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| CMS-SMP-23-004 ; CERN-EP-2024-117 | ||
| Stairway to discovery: a report on the CMS programme of cross section measurements from millibarns to femtobarns | ||
| CMS Collaboration | ||
| 29 May 2024 | ||
| Submitted to Physics Reports | ||
| Abstract: The Large Hadron Collider at CERN, delivering proton-proton collisions at much higher energies and far higher luminosities than previous machines, has enabled a comprehensive programme of measurements of the standard model (SM) processes by the CMS experiment. These unprecedented capabilities facilitate precise measurements of the properties of a wide array of processes, the most fundamental being cross sections. The discovery of the Higgs boson and the measurement of its mass became the keystone of the SM. Knowledge of the mass of the Higgs boson allows precision comparisons of the predictions of the SM with the corresponding measurements. These measurements span the range from one of the most copious SM processes, the total inelastic cross section for proton-proton interactions, to the rarest ones, such as Higgs boson pair production. They cover the production of Higgs bosons, top quarks, single and multibosons, and hadronic jets. Associated parameters, such as coupling constants, are also measured. These cross section measurements can be pictured as a descending stairway, on which the lowest steps represent the rarest processes allowed by the SM, some never seen before. | ||
| Links: e-print arXiv:2405.18661 [hep-ex] (PDF) ; CDS record ; inSPIRE record ; CADI line (restricted) ; | ||
| We dedicate this work to the memory of Prof. Peter Ware Higgs, whose transformative and groundbreaking ideas laid the foundation for the physics of the standard model and of the Higgs particle, which are the subjects of this Report. |
| Figures | |
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Figure 1:
Cross sections of selected high-energy processes measured by the CMS experiment. Measurements performed at different LHC pp collision energies are marked by unique symbols and the coloured bands indicate the combined statistical and systematic uncertainty of the measurement. Grey bands indicate the uncertainty of the corresponding SM theory predictions. Shaded hashed bars indicate the excluded cross section region for a production process with the measured 95% CL upper limit on the process indicated by the solid line of the same colour. |
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Figure 2:
The CMS detector for the data-taking period 2017-2018. |
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Figure 3:
The inclusive jet production cross sections as functions of the jet transverse momentum $ p_{\mathrm{T}} $ measured in intervals of the absolute rapidity $ |y| $. The cross section obtained for jets clustered using the anti-$ k_{\mathrm{T}} $ algorithm with $ \Delta R = $ 0.4 is shown. The results in different $ |y| $ intervals are scaled by constant factors for presentation purposes. The data in different $ |y| $ intervals are shown by markers of different styles. The statistical uncertainties are too small to be visible; the systematic uncertainties are not shown. The measurements are compared with NNLO QCD predictions (solid line) using the CT14nnlo PDF set and corrected for EW and NP effects. Figure and caption taken from Ref. [146]. |
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Figure 4:
Differential cross section of jet production as a function of the exclusive jet multiplicity (inclusive for 7 jets) in bins of $ p_{\mathrm{T}} $ and $ \Delta\phi_{12} $. The data are compared with the NLO dijet predictions from MadGraph-5_aMC@NLO: MG5_aMC+Py8 (jj) and MG5_aMC+CA3 (jj), as well as the NLO three-jet prediction of MG5_aMC+CA3 (jjj), where parton showering is performed by PYTHIA 8 (Py8) and CASCADE 3 [85] (CA3). The vertical error bars correspond to the statistical uncertainty, the yellow band shows the total experimental uncertainty. The shaded bands show the uncertainty from a variation of the normalization and factorization scales. The predictions are normalized to the measured inclusive dijet cross section using the scaling factors shown in the legend. Figure taken from Ref. [149]. |
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Figure 5:
The gluon distribution, shown as a function of $ x $ for the factorization scale $ \mu_{\mathrm f} = m_\mathrm{t} $. The filled (hatched) band represents the results of the NNLO fit using HERA DIS and the CMS inclusive jet cross section at $ \sqrt{s} = $ 13 TeV (using the HERA DIS data only). The PDFs are shown with their total uncertainty. In the lower panel, the comparison of the relative PDF uncertainties is shown for each distribution. The solid line corresponds to the ratio of the central PDF values of the two variants of the fit. Figure and caption taken from Ref. [146]. |
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Figure 6:
A summary of $ \alpha_\mathrm{S}(m_ \mathrm{Z}) $ extractions from the CMS experiment compared with the 2023 PDG world-average. For each measurement, pp collision energy and the QCD perturbative order of the $ \alpha_\mathrm{S}(m_ \mathrm{Z}) $ extraction are listed. Results are grouped by the type of the final state used: vector boson, $ \mathrm{t} \overline{\mathrm{t}} $, and jets. |
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Figure 7:
Running of the strong coupling as a function of momentum transfer, $ \alpha_\mathrm{S}(\mathrm{Q}) $ (dashed line), evolved using the 2023 world-average value, $ \alpha_\mathrm{S}(m_ \mathrm{Z}) = $ 0.1179 $ \pm $ 0.0009, together with its associated total uncertainty (yellow band). The CMS extractions, which extend above 2 TeV, are compared with results from the H1, ZEUS, D0, and ATLAS experiments. The vertical error bars indicate the total uncertainty (experimental and theoretical). All the experimental results shown in this figure are based on predictions at NLO accuracy in perturbative QCD. Figure from Ref. [193]. |
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Figure 8:
Selected measurements of the effective DPS cross section in pp collisions at the LHC by the CMS and ATLAS experiments, and in $ \mathrm{p}\overline{\mathrm{p}} $ collisions at the Tevatron by the CDF and D0 experiments. The horizontal bars indicate the combined statistical and systematic uncertainty for each measurement. Figure taken from Ref. \protect [205]. |
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Figure 9:
The Feynman diagram for Drell-Yan production of W and Z bosons (left). The Z boson production process involves annihilation of quark-antiquark pairs of same flavour. The W boson production process requires different-flavour quarks, such as $ \mathrm{u}\overline{\mathrm{d}} $ or $ \overline{\mathrm{u}}\mathrm{d} $ pairs. The NLO diagrams with real emission of a jet for the production of single vector bosons and one jet with a final-state gluon jet (middle) or quark jet (right). |
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Figure 9-a:
The Feynman diagram for Drell-Yan production of W and Z bosons (left). The Z boson production process involves annihilation of quark-antiquark pairs of same flavour. The W boson production process requires different-flavour quarks, such as $ \mathrm{u}\overline{\mathrm{d}} $ or $ \overline{\mathrm{u}}\mathrm{d} $ pairs. The NLO diagrams with real emission of a jet for the production of single vector bosons and one jet with a final-state gluon jet (middle) or quark jet (right). |
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Figure 9-b:
The Feynman diagram for Drell-Yan production of W and Z bosons (left). The Z boson production process involves annihilation of quark-antiquark pairs of same flavour. The W boson production process requires different-flavour quarks, such as $ \mathrm{u}\overline{\mathrm{d}} $ or $ \overline{\mathrm{u}}\mathrm{d} $ pairs. The NLO diagrams with real emission of a jet for the production of single vector bosons and one jet with a final-state gluon jet (middle) or quark jet (right). |
