Pair Production Cross Section Research Articles

Analytic NNLO QCD corrections to top quark pair production in electron-positron collisions

We present the analytic total cross section of top quark pair production in electron-positron annihilation at next-to-next-to-leading order (NNLO) in Quantum Chromodynamics (QCD). By utilizing the optical theorem, the NNLO corrections are related to the imaginary parts of three-loop self-energy Feynman diagrams, of which the master integrals are calculated with canonical differential equations. The analytic results for the NNLO corrections are expressed in terms of multiple polylogarithms as well as elliptic functions. We discuss the asymptotic expansions near the threshold and in the high energy limit in detail. Numerical results are provided for the total cross section of top quark pair production at future lepton colliders.

Measurement of differential cross-sections in tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document} and tt¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ t\\overline{t} $$\\end{document}+jets production in the lepton+jets final state in pp collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV using 140 fb−1 of ATLAS

Differential cross-sections for top-quark pair production, inclusively and in association with jets, are measured in pp collisions at a centre-of-mass energy of 13 TeV with the ATLAS detector at the LHC using an integrated luminosity of 140 fb−1. The events are selected with one charged lepton (electron or muon) and at least four jets. The differential cross-sections are presented at particle level as functions of several jet observables, including angular correlations, jet transverse momenta and invariant masses of the jets in the final state, which characterise the kinematics and dynamics of the top-antitop system and the hard QCD radiation in the system with associated jets. The typical precision is 5%–15% for the absolute differential cross-sections and 2%–4% for the normalised differential cross-sections. Next-to-leading-order and next-to-next-to-leading-order QCD predictions are found to provide an adequate description of the rate and shape of the jet-angular observables. The description of the transverse momentum and invariant mass observables is improved when next-to-next-to-leading-order QCD corrections are included.

Search for non-resonant Higgs boson pair production in final states with leptons, taus, and photons in pp collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV with the ATLAS detector

A search is presented for non-resonant Higgs boson pair production, targeting the bbZZ, 4V (V = W or Z), VVττ, 4τ, γγVV and γγττ decay channels. Events are categorised based on the multiplicity of light charged leptons (electrons or muons), hadronically decaying tau leptons, and photons. The search is based on a data sample of proton-proton collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV recorded with the ATLAS detector during Run 2 of the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb−1. No evidence of the signal is found and the observed (expected) upper limit on the cross-section for non-resonant Higgs boson pair production is determined to be 17 (11) times the Standard Model predicted cross-section at 95% confidence level under the background-only hypothesis. The observed (expected) constraints on the HHH coupling modifier, κλ, are determined to be −6.2 < κλ< 11.6 (−4.5 < κλ< 9.6) at 95% confidence level, assuming the Standard Model for the expected limits and that new physics would only affect κλ.

Search for the nonresonant production of Higgs boson pairs via gluon fusion and vector-boson fusion in the bb¯τ+τ− final state in proton-proton collisions at s=13 TeV with the ATLAS detector

A search for the nonresonant production of Higgs boson pairs in the HH→bb¯τ+τ− channel is performed using 140 fb−1 of proton-proton collisions at a center-of-mass energy of 13 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. The analysis strategy is optimized to probe anomalous values of the Higgs boson self-coupling modifier κλ and of the quartic HHVV (V=W,Z) coupling modifier κ2V. No significant excess above the expected background from Standard Model processes is observed. An observed (expected) upper limit μHH&lt;5.9(3.3) is set at 95% confidence-level on the Higgs boson pair production cross section normalized to its Standard Model prediction. The coupling modifiers are constrained to an observed (expected) 95% confidence interval of −3.1&lt;κλ&lt;9.0 (−2.5&lt;κλ&lt;9.3) and −0.5&lt;κ2V&lt;2.7 (−0.2&lt;κ2V&lt;2.4), assuming all other Higgs boson couplings are fixed to the Standard Model prediction. The results are also interpreted in the context of effective field theories via constraints on anomalous Higgs boson couplings and Higgs boson pair production cross sections assuming different kinematic benchmark scenarios. © 2024 CERN, for the ATLAS Collaboration 2024 CERN

Prompt-critical power excursion measurements with optical fibers in the CABRI experimental reactor

