks, are presented. The signal is characterised by the presence of a single charged lepton ($e^{\pm}$ or $\mu^{\pm}$) from a $W$ boson decay, jets, and missing transverse momentum. The analysis is performed using 139 fb$^{-1}$ of proton-proton collision data taken at a centre-of-mass energy $\sqrt{s}=13$ TeV delivered by the Large Hadron Collider and recorded by the ATLAS experiment. No statistically significant excess of events above the Standard Model expectation is found. Limits are set on the direct production of squarks and gluinos in simplified models. Masses of gluino (squark) up to 2.2 TeV (1.4 TeV) are excluded at 95% confidence level for a light $\tilde\chi^0_1$.

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Post-fit $m_{T}$ distribution in the SR 2J b-veto N-1 region. N-1 refers to all cuts except for the requirement on $m_T$ being applied. Uncertainties include statistical and systematic uncertainties. The value 9999 is used as a placeholder for infinity.

Post-fit $m_{T}$ distribution in the SR 2J b-veto N-1 region. N-1 refers to all cuts except for the requirement on $m_T$ being applied. Uncertainties include statistical and systematic uncertainties. The value 9999 is used as a placeholder for infinity.

Post-fit $m_{T}$ distribution in the SR 2J b-tag N-1 region. N-1 refers to all cuts except for the requirement on $m_T$ being applied. Uncertainties include statistical and systematic uncertainties. The value 9999 is used as a placeholder for infinity.

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Version 2
Measurement of the energy asymmetry in $t\bar{t}j$ production at 13 TeV with the ATLAS experiment and interpretation in the SMEFT framework

The ATLAS collaboration Aad, Georges ; Abbott, Braden Keim ; Abbott, Dale ; et al.
Eur.Phys.J.C 82 (2022) 374, 2022.
Inspire Record 1941095 DOI 10.17182/hepdata.111348

A measurement of the energy asymmetry in jet-associated top-quark pair production is presented using 139 $\mathrm{fb}^{-1}$ of data collected by the ATLAS detector at the Large Hadron Collider during $pp$ collisions at $\sqrt{s}=13$ TeV. The observable measures the different probability of top and antitop quarks to have the higher energy as a function of the jet scattering angle with respect to the beam axis. The energy asymmetry is measured in the semileptonic $t\bar{t}$ decay channel, and the hadronically decaying top quark must have transverse momentum above $350$ GeV. The results are corrected for detector effects to particle level in three bins of the scattering angle of the associated jet. The measurement agrees with the SM prediction at next-to-leading-order accuracy in quantum chromodynamics in all three bins. In the bin with the largest expected asymmetry, where the jet is emitted perpendicular to the beam, the energy asymmetry is measured to be $-0.043\pm0.020$, in agreement with the SM prediction of $-0.037\pm0.003$. Interpreting this result in the framework of the Standard Model effective field theory (SMEFT), it is shown that the energy asymmetry is sensitive to the top-quark chirality in four-quark operators and is therefore a valuable new observable in global SMEFT fits.

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Data measurements and predictions of the energy asymmetry in three bins of the jet angle $\theta_j$. The SM prediction was obtained from simulations of $t\bar{t}j$ events with MadGraph5_aMC@NLO + Pythia 8 at NLO in QCD for $t\bar{t}j$ + PS, including MC statistical and scale uncertainties.

Data Measurements and predictions of the energy asymmetry in three bins of the jet angle $\theta_j$. The SM prediction was obtained from simulations of $t\bar{t}j$ events with MadGraph5_aMC@NLO + Pythia 8 at NLO in QCD for $t\bar{t}j$ + PS, including MC statistical and scale uncertainties.

Correlation coefficients $\rho_{i,j}$ for the statistical and systematic uncertainties between the $i$-th and $j$-th bin of the differential $A_E$ measurement as a function of the jet scattering angle $\theta_j$

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