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Figure 9-c:
The Feynman diagram for Drell-Yan production of W and Z bosons (left). The Z boson production process involves annihilation of quark-antiquark pairs of same flavour. The W boson production process requires different-flavour quarks, such as $ \mathrm{u}\overline{\mathrm{d}} $ or $ \overline{\mathrm{u}}\mathrm{d} $ pairs. The NLO diagrams with real emission of a jet for the production of single vector bosons and one jet with a final-state gluon jet (middle) or quark jet (right). |
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Figure 10:
Differential cross sections for isolated-photon production in four photon rapidity intervals. The points show the measured values and their total uncertainties; the lines represent the NLO JETPHOX predictions with the NNPDF3.0 PDF set. Figure and caption taken from Ref. [214]. |
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Figure 11:
Summary of the production cross section of weak gauge bosons, measured by CMS, plotted against the pp centre-of-mass energy ranging from 2.76 to 13 TeV. The error bars around the experimental data points represent the total uncertainty of the measurement. The measurements are compared with theoretical predictions (black lines) obtained at $ \text{N}^3\text{LO} $ in QCD using the MSHT20a$ \text{N}^3\text{LO} $ PDF set. The grey band shows the envelope from normalization and factorization scale variations. |
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Figure 12:
Summary of the production cross section of weak gauge bosons in pp collisions, measured by CMS, and in $ \mathrm{p}\overline{\mathrm{p}} $ collisions, by the UA1, UA2, CDF, and D0 experiments, plotted against the pp or $ \mathrm{p}\overline{\mathrm{p}} $ centre-of-mass energy ranging from 0.63 to 13 TeV. The measurements are compared with theoretical predictions (blue lines) obtained at NNLO in QCD by using DYTURBO and the NNPDF4.0 PDF set. Figure taken from Ref. [219]. |
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Figure 13:
Measured and predicted $ \mathrm{W^+} $ versus $ \mathrm{W^-} $ production fiducial cross sections times branching fractions. The ellipses illustrate the 68% CL coverage for total uncertainties (open) and excluding the integrated luminosity uncertainty (filled). The uncertainties in the theoretical predictions correspond to the PDF uncertainty components only and are evaluated for three PDF sets: NNPDF2.3, CTEQ CT10, and MSTW 2008 NLO. Figure taken from Ref. [222]. |
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Figure 14:
Measured W boson charge asymmetry as a function of $ |y_{\mathrm{W}}| $ from the combination of the electron and muon channels (black dots), compared with different theoretical predictions. The vertical errors bars around the experimental data points show the total uncertainty of the measurements. The yellow band represents the default generator used in this analysis, MG5_aMC with the NNPDF3.0 PDF set, the pink band represents the FEWZ generator with the NNPDF3.1 PDF set, and the cyan band represents the FEWZ generator with the CT18 PDF set. The uncertainty bands of the prediction include the PDF uncertainties only, which are dominant with respect to $ \alpha_\mathrm{S} $, or renormalization and factorization scale variations for this quantity. Figure taken from Ref. [235]. |
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Figure 15:
The differential cross section of $ \mathrm{Z} \to \ell^+\ell^- $+jets production as a function of inclusive jet multiplicity, compared with the predictions calculated with MadGraph-5_aMC@NLO (LO) + PYTHIA 8, MadGraph-5_aMC@NLO (NLO) + PYTHIA 8, and GENEVA. The lower panels show the ratios of the theoretical predictions to the measurements. The measurement statistical (systematic) uncertainties are presented with vertical error bars (hashed areas). The boxes around the MadGraph-5_aMC@NLO (NLO) + PYTHIA 8 to measurement ratio represent the uncertainty in the prediction as listed in the legend. Figure taken from Ref. [240]. |
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Figure 16:
The differential cross section for $ \mathrm{Z} \to \ell^+\ell^- + $ jets production as a function of the absolute value of the 4$ \text{th} $ jet's rapidity compared with the predictions calculated with MADGRAPH 5+PYTHIA 6, SHERPA 2, and MG5_aMC +PYTHIA 8. The lower panels show the ratios of the theoretical predictions to the measurements. Error bars around the experimental points show the statistical uncertainty and the cross-hatched bands indicate the statistical and systematic uncertainties added in quadrature. The boxes around the MG5_aMC + PYTHIA 8 to measurement ratio represent the uncertainty in the prediction, including statistical, theoretical (from scale variations), and PDF uncertainties. The dark green area represents the statistical and theoretical uncertainties only and the light green area represents the statistical uncertainty alone. Figure taken from Ref. [248]. |
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Figure 17:
Differential cross section ratio of Z+jets to $ \gamma $+jets as a function of the vector boson (V) transverse momentum compared with the theoretical prediction from MadGraph-5_aMC@NLO and SHERPA + OPENLOOPS. Only bosons produced centrally, with $ |y| < $ 1.4, in association with one or more jets are considered. The panel shows the ratio of the theoretical prediction to the unfolded data. The vertical errors bars around the experimental data points show the statistical uncertainties of the measurements. The hatched band is the sum in quadrature of the statistical and systematic uncertainty components in the measurement. The dark (light) shaded band on the NLO prediction from MadGraph-5_aMC@NLO represents the PDF (scale) uncertainties, which are treated as uncorrelated between Z+jets and $ \gamma $+jets, whereas the statistical uncertainties are barely visible. The shaded band on the SHERPA + OPENLOOPS calculation is the statistical uncertainty. Figure taken from Ref. [261]. |
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Figure 18:
Production of W or Z bosons with heavy-flavour quarks. Examples of lowest order Feynman diagrams include W + charm (left), Z + charm or bottom (middle), W or Z production with two heavy-flavour quarks (right). |
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Figure 18-a:
Production of W or Z bosons with heavy-flavour quarks. Examples of lowest order Feynman diagrams include W + charm (left), Z + charm or bottom (middle), W or Z production with two heavy-flavour quarks (right). |
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Figure 18-b:
Production of W or Z bosons with heavy-flavour quarks. Examples of lowest order Feynman diagrams include W + charm (left), Z + charm or bottom (middle), W or Z production with two heavy-flavour quarks (right). |
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Figure 18-c:
Production of W or Z bosons with heavy-flavour quarks. Examples of lowest order Feynman diagrams include W + charm (left), Z + charm or bottom (middle), W or Z production with two heavy-flavour quarks (right). |
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Figure 19:
Feynman diagrams for WZ diboson production. Shown are radiative production (left), where the vector bosons are radiated off a quark, and a TGC production (right), where a W boson is created by $ \mathrm{q}\overline{\mathrm{q}} $ annihilation and splits into W and Z bosons. These diagrams are representative of all diboson production mechanisms that involve radiative or TGC processes. In the case of neutral final states TGCs are forbidden in the SM and only anomalous coupling due to new physics could lead to contributions from that type of diagram. |