This paper presents our experimental work to assess the capability of estimating the transient-induced power distribution evolution in the CABRI experimental reactor, using Cherenkov radiation in optical fibers. The CABRI reactor is designed to produce power transients from 100 kW up to 21 GW in less than 100 ms, in order to irradiate a test fuel pin under conditions representative of a Reactivity Insertion Accident in pressurized water reactors. Because of the wide response range and short response time required to follow the reactor power evolution during a complete transient, the usual means of detection, such as ionization or fission chamber, are rendered inoperable, especially for in-core or core vicinity measurements. For this reason, we suggest measuring the Cherenkov light produced within the optical fibers. The Cherenkov light emission is linked to local electron production, which is proportional to local gamma flux through the Compton or pair production cross-section. In other words, the intensity of Cherenkov radiation is related to the photon flux intensity. Knowledge of the fission photons emitted by the reactor gives direct insight into the fission rate, hence a spatial power density distribution could be reconstructed by using the measurement of Cherenkov light at different points in the reactor. The radio-luminescence measurements taken using photodiodes show very good linearity with the reactor power monitoring system despite the transient radiation induced attenuation observed in the optical fibers. The radio-luminescent light shows steady values with around 5% of variations over the 15 transients for low OH fibers and high OH fibers. Low OH tends to overestimate the FWHM of the power peak by 1–4%.

Production of D(*)D¯(*) near the thresholds in e+e− annihilation

It is shown that the nontrivial energy dependencies of DD¯, DD¯*, and D*D¯* pair production cross sections in e+e− annihilation are well described within the approach based on an account of the final-state interaction of produced particles. This statement is valid for the production of charged and neutral particles. Interaction of D(*) and D¯(*) is taken into account using the effective potential method. Its applicability is based on the fact that for near-threshold resonance the characteristic width of peak in the wave function is much larger than the interaction radius. The transition amplitudes between all three channels play an important role in the description of cross sections. These transitions are possible since all channels have the same quantum numbers JPC=1−−. Published by the American Physical Society 2024

Combination of Searches for Resonant Higgs Boson Pair Production Using pp Collisions at sqrt[s]=13 TeV with the ATLAS Detector.

A combination of searches for a new resonance decaying into a Higgs boson pair is presented, using up to 139 fb^{-1} of pp collision data at sqrt[s]=13 TeV recorded with the ATLAS detector at the LHC. The combination includes searches performed in three decay channels: bb[over ¯]bb[over ¯], bb[over ¯]τ^{+}τ^{-}, and bb[over ¯]γγ. No excess above the expected Standard Model background is observed and upper limits are set at the 95% confidence level on the production cross section of Higgs boson pairs originating from the decay of a narrow scalar resonance with mass in the range 251GeV-5TeV. The observed (expected) limits are in the range 0.96-600fb (1.2-390fb). The limits are interpreted in the type-I two-Higgs-doublet model and the minimal supersymmetric standard model, and constrain parameter space not previously excluded by other searches.

Heavy-Quark Pair Production at Lepton Colliders at NNNLO in QCD.

We compute the total cross section and invariant mass distribution for heavy-quark pair production in e^{+}e^{-} annihilation at the next-to-next-to-next-to-leading order in QCD. The obtained results are expressed as piecewise functions defined by several deeply expanded power series, facilitating a rapid numerical evaluation. Utilizing top-pair production at a collision energy of 500GeV as a benchmark, we observe a correction of approximately 0.1% for the total cross section and around 10% for the majority of the invariant mass distribution range. These results play a crucial role in significantly reducing theoretical uncertainty: the scale dependence has been diminished to 0.06% for the total cross section and to 5% for the invariant mass distribution. This reduction of uncertainty meets the stringent requirements of future lepton colliders.

Search for non-resonant Higgs boson pair production in the 2b+2ℓ+ETmiss\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ 2b+2\\ell +{E}_{\ extrm{T}}^{\ extrm{miss}} $$\\end{document} final state in pp collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV with the ATLAS detector

A search for non-resonant Higgs boson pair (HH) production is presented, in which one of the Higgs bosons decays to a b-quark pair (bb¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\\overline{b} $$\\end{document}) and the other decays to WW*, ZZ*, or τ+τ−, with in each case a final state with ℓ+ℓ−+ neutrinos (ℓ = e, μ). The analysis targets separately the gluon-gluon fusion and vector boson fusion production modes. Data recorded by the ATLAS detector in proton-proton collisions at a centre-of-mass energy of 13 TeV at the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb−1, are used in this analysis. Events are selected to have exactly two b-tagged jets and two leptons with opposite electric charge and missing transverse momentum in the final state. These events are classified using multivariate analysis algorithms to separate the HH events from other Standard Model processes. No evidence of the signal is found. The observed (expected) upper limit on the cross-section for non-resonant Higgs boson pair production is determined to be 9.7 (16.2) times the Standard Model prediction at 95% confidence level. The Higgs boson self-interaction coupling parameter κλ and the quadrilinear coupling parameter κ2V are each separately constrained by this analysis to be within the ranges [−6.2, 13.3] and [−0.17, 2.4], respectively, at 95% confidence level, when all other parameters are fixed.

Studies of new Higgs boson interactions through nonresonant HH production in the bb¯γγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\\overline{b}\\gamma \\gamma $$\\end{document} final state in pp collisions at s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 13 TeV with the ATLAS detector

A search for nonresonant Higgs boson pair production in the bb¯γγ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ b\\overline{b}\\gamma \\gamma $$\\end{document} final state is performed using 140 fb−1 of proton-proton collisions at a centre-of-mass energy of 13 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. This analysis supersedes and expands upon the previous nonresonant ATLAS results in this final state based on the same data sample. The analysis strategy is optimised to probe anomalous values not only of the Higgs (H) boson self-coupling modifier κλ but also of the quartic HHVV (V = W, Z) coupling modifier κ2V. No significant excess above the expected background from Standard Model processes is observed. An observed upper limit μHH < 4.0 is set at 95% confidence level on the Higgs boson pair production cross-section normalised to its Standard Model prediction. The 95% confidence intervals for the coupling modifiers are −1.4 < κλ < 6.9 and −0.5 < κ2V < 2.7, assuming all other Higgs boson couplings except the one under study are fixed to the Standard Model predictions. The results are interpreted in the Standard Model effective field theory and Higgs effective field theory frameworks in terms of constraints on the couplings of anomalous Higgs boson (self-)interactions.

Top-quark pair production by electron–positron scattering in a linearly polarized laser field

In a previous paper, we showed theoretically that the total cross-section of the top-quark pair production by electron–positron annihilation is strongly reduced by the presence of a circularly polarized laser field. In this paper, we present the result for the case of a linearly polarized laser field. This time, the total cross-section is significantly enhanced by the laser field.

Probing initial state effects in nuclear collisions via jet and top-quark measurements with the ATLAS detector

Proton-lead collisions at the Large Hadron Collider energies offer a unique possibility to investigate initial state effects in nuclear collisions. Thanks to its wide acceptance, ATLAS can measure several probes that can help characterise these effects over a wide kinematic range. By analyzing the centrality dependence of dijet production, it is possible to investigate the suppression of dijet events in central collisions compared to peripheral ones and correlate it to the kinematic of the parton-parton scattering, accessible via the measurement of both jets in the final state. Also, the first measurement of the inclusive crosssection for top-quark pair production in dilepton and lepton+jet decay modes is reported. This process is sensitive to effects at high Bjorken-x values, which are hard to access experimentally using other available probes, and thus provides complementary information on the behavior of nuclear parton densities. In 2016, the ATLAS experiment collected 165 nb−1 of proton-lead collisions at a center-of-mass energy of 8.16 TeV per nucleon pair. In this article, new measurements of the centrality dependence of dijet production and the observation of top-quark pair production using this dataset are presented.

Nanophotonics for pair production

The transformation of electromagnetic energy into matter represents a fascinating prediction of relativistic quantum electrodynamics that is paradigmatically exemplified by the creation of electron-positron pairs out of light. However, this phenomenon has a very low probability, so positron sources rely instead on beta decay, which demands elaborate monochromatization and trapping schemes to achieve high-quality beams. Here, we propose to use intense, strongly confined optical near fields supported by a nanostructured material in combination with high-energy photons to create electron-positron pairs. Specifically, we show that the interaction between near-threshold γ-rays and polaritons yields higher pair-production cross sections, largely exceeding those associated with free-space photons. Our work opens an unexplored avenue toward generating tunable pulsed positrons from nanoscale regions at the intersection between particle physics and nanophotonics.