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Figure 19-a:
Feynman diagrams for WZ diboson production. Shown are radiative production (left), where the vector bosons are radiated off a quark, and a TGC production (right), where a W boson is created by $ \mathrm{q}\overline{\mathrm{q}} $ annihilation and splits into W and Z bosons. These diagrams are representative of all diboson production mechanisms that involve radiative or TGC processes. In the case of neutral final states TGCs are forbidden in the SM and only anomalous coupling due to new physics could lead to contributions from that type of diagram. |
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Figure 19-b:
Feynman diagrams for WZ diboson production. Shown are radiative production (left), where the vector bosons are radiated off a quark, and a TGC production (right), where a W boson is created by $ \mathrm{q}\overline{\mathrm{q}} $ annihilation and splits into W and Z bosons. These diagrams are representative of all diboson production mechanisms that involve radiative or TGC processes. In the case of neutral final states TGCs are forbidden in the SM and only anomalous coupling due to new physics could lead to contributions from that type of diagram. |
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Figure 20:
Feynman diagrams for ZZ diboson production including radiative production (left) and NNLO production via a gluon-gluon initial state (right), which increases the total production cross section significantly. |
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Figure 20-a:
Feynman diagrams for ZZ diboson production including radiative production (left) and NNLO production via a gluon-gluon initial state (right), which increases the total production cross section significantly. |
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Figure 20-b:
Feynman diagrams for ZZ diboson production including radiative production (left) and NNLO production via a gluon-gluon initial state (right), which increases the total production cross section significantly. |
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Figure 21:
Summary of cross section measurements for diboson production shown as a ratio over the NNLO or NLO QCD predictions. The yellow bands indicate the uncertainties in the theoretical predictions and the error bars on the points are the statistical uncertainties, whereas the outer bars are the combined statistical and systematic uncertainties. |
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Figure 22:
The total $ \mathrm{W}^{\pm}\mathrm{W}^{\mp} $, WZ and ZZ cross sections as functions of the pp centre-of-mass energy. Results from the CMS and ATLAS experiments for pp collisions are compared with the predictions from MATRIX at NNLO in QCD and NLO in EW, and at NLO in QCD. Also shown are results from $ \mathrm{p\overline{p}} $ collisions at the CDF and D0 experiments compared with MATRIX predictions as above. The inner vertical errors bars around the experimental data points show the statistical uncertainties of the measurements, whereas the outer bars show the total uncertainties. Measurements at the same centre-of-mass energy are shifted slightly along the horizontal axis for clarity. Figure taken from Ref. [287]. |
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Figure 23:
The total ZZ cross section as a function of the pp centre-of-mass energy. Results from the CMS and ATLAS [299,300,301] experiments are compared with the predictions from MATRIX and MCFM, as described in the text. The ATLAS measurements were performed with a Z boson mass window of 66-116 GeV, instead of 60-120 GeV used by CMS, and are corrected for the resulting 1.6% difference in acceptance. The inner vertical errors bars around the experimental data points show the statistical uncertainties of the measurements, whereas the outer bars show the total uncertainties. Measurements at the same centre-of-mass energy are shifted slightly along the horizontal axis for clarity. Figure taken from Ref. [292]. |
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Figure 24:
Differential cross section normalized to the fiducial cross section as a function of $ m_{4\ell} $. The on-shell Z requirement 60 $ < m_{ \mathrm{Z}} < $ 120 GeV is applied for both Z boson candidates. Points represent the unfolded data, the solid lines the (MadGraph-5_aMC@NLO $ \mathrm{q}\overline{\mathrm{q}} \to \mathrm{Z} \mathrm{Z} $) + (MCFM} \mathrm{g} \mathrm{g} \TO \mathrm{Z}\mathrm{Z}) + ( POWHEG $ \mathrm{H} \to \mathrm{Z} \mathrm{Z} $) predictions, and red dashed lines the ( POWHEG $ \mathrm{q}\overline{\mathrm{q}} \to \mathrm{Z} \mathrm{Z} $) + (MCFM} \mathrm{g} \mathrm{g} \TO \mathrm{Z}\mathrm{Z}) + (POWHEG $ \mathrm{H} \to \mathrm{Z} \mathrm{Z} $) predictions. The MadGraph-5_aMC@NLO EW ZZ predictions are included. The purple dashed lines represent the nNNLO+PS predictions, and the yellow dashed lines represent the nNNLO+PS prediction with EW corrections applied. Vertical bars on the MC predictions represent the statistical uncertainties. The lower panels show the ratio of the measured to the predicted cross sections. The shaded areas represent the full uncertainties calculated as the sum in quadrature of the statistical and systematic uncertainties and the vertical bars around the data points represent the statistical uncertainties only. The overflow events are included in the last bin of the distributions. Figure and caption taken from Ref. [308]. |
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Figure 25:
Confidence regions in the $ f_{\mathrm{L}}^{ \mathrm{Z}} \mbox{\textsl{vs.}} f_{\mathrm{R}}^{ \mathrm{Z}} - f_{0}^{ \mathrm{Z}} $ parameter plane for the Z boson polarization. The results are obtained with no additional requirement for the charge of the W boson. The blue, magenta, and red contours present the 68, 95, and 99% confidence levels, respectively. Figure from Ref. [290]. The cross indicates the best fit to the observed data and the diamond shows the result of the POWHEG +PYTHIA simulation. |
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Figure 26:
The differential cross section normalized to the fiducial cross section as a function of the number of jets. The on-shell Z requirement 60 $ < m_{ \mathrm{Z}} < $ 120 GeV is applied for both Z boson candidates. Points represent the unfolded data, the solid lines the (MadGraph-5_aMC@NLO $ \mathrm{q}\overline{\mathrm{q}} \to \mathrm{Z} \mathrm{Z} $) + (MCFM} \mathrm{g} \mathrm{g} \TO \mathrm{Z} \mathrm{Z}) + ( POWHEG $ \mathrm{H} \to \mathrm{Z} \mathrm{Z} $) predictions, and red dashed lines the ( POWHEG $ \mathrm{q}\overline{\mathrm{q}} \to \mathrm{Z} \mathrm{Z} $) + (MCFM} \mathrm{g} \mathrm{g} \TO \mathrm{Z} \mathrm{Z}) + ( POWHEG $ \mathrm{H} \to \mathrm{Z} \mathrm{Z} $) predictions. The MadGraph-5_aMC@NLO EW ZZ predictions are included. The purple dashed lines represent the nNNLO+PS predictions. Vertical bars on the MC predictions represent the statistical uncertainties. The lower panels show the ratio of the measured to the predicted cross sections. The shaded areas represent the full uncertainties calculated as the sum in quadrature of the statistical and systematic uncertainties and the vertical bars around the data points represent the statistical uncertainties only. The overflow events are included in the last bin of the distributions. Figure and caption taken from Ref. [308]. |
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Figure 27:
Triboson $ \mathrm{W} \mathrm{Z} \mathrm{Z} $ production via diagrams involving radiative production (left), TGCs (centre), and QGCs (right). This set of triboson Feynman diagrams is representative of most triboson signatures, with the caveat that neutral TGCs and some QGC combinations are not allowed in the SM. |
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Figure 27-a:
Triboson $ \mathrm{W} \mathrm{Z} \mathrm{Z} $ production via diagrams involving radiative production (left), TGCs (centre), and QGCs (right). This set of triboson Feynman diagrams is representative of most triboson signatures, with the caveat that neutral TGCs and some QGC combinations are not allowed in the SM. |
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Figure 27-b:
Triboson $ \mathrm{W} \mathrm{Z} \mathrm{Z} $ production via diagrams involving radiative production (left), TGCs (centre), and QGCs (right). This set of triboson Feynman diagrams is representative of most triboson signatures, with the caveat that neutral TGCs and some QGC combinations are not allowed in the SM. |
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Figure 27-c:
Triboson $ \mathrm{W} \mathrm{Z} \mathrm{Z} $ production via diagrams involving radiative production (left), TGCs (centre), and QGCs (right). This set of triboson Feynman diagrams is representative of most triboson signatures, with the caveat that neutral TGCs and some QGC combinations are not allowed in the SM. |
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Figure 28:
Comparison of the observed numbers of events to the predicted yields. For the $ \mathrm{W}\mathrm{W}\mathrm{W} $ and $ \mathrm{W}\mathrm{W} \mathrm{Z} $ channels, the results from boosted decision tree (BDT) based selections are used. For the other results different categorizations based on the number of jets, whether dijet masses are inside or outside a selection window used to identify the boson, and specific lepton combinations or the number of same-flavour, opposite-sign (SFOS) leptons are shown. The VVV signal is shown stacked on top of the total background. The points represent the data and the error bars show the statistical uncertainties. The expected significance $ L $ in the middle panel represents the number of standard deviations (sd) with which the null hypothesis (no signal) is rejected. The lower panel shows the pulls for the fit result. Figure taken from Ref. [316]. |
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Figure 29:
Production of oppositely charged W bosons via vector boson scattering. Example Feynman diagrams include: scattering via Z boson and two TGC vertices (left), a QGC vertex (middle), and scattering via a Higgs boson in $ t $-channel (right). |
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Figure 29-a:
Production of oppositely charged W bosons via vector boson scattering. Example Feynman diagrams include: scattering via Z boson and two TGC vertices (left), a QGC vertex (middle), and scattering via a Higgs boson in $ t $-channel (right). |
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Figure 29-b:
Production of oppositely charged W bosons via vector boson scattering. Example Feynman diagrams include: scattering via Z boson and two TGC vertices (left), a QGC vertex (middle), and scattering via a Higgs boson in $ t $-channel (right). |
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Figure 29-c:
Production of oppositely charged W bosons via vector boson scattering. Example Feynman diagrams include: scattering via Z boson and two TGC vertices (left), a QGC vertex (middle), and scattering via a Higgs boson in $ t $-channel (right). |
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Figure 30:
Feynman diagrams for vector boson fusion production of Z (left) and W bosons (middle) via the $ \mathrm{W}\mathrm{W} \mathrm{Z} $ TGC vertex and W via the $ \mathrm{W}\mathrm{W}\gamma $ TGC vertex (right). |
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Figure 30-a:
Feynman diagrams for vector boson fusion production of Z (left) and W bosons (middle) via the $ \mathrm{W}\mathrm{W} \mathrm{Z} $ TGC vertex and W via the $ \mathrm{W}\mathrm{W}\gamma $ TGC vertex (right). |
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Figure 30-b:
Feynman diagrams for vector boson fusion production of Z (left) and W bosons (middle) via the $ \mathrm{W}\mathrm{W} \mathrm{Z} $ TGC vertex and W via the $ \mathrm{W}\mathrm{W}\gamma $ TGC vertex (right). |
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Figure 30-c:
Feynman diagrams for vector boson fusion production of Z (left) and W bosons (middle) via the $ \mathrm{W}\mathrm{W} \mathrm{Z} $ TGC vertex and W via the $ \mathrm{W}\mathrm{W}\gamma $ TGC vertex (right). |
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Figure 31:
Distribution for a BDT discriminant used to select VBF Z events in dimuon events. The contributions from the different background sources and the signal are shown stacked, with data points superimposed. The vertical errors bars around the experimental data points show the total uncertainties. The expected signal-only contribution is also shown as an open histogram. The lower panel shows the relative difference between the data and expectations, as well as the uncertainty envelopes for the jet energy scale, and renormalization and factorization scale uncertainties. Figure taken from Ref. [328]. |
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Figure 32:
Summary of cross section measurements of EW single or diboson production processes including vector boson fusion, vector boson scattering, and scattering via exclusive processes. Production of pairs of W bosons can occur in same-sign (ss) $ \mathrm{W}^{\pm}\mathrm{W}^{\pm} $, opposite-sign (os), $ \mathrm{W}^{\pm}\mathrm{W}^{\mp} $, or exclusive production where photons are radiated from the incoming protons and form $ \mathrm{W}^{\pm}\mathrm{W}^{\mp} $ pairs via EW scattering. Results are displayed as a ratio of the experimental measurement over the SM prediction. The yellow bands indicate the uncertainties in the theoretical predictions and the error bars on the points are the experimental uncertainties, with the outer bar being the combined statistical and systematic uncertainty. |
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Figure 33:
Feynman diagrams illustrating the pure EW contributions to single top quark production at the LHC at Born level. Charge conjugate states are implied. From left to right: the $ t $-channel production, (a) with and (b) without a b quark in the initial state; (c) the $ s $-channel; and (d) the $ \mathrm{t}\mathrm{W} $-production. In all diagrams the $ \mathrm{t}\mathrm{W}\mathrm{q} $ vertex is marked with a purple dot. |
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Figure 33-a:
Feynman diagrams illustrating the pure EW contributions to single top quark production at the LHC at Born level. Charge conjugate states are implied. From left to right: the $ t $-channel production, (a) with and (b) without a b quark in the initial state; (c) the $ s $-channel; and (d) the $ \mathrm{t}\mathrm{W} $-production. In all diagrams the $ \mathrm{t}\mathrm{W}\mathrm{q} $ vertex is marked with a purple dot. |
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Figure 33-b:
Feynman diagrams illustrating the pure EW contributions to single top quark production at the LHC at Born level. Charge conjugate states are implied. From left to right: the $ t $-channel production, (a) with and (b) without a b quark in the initial state; (c) the $ s $-channel; and (d) the $ \mathrm{t}\mathrm{W} $-production. In all diagrams the $ \mathrm{t}\mathrm{W}\mathrm{q} $ vertex is marked with a purple dot. |
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Figure 33-c:
Feynman diagrams illustrating the pure EW contributions to single top quark production at the LHC at Born level. Charge conjugate states are implied. From left to right: the $ t $-channel production, (a) with and (b) without a b quark in the initial state; (c) the $ s $-channel; and (d) the $ \mathrm{t}\mathrm{W} $-production. In all diagrams the $ \mathrm{t}\mathrm{W}\mathrm{q} $ vertex is marked with a purple dot. |
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Figure 33-d:
Feynman diagrams illustrating the pure EW contributions to single top quark production at the LHC at Born level. Charge conjugate states are implied. From left to right: the $ t $-channel production, (a) with and (b) without a b quark in the initial state; (c) the $ s $-channel; and (d) the $ \mathrm{t}\mathrm{W} $-production. In all diagrams the $ \mathrm{t}\mathrm{W}\mathrm{q} $ vertex is marked with a purple dot. |
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Figure 34:
Single top quark cross section summary of CMS measurements as a function of the pp centre-of-mass energy. Where available the results from the full LHC combination are also overlaid for comparison. The theoretical calculations for $ t $-channel, $ s $-channel, and W-associated production are from Refs. [370,371,372,373]. |
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Figure 35:
Summary of the CMS measurements of $ R_\mathrm{t}=\sigma_\mathrm{t}/\sigma_\overline{\mathrm{t}} $, the cross section ratio between $ t $-channel top quark and $ t $-channel top antiquark production. The measurements are compared with NNLO QCD calculations using the PDF sets CT18 and PDF4LHC21. The coloured bands represent the uncertainties in the theoretical predictions (scale and PDF uncertainties). The PDF uncertainties are estimated using the PDF4LHC21 prescription [383]. |
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Figure 36:
Leading order Feynman diagrams for $ \mathrm{t} \overline{\mathrm{t}} $ production. |
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Figure 36-a:
Leading order Feynman diagrams for $ \mathrm{t} \overline{\mathrm{t}} $ production. |
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Figure 36-b:
Leading order Feynman diagrams for $ \mathrm{t} \overline{\mathrm{t}} $ production. |
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Figure 36-c:
Leading order Feynman diagrams for $ \mathrm{t} \overline{\mathrm{t}} $ production. |
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Figure 36-d:
Leading order Feynman diagrams for $ \mathrm{t} \overline{\mathrm{t}} $ production. |
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Figure 37:
Summary of top quark-antiquark pair cross section measurements by the CMS Collaboration in comparison with the theory calculation at NNLO+NNLL accuracy. The Tevatron measurements are also shown. The lower panel displays the ratio between the different measurements and the theory prediction. The coloured bands represent the theory uncertainty, while the error bars represent the uncertainty on the measurements. |
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Figure 38:
Summary of CMS top quark-antiquark pair cross section measurements at different $ \sqrt{s} $, normalized to the theory calculation at NNLO+NNLL accuracy. The different final states and $ \sqrt{s} $ are respectively represented by various markers and colours. The total (statistical) uncertainty associated with the measurements is represented by the outer (inner) error bars. |
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Figure 39:
Differential cross sections at the parton level as a function of the hadronically decaying top quark $ p_{\mathrm{T}} $ (left) and of the $ \mathrm{t} \overline{\mathrm{t}} $ invariant mass (right). The analysis was performed using $ \mathrm{t} \overline{\mathrm{t}} $ events in the $ \ell $+jets final state. The data are shown as points with grey (yellow) bands indicating the statistical (statistical and systematic) uncertainties. The cross sections are compared with the predictions of POWHEG combined with PYTHIA (P8) or HERWIG (H7), the multiparton simulation MadGraph-5_aMC@NLO (MG)+PYTHIA FXFX, and the NNLO QCD calculations obtained with MATRIX. The error bars represent the theory uncertainty in the predictions. The ratios of the various predictions to the measured cross sections are shown in the lower panels. Figure from Ref. [403]. |
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Figure 39-a:
Differential cross sections at the parton level as a function of the hadronically decaying top quark $ p_{\mathrm{T}} $ (left) and of the $ \mathrm{t} \overline{\mathrm{t}} $ invariant mass (right). The analysis was performed using $ \mathrm{t} \overline{\mathrm{t}} $ events in the $ \ell $+jets final state. The data are shown as points with grey (yellow) bands indicating the statistical (statistical and systematic) uncertainties. The cross sections are compared with the predictions of POWHEG combined with PYTHIA (P8) or HERWIG (H7), the multiparton simulation MadGraph-5_aMC@NLO (MG)+PYTHIA FXFX, and the NNLO QCD calculations obtained with MATRIX. The error bars represent the theory uncertainty in the predictions. The ratios of the various predictions to the measured cross sections are shown in the lower panels. Figure from Ref. [403]. |
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Figure 39-b:
Differential cross sections at the parton level as a function of the hadronically decaying top quark $ p_{\mathrm{T}} $ (left) and of the $ \mathrm{t} \overline{\mathrm{t}} $ invariant mass (right). The analysis was performed using $ \mathrm{t} \overline{\mathrm{t}} $ events in the $ \ell $+jets final state. The data are shown as points with grey (yellow) bands indicating the statistical (statistical and systematic) uncertainties. The cross sections are compared with the predictions of POWHEG combined with PYTHIA (P8) or HERWIG (H7), the multiparton simulation MadGraph-5_aMC@NLO (MG)+PYTHIA FXFX, and the NNLO QCD calculations obtained with MATRIX. The error bars represent the theory uncertainty in the predictions. The ratios of the various predictions to the measured cross sections are shown in the lower panels. Figure from Ref. [403]. |
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Figure 40:
Normalized differential cross sections as a function of $ p_{\mathrm{T}}(\mathrm{t}) $ in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ (upper), and as a function of $ y({\mathrm{t}\overline{\mathrm{t}}} ) $ in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ (lower). The data, shown as bullets with grey and yellow bands indicating the statistical and total uncertainties, are compared with the prediction from POWHEG +PYTHIA 8 and various theoretical predictions (see text). The error bars represent the theory uncertainty in some of the predictions. The lower panel in each figure shows the ratios of the predictions to the data. Figure from Ref. [420]. |
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Figure 40-a:
Normalized differential cross sections as a function of $ p_{\mathrm{T}}(\mathrm{t}) $ in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ (upper), and as a function of $ y({\mathrm{t}\overline{\mathrm{t}}} ) $ in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ (lower). The data, shown as bullets with grey and yellow bands indicating the statistical and total uncertainties, are compared with the prediction from POWHEG +PYTHIA 8 and various theoretical predictions (see text). The error bars represent the theory uncertainty in some of the predictions. The lower panel in each figure shows the ratios of the predictions to the data. Figure from Ref. [420]. |
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Figure 40-b:
Normalized differential cross sections as a function of $ p_{\mathrm{T}}(\mathrm{t}) $ in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ (upper), and as a function of $ y({\mathrm{t}\overline{\mathrm{t}}} ) $ in bins of $ m({\mathrm{t}\overline{\mathrm{t}}} ) $ (lower). The data, shown as bullets with grey and yellow bands indicating the statistical and total uncertainties, are compared with the prediction from POWHEG +PYTHIA 8 and various theoretical predictions (see text). The error bars represent the theory uncertainty in some of the predictions. The lower panel in each figure shows the ratios of the predictions to the data. Figure from Ref. [420]. |
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Figure 41:
Normalized differential cross section as a function of the azimuthal opening angle between the two charged leptons in a $ \mathrm{t} \overline{\mathrm{t}} $ dilepton final state ($ |\Delta\phi_{\ell^+\ell^-}| $) from data (points); parton-level predictions from MC@NLO (dashed histograms); and theoretical predictions at NLO with (SM) and without (no spin corr.) spin correlations (solid and dotted histograms, respectively). The ratio of the data to the MC@NLO prediction is shown in the lower panel. The inner and outer vertical bars on the data points represent the statistical and total uncertainties, respectively. The hatched bands represent variations of $ \mu_\text{R} $ and $ \mu_\text{F} $ simultaneously up and down by a factor of 2. Figure from Ref. [424]. |
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Figure 42:
Example Feynman diagrams for the production of $ \mathrm{t} \overline{\mathrm{t}} $ with a vector boson through initial state radiation (a) or a direct coupling to the top quark (b and c). The latter is only possible for neutral bosons $ \text{V}^0=\gamma, \mathrm{Z} $. |
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Figure 42-a:
Example Feynman diagrams for the production of $ \mathrm{t} \overline{\mathrm{t}} $ with a vector boson through initial state radiation (a) or a direct coupling to the top quark (b and c). The latter is only possible for neutral bosons $ \text{V}^0=\gamma, \mathrm{Z} $. |
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Figure 42-b:
Example Feynman diagrams for the production of $ \mathrm{t} \overline{\mathrm{t}} $ with a vector boson through initial state radiation (a) or a direct coupling to the top quark (b and c). The latter is only possible for neutral bosons $ \text{V}^0=\gamma, \mathrm{Z} $. |
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Figure 42-c:
Example Feynman diagrams for the production of $ \mathrm{t} \overline{\mathrm{t}} $ with a vector boson through initial state radiation (a) or a direct coupling to the top quark (b and c). The latter is only possible for neutral bosons $ \text{V}^0=\gamma, \mathrm{Z} $. |
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Figure 43:
Example Feynman diagrams for the production of $ \mathrm{t} \mathrm{Z}\mathrm{q} $. |
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Figure 43-a:
Example Feynman diagrams for the production of $ \mathrm{t} \mathrm{Z}\mathrm{q} $. |
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Figure 43-b:
Example Feynman diagrams for the production of $ \mathrm{t} \mathrm{Z}\mathrm{q} $. |
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Figure 43-c:
Example Feynman diagrams for the production of $ \mathrm{t} \mathrm{Z}\mathrm{q} $. |
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Figure 44:
Summary of CMS $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $ and $ {\mathrm{t}\overline{\mathrm{t}}} \text{V}^0 $ cross section measurements with respect to the SM prediction. The horizontal bars display separately the statistical and the total uncertainties of the experimental measurements. The uncertainty associated to the theory predictions is represented by shaded bands and includes the variations of the renormalization and factorization scales and parton density functions. |
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Figure 45:
Summary of CMS measurements of $ \mathrm{t} \text{V}^0 \mathrm{q} $ ($ \text{V}^0= \mathrm{Z},\gamma $) cross sections at 13 TeV. The cross section measurements are compared with the NLO QCD theoretical calculation. The horizontal bars display separately the statistical and the total uncertainties. The uncertainty associated to the theory predictions is represented by shaded bands and includes the variations of the renormalization and factorization scales and parton density functions. |
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Figure 46:
Feynman diagrams contributing to the associated production of top quarks with heavy-flavoured jets. |
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Figure 46-a:
Feynman diagrams contributing to the associated production of top quarks with heavy-flavoured jets. |
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Figure 46-b:
Feynman diagrams contributing to the associated production of top quarks with heavy-flavoured jets. |
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Figure 46-c:
Feynman diagrams contributing to the associated production of top quarks with heavy-flavoured jets. |
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Figure 47:
Summary of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{b}\overline{\mathrm{b}} $ cross section measurements. The left plot depicts the measurements performed in the full phase space using different final states and data sets, compared with different MC predictions. The right plot shows the ratio between the theoretical and measured cross. The statistical and total uncertainties on the measurements are represented by different shaded bands, while the uncertainty on the predictions are represented by error bars. |
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Figure 47-a:
Summary of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{b}\overline{\mathrm{b}} $ cross section measurements. The left plot depicts the measurements performed in the full phase space using different final states and data sets, compared with different MC predictions. The right plot shows the ratio between the theoretical and measured cross. The statistical and total uncertainties on the measurements are represented by different shaded bands, while the uncertainty on the predictions are represented by error bars. |
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Figure 47-b:
Summary of $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{b}\overline{\mathrm{b}} $ cross section measurements. The left plot depicts the measurements performed in the full phase space using different final states and data sets, compared with different MC predictions. The right plot shows the ratio between the theoretical and measured cross. The statistical and total uncertainties on the measurements are represented by different shaded bands, while the uncertainty on the predictions are represented by error bars. |
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Figure 48:
Representation of different Feynman diagrams contributing to $ \mathrm{t} \overline{\mathrm{t}} $ $ \mathrm{t} \overline{\mathrm{t}} $ production at the LHC. Diagrams that involve strong coupling vertices, shown in (a), are expected to dominate. |
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Figure 48-a:
Representation of different Feynman diagrams contributing to $ \mathrm{t} \overline{\mathrm{t}} $ $ \mathrm{t} \overline{\mathrm{t}} $ production at the LHC. Diagrams that involve strong coupling vertices, shown in (a), are expected to dominate. |
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Figure 48-b:
Representation of different Feynman diagrams contributing to $ \mathrm{t} \overline{\mathrm{t}} $ $ \mathrm{t} \overline{\mathrm{t}} $ production at the LHC. Diagrams that involve strong coupling vertices, shown in (a), are expected to dominate. |
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Figure 48-c:
Representation of different Feynman diagrams contributing to $ \mathrm{t} \overline{\mathrm{t}} $ $ \mathrm{t} \overline{\mathrm{t}} $ production at the LHC. Diagrams that involve strong coupling vertices, shown in (a), are expected to dominate. |
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Figure 49:
Summary of CMS measurements of the $ \mathrm{t} \overline{\mathrm{t}} $ $ \mathrm{t} \overline{\mathrm{t}} $ production cross section at 13 TeV in various channels. The total (statistical) uncertainty associated with the measurements is represented by the outer (inner) error bars. The cross section measurements are compared with the NLO QCD and EW theoretical calculation. The theoretical band represents uncertainties due to renormalization and factorization scales. Complementary theory predictions are also available in Ref. [476]. |
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Figure 50:
Summary of $ \alpha_\mathrm{S} $ determinations from inclusive and differential top quark cross section measurements. The error bars represent the total uncertainty of the measurements. The results obtained with different PDF sets are compared with the world average [123] and the reference $ \alpha_\mathrm{S} $ in the corresponding PDF set. The 68% confidence intervals are represented by the error bars and the coloured ranges. The PDFs marked with a $ \dagger $ include LHC top quark data in their fits. |
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Figure 51:
Summary of $ |V_{\mathrm{t}\mathrm{b}}| $ determinations from top quark events using different techniques. The values measured and the corresponding references are given in the figures. The error bars represent separately different uncertainties, as described in the legend. In the LHC combinations, the reference theory cross section used in the $ t $- and $ s $-channel measurements is computed at NLO QCD accuracy [371] with the PDF4LHC prescription for the PDF uncertainty using CT10nlo, MCSTW2008nlo, and NNPDF2.3nlo [483], whereas in the $ \mathrm{t}\mathrm{W} $ channel the theory reference is computed at NNLO+NNLL QCD accuracy [484] using the MSTW2008 NNLO PDF [109]. A line at $ |V_{\mathrm{t}\mathrm{b}}|= $ 1 is used as a common reference. |
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Figure 52:
Summary of production cross section measurements involving top quarks. Measurements performed at different LHC pp collision energies are marked by unique symbols and the coloured bands indicate the combined statistical and systematic uncertainty of the measurement. Grey bands indicate the uncertainty of the corresponding SM theory predictions. Shaded hashed bars indicate the excluded cross section region for a production process with the measured 95% C.L. upper limit on the process indicated by the solid line of the same colour. |
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Figure 53:
Higgs boson production in (a) gluon-gluon fusion (ggH), (b) vector boson fusion (VBF), (c) associated production with a W or Z (V) boson (VH), (d) associated production with a top or bottom quark pair ($ \mathrm{t}\mathrm{t}\mathrm{H} $ or $ \mathrm{b}\mathrm{b}\mathrm{H} $), (e, f) associated production with a single top quark ($ \mathrm{t}\mathrm{H} $); with Higgs boson decays into (g) heavy vector boson pairs, (h) fermion-antifermion pairs, and (i, j) photon pairs or $ \mathrm{Z}\gamma $; Higgs boson pair production: (k, l) via gluon-gluon fusion, and (m, n, o) via vector boson fusion. The corresponding Higgs boson interactions are labelled with the coupling modifiers $ \kappa $, and highlighted in different colours for Higgs-fermion interactions (red), Higgs-gauge-boson interactions (blue), and multiple Higgs boson interactions (green). The distinction between a particle and its antiparticle is dropped. Figure taken from Ref. [512]. |
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Figure 54:
Signal strength parameters per individual production mode and decay channel $ \mu_{i}^{f} $, and combined per production mode $ \mu_{i} $ and decay channel $ \mu^{f} $. The SM expectation at 1 (dashed vertical lines) is shown as a reference. Light-grey shading indicates that $ \mu $ is constrained to be positive. Dark-grey shading indicates the absence of a measurement. The measured value for each production cross section modifier obtained from the combination across the decay channels, $ \mu_i $, is indicated by the blue vertical line. The corresponding 68% CL interval is indicated by the blue bands. The arrows indicate cases where the confidence intervals exceed the scale of the horizontal axis. Figure taken from Ref. [512]. |
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Figure 55:
Measured cross sections for the main Higgs boson production modes. The best fit cross sections are plotted together with the respective 68% confidence level intervals. The systematic components of the uncertainty in each parameter are shown by the coloured boxes. The grey boxes indicate the theoretical uncertainties in the SM predictions. The lower panel shows the ratio of the fitted values to the SM predictions. |
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Figure 56:
The measured inclusive fiducial cross section for $ \mathrm{H}\to \mathrm{Z} \mathrm{Z}\to 4\ell $ as a function of $ \sqrt{s} $. The acceptance is calculated using HRES [530,531] at 7 and 8 TeV, and POWHEG at 13 TeV, and the total gluon fusion cross section and uncertainty are taken from Ref. [532]. The SM predictions and measurements are calculated at $ m_{\mathrm{H}}= $ 125.0 GeV for $ \sqrt{s}= $ 6-9 TeV, and at $ m_{\mathrm{H}}= $ 125.38 GeV for 12-14 TeV. Figure taken from Ref. [492]. |
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Figure 57:
Differential fiducial cross sections for Higgs boson production in the $ \mathrm{H}\to\gamma\gamma $ [526] (upper) and $ \mathrm{H}\to \mathrm{b}\overline{\mathrm{b}} $ [537] (lower) decay channels as functions of the transverse momentum of the Higgs boson $ p_\text{T}^{\mathrm{H}} $. Figure compiled from Refs. [526,537]. |
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Figure 57-a:
Differential fiducial cross sections for Higgs boson production in the $ \mathrm{H}\to\gamma\gamma $ [526] (upper) and $ \mathrm{H}\to \mathrm{b}\overline{\mathrm{b}} $ [537] (lower) decay channels as functions of the transverse momentum of the Higgs boson $ p_\text{T}^{\mathrm{H}} $. Figure compiled from Refs. [526,537]. |
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Figure 57-b:
Differential fiducial cross sections for Higgs boson production in the $ \mathrm{H}\to\gamma\gamma $ [526] (upper) and $ \mathrm{H}\to \mathrm{b}\overline{\mathrm{b}} $ [537] (lower) decay channels as functions of the transverse momentum of the Higgs boson $ p_\text{T}^{\mathrm{H}} $. Figure compiled from Refs. [526,537]. |
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Figure 58:
Differential fiducial cross sections for Higgs boson production as functions of the number of jets in the event, for the $ \mathrm{H}\to \mathrm{W}\mathrm{W} $ [529] (upper) and $ \mathrm{H}\to \tau\tau $ [528] (lower) decay modes. Figure compiled from Refs. [526,537]. |
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Figure 58-a:
Differential fiducial cross sections for Higgs boson production as functions of the number of jets in the event, for the $ \mathrm{H}\to \mathrm{W}\mathrm{W} $ [529] (upper) and $ \mathrm{H}\to \tau\tau $ [528] (lower) decay modes. Figure compiled from Refs. [526,537]. |
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Figure 58-b:
Differential fiducial cross sections for Higgs boson production as functions of the number of jets in the event, for the $ \mathrm{H}\to \mathrm{W}\mathrm{W} $ [529] (upper) and $ \mathrm{H}\to \tau\tau $ [528] (lower) decay modes. Figure compiled from Refs. [526,537]. |
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Figure 59:
Double-differential cross sections for Higgs boson production in the $ \mathrm{H}\to \mathrm{Z} \mathrm{Z}\to 4\ell $ decay channel. The cross section is measured in bins of the rapidity of the Higgs boson $ |y_{\mathrm{H}}| $, as a function of the Higgs boson transverse momentum $ p_\text{T}^{\mathrm{H}} $. Figure taken from Ref. [527]. |
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Figure 60:
Observed results of the minimal merging scheme STXS fit for $ \mathrm{H}\to\gamma\gamma $ at 13 TeV. The best fit cross sections are plotted together with the respective 68% confidence level intervals. Figure taken from Ref. [495]. |
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Figure 61:
The expected and observed upper limits on the production of Higgs boson pairs. The results are expressed as a ratio to the SM prediction for the cross section ($ \sigma(\mathrm{p}\mathrm{p}\to \mathrm{H}\mathrm{H})/\sigma_\text{SM} $). A vertical red line at $ \sigma(\mathrm{p}\mathrm{p}\to \mathrm{H}\mathrm{H})/\sigma_\text{SM}= $ 1 is drawn to guide the eye. The search modes are ordered, from upper to lower, by their expected sensitivities from the least to the most sensitive. The overall combination of all searches is shown by the lowest entry. Figure taken from Ref. [512]. |
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Figure 62:
Summary of electroweak cross section measurements. Measurements performed at different LHC pp collision energies are marked by unique symbols and the coloured bands indicate the combined statistical and systematic uncertainty of the measurement. Grey bands indicate the uncertainty of the corresponding SM theory predictions. Shaded hashed bars indicate the excluded cross section region for a production process with the measured 95% C.L. upper limit on the process indicated by the solid line of the same colour. |
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Figure 63:
Summary of measurements of jet cross sections and electroweak processes in association with jets. |
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Figure 64:
Summary of top quark production cross section measurements. |
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Figure 65:
Summary of Higgs boson production cross section measurements. |
| Tables | |
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Table 1:
Integrated pp collision luminosity $ \mathcal{L} $, analyzed by the CMS experiment during LHC Runs 1, 2 and 3, as well as during pp reference runs for the heavy ion physics programme at 2.76 and 5.02 TeV. |
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Table 2:
Monte Carlo programs used by analyses included in this Report. |
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Table 3:
Sets of PDFs used for analyses included in this Report. |
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Table 4:
The measured inclusive fiducial jet production cross sections for four pp collision energies for inclusive production of anti-$ k_{\mathrm{T}} R = $ 0.7 jets satisfying $ p_{\mathrm{T}} > $ 133 GeV and $ |y| < $ 2.0. Results are compared with predictions at NNLO QCD and NLO EW precision. The statistical uncertainty in the theory predictions is negligible. |
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Table 5:
The CMS analyses where PDF fits were performed. The table lists the final state and distributions considered, the pp collision energy, the HERA data set used or global PDF provided, the QCD perturbative order of the fit, and the most constrained PDFs. Whenever data from multiple analyses are used, the first analysis listed contains the PDF extraction. In the 13 TeV analysis the inclusive jet data are used in an NNLO PDF fit, whereas the inclusive jet and $ \mathrm{t} \overline{\mathrm{t}} $ data are used in an NLO PDF fit. |
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Table 6:
Overview of $ \alpha_\mathrm{S}(m_ \mathrm{Z}) $ from CMS analyses. Results where $ \alpha_\mathrm{S} $ is determined by profiling a global PDF set, list the set used. The other results were obtained using a combined PDF and $ \alpha_\mathrm{S} $ fit of the CMS and HERA data as described in the text. The 2D inclusive jet [144] analysis only uses the HERA-I data, whereas the other combined PDF and $ \alpha_\mathrm{S} $ fits use the combined HERA-I and HERA-II data. The QCD perturbative order (pQCD order) of the determination is also given. For publications where more than one value is extracted, only one is reported. Whenever data from other analyses are used in the $ \alpha_\mathrm{S} $ determination, the first analysis listed documents the $ \alpha_\mathrm{S} $ extraction. |
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Table 7:
Measured inclusive cross sections for Z boson production at pp collision energies from 2.76 to 13 TeV. Total uncertainties in the experimental measurements are given in pb and as a percentage. Separate components of the experimental statistical and systematic uncertainties other than the dominant integrated luminosity uncertainty were not published for the 2.76 TeV cross section measurement. The statistical uncertainties of the 7 and 8 TeV measurements are smaller than 1 pb and are not shown. The measurements are compared with theoretical predictions obtained at $ \text{N}^3\text{LO} $ in QCD using the MSHT20a$ \text{N}^3\text{LO} $ PDF set. The theoretical uncertainty is from normalization and factorization scale variations. |
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Table 8:
Measured fiducial cross sections for Z boson production and decay to electrons and muons in pp collisions at energies from 5.02 to 13 TeV. Total uncertainties in the experimental measurements are given in pb and as a percentage. The measurements are compared with theoretical predictions at NNLO in QCD described in the references above. In each case, the uncertainty in the CMS measurement of the fiducial Z boson cross section is reduced compared with the inclusive measurement and the integrated luminosity uncertainty dominates the overall uncertainty of the measurements. |
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Table 9:
Measured ratios, $ R_\text{exp} $, of inclusive cross sections for W and Z boson production times the branching fractions $ \mathcal{B}(\mathrm{W} \to \ell\nu) $ and $ \mathcal{B}( \mathrm{Z} \to \ell^+\ell^-) $ (with the dilepton mass between 60 and 120 GeV), respectively. Ratios $ R_{\mathrm{W^+}/\mathrm{W^-}} = \sigma(\mathrm{W^+}) \mathcal{B}(\mathrm{W^+} \to \ell^+\nu)/ \sigma(\mathrm{W^-}) \mathcal{B}(\mathrm{W^-} \to \ell^-\overline{\nu}) $ and $ R_{\mathrm{W}/ \mathrm{Z}} = \sigma(\mathrm{W}) \mathcal{B}(\mathrm{W} \to \ell\nu)/\sigma( \mathrm{Z}) \mathcal{B}( \mathrm{Z} \to \ell^+\ell^-) $ are shown for pp collision energies from 5.02 to 13 TeV. The total uncertainty in the experimental measurement is shown in the standard and percentage forms. The measurements are compared with theoretical predictions, $ \mathrm{R_{\text{SM}}} $, obtained at NNLO in QCD. The theoretical uncertainties, expressed as percentages, are from renormalization and factorization scale variations, $ \alpha_\mathrm{S} $, and the PDF uncertainty. |
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Table 10:
Measured ratios, $ R_\text{exp} $, of fiducial cross sections for W and Z boson production times the branching fractions $ \mathcal{B}(\mathrm{W} \to \ell\nu) $ and $ \mathcal{B}( \mathrm{Z} \to \ell^+\ell^-) $, respectively. Ratios $ R_{\mathrm{W^+}/\mathrm{W^-}} = \sigma(\mathrm{W^+}) \mathcal{B}(\mathrm{W^+} \to \ell^+\nu)/ \sigma(\mathrm{W^-}) \mathcal{B}(\mathrm{W^-}\to \ell^-\overline{\nu}) $ and $ R_{\mathrm{W}/ \mathrm{Z}} = \sigma(\mathrm{W}) \mathcal{B}(\mathrm{W} \to \ell\nu)/ \sigma( \mathrm{Z}) \mathcal{B}( \mathrm{Z}\to \ell^+\ell^-) $ are shown for at pp collision energies from 5.02 to 13 TeV. The total uncertainty in the experimental measurement is shown in the standard and percentage forms. The measurements are compared with theoretical predictions, $ R_\text{SM} $, obtained at NNLO in QCD. The theoretical uncertainties, expressed as percentages, are from normalization and factorization scale variations, $ \alpha_\mathrm{S} $, and PDF uncertainty. |
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Table 11:
Measurements of W and Z boson production in association with jets and the MC generators used for comparison to the measured cross sections. All measurements are inclusive cross sections for the vector boson produced in association with the listed or higher number of jets. For each measurement, the pp collision energy, ME generator, largest number of hard partons generated, largest number of hard partons generated at NLO accuracy, PS generator, and the ME-PS matching scheme are