Exploring mixed lepton-quark interactions in non-resonant leptoquark production at the LHC

Searches for new physics (NP) at particle colliders typically involve multivariate analysis of kinematic distributions of final state particles produced in a decay of a hypothetical NP resonance. Since the pair-production cross-sections mediated by such resonances are strongly suppressed by the NP scale, this analysis becomes less relevant for NP searches for masses of the BSM resonance above 1 TeV. On the other hand, t-channel processes are less sensitive to the mass of the virtual mediator and therefore larger phase-space can be potentially probed as well as the couplings between the NP particles and the Standard Model fields. The fact that transitions between different generations of quarks and leptons may exist, the potential of the search presented in this article can be used, as a reference guide, to enlarge significantly the scope of searches performed at the LHC to flavour off-diagonal channels, in a theoretically consistent approach. In this work, we study non-resonant production of scalar leptoquarks which have been proposed in the literature to provide a potential avenue for radiative generation of neutrino masses, accommodating as well the existing flavour physics data. Final states involving just two muons at the LHC (μ+μ−), are used as a well-motivated case study.

Exploring the higher-order QED effects on the differential distributions of vacuum pair production in relativistic heavy-ion collisions

Extensive studies have been conducted in the past few decades to investigate potential signatures of higher-order QED effects in high-energy electromagnetic scattering processes. In our previous work, we have identified evidence of higher-order corrections in the total cross-section for the vacuum pair production in relativistic heavy-ion collisions. However, the presence of higher-order QED corrections cannot be unambiguously proven solely based on total cross-section measurements due to substantial experimental and theoretical uncertainties. The objective of this paper is to explore the sensitivity of specific differential observables in the vacuum pair production to higher-order QED effects in high-energy heavy-ion collisions. These investigations will provide guidance in determining the presence or absence of higher-order QED processes by conducting precise measurements in future experiments.

First measurement of the top quark pair production cross section in proton-proton collisions at sqrt{s} = 13.6 TeV

The first measurement of the top quark pair ( textrm{t}overline{textrm{t}} ) production cross section in proton-proton collisions at sqrt{s} = 13.6 TeV is presented. Data recorded with the CMS detector at the CERN LHC in Summer 2022, corresponding to an integrated luminosity of 1.21 fb−1, are analyzed. Events are selected with one or two charged leptons (electrons or muons) and additional jets. A maximum likelihood fit is performed in event categories defined by the number and flavors of the leptons, the number of jets, and the number of jets identified as originating from b quarks. An inclusive textrm{t}overline{textrm{t}} production cross section of 881 ± 23 (stat + syst) ± 20 (lumi) pb is measured, in agreement with the standard model prediction of {924}_{-40}^{+32} pb.

Measurement of the cross section of top quark-antiquark pair production in association with a W boson in proton-proton collisions at sqrt{s} = 13 TeV

The production of a top quark-antiquark pair in association with a W boson ( textrm{t}overline{textrm{t}}textrm{W} ) is measured in proton-proton collisions at a center-of-mass energy of 13 TeV. The analyzed data was recorded by the CMS experiment at the CERN LHC and corresponds to an integrated luminosity of 138 fb−1. Events with two or three leptons (electrons and muons) and additional jets are selected. In events with two leptons, a multiclass neural network is used to distinguish between the signal and background processes. Events with three leptons are categorized based on the number of jets and of jets originating from b quark hadronization, and the lepton charges. The inclusive textrm{t}overline{textrm{t}}textrm{W} production cross section in the full phase space is measured to be 868 ± 40(stat) ± 51(syst) fb. The textrm{t}overline{textrm{t}}textrm{W} + and textrm{t}overline{textrm{t}}textrm{W} − cross sections are also measured as 553 ± 30(stat) ± 30(syst) and 343 ± 26(stat) ± 25(syst) fb, respectively, and the corresponding ratio of the two cross sections is found to be 1.61pm 0.15{left(textrm{stat}right)}_{-0.05}^{+0.07}left(textrm{syst}right) . The measured cross sections are larger than but consistent with the standard model predictions within two standard deviations, and represent the most precise measurement of these cross sections to date.

Combination of inclusive top-quark pair production cross-section measurements using ATLAS and CMS data at sqrt{s} = 7 and 8 TeV

A combination of measurements of the inclusive top-quark pair production cross-section performed by ATLAS and CMS in proton–proton collisions at centre-of-mass energies of 7 and 8 TeV at the LHC is presented. The cross-sections are obtained using top-quark pair decays with an opposite-charge electron–muon pair in the final state and with data corresponding to an integrated luminosity of about 5 fb−1 at sqrt{s} = 7 TeV and about 20 fb−1 at sqrt{s} = 8 TeV for each experiment. The combined cross-sections are determined to be 178.5 ± 4.7 pb at sqrt{s} = 7 TeV and {243.3}_{-5.9}^{+6.0} pb at sqrt{s} = 8 TeV with a correlation of 0.41, using a reference top-quark mass value of 172.5 GeV. The ratio of the combined cross-sections is determined to be R8/7 = 1.363 ± 0.032. The combined measured cross-sections and their ratio agree well with theory calculations using several parton distribution function (PDF) sets. The values of the top-quark pole mass (with the strong coupling fixed at 0.118) and the strong coupling (with the top-quark pole mass fixed at 172.5 GeV) are extracted from the combined results by fitting a next-to-next-to-leading-order plus next-to-next-to-leading-log QCD prediction to the measurements. Using a version of the NNPDF3.1 PDF set containing no top-quark measurements, the results obtained are {m}_t^{textrm{pole}}={173.4}_{-2.0}^{+1.8} GeV and {alpha}_{textrm{s}}left({m}_Zright)={0.1170}_{-0.0018}^{+0.0021} .

Inclusive and differential cross-sections for dilepton toverline{t} production measured in sqrt{s} = 13 TeV pp collisions with the ATLAS detector

Differential and double-differential distributions of kinematic variables of leptons from decays of top-quark pairs ( toverline{t} ) are measured using the full LHC Run 2 data sample collected with the ATLAS detector. The data were collected at a pp collision energy of sqrt{s} = 13 TeV and correspond to an integrated luminosity of 140 fb−1. The measurements use events containing an oppositely charged eμ pair and b-tagged jets. The results are compared with predictions from several Monte Carlo generators. While no prediction is found to be consistent with all distributions, a better agreement with measurements of the lepton pT distributions is obtained by reweighting the toverline{t} sample so as to reproduce the top-quark pT distribution from an NNLO calculation. The inclusive top-quark pair production cross-section is measured as well, both in a fiducial region and in the full phase-space. The total inclusive cross-section is found to beσtt¯=829±1stat±13syst±8lumi±2beampb,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\sigma}_{t\\overline{t}}=829\\pm 1\\ \\left(\ extrm{stat}\\right)\\pm 13\\ \\left(\ extrm{syst}\\right)\\pm 8\\ \\left(\ extrm{lumi}\\right)\\pm 2\\ \\left(\ extrm{beam}\\right)\\ \ extrm{pb}, $$\\end{document}where the uncertainties are due to statistics, systematic effects, the integrated luminosity and the beam energy. This is in excellent agreement with the theoretical expectation.

Measurement of the toverline{t} production cross-section in pp collisions at sqrt{s} = 5.02 TeV with the ATLAS detector

The inclusive top-quark pair ( toverline{t} ) production cross-section {sigma}_{toverline{t}} is measured in proton–proton collisions at a centre-of-mass energy sqrt{s} = 5.02 TeV, using 257 pb−1 of data collected in 2017 by the ATLAS experiment at the LHC. The toverline{t} cross-section is measured in both the dilepton and single-lepton final states of the toverline{t} system and then combined. The combination of the two measurements yieldsσtt¯=67.5±0.9stat.±2.3syst.±1.1lumi.±0.2beampb,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\sigma}_{t\\overline{t}}=67.5\\pm 0.9\\left(\ extrm{stat}.\\right)\\pm 2.3\\left(\ extrm{syst}.\\right)\\pm 1.1\\left(\ extrm{lumi}.\\right)\\pm 0.2\\left(\ extrm{beam}\\right)\ extrm{pb}, $$\\end{document}where the four uncertainties reflect the limited size of the data sample, experimental and theoretical systematic effects, and imperfect knowledge of both the integrated luminosity and the LHC beam energy, giving a total uncertainty of 3.9%. The result is in agreement with theoretical quantum chromodynamic calculations at next-to-next-to-leading order in the strong coupling constant, including the resummation of next-to-next-to-leading logarithmic soft-gluon terms, and constrains the parton distribution functions of the proton at large Bjorken-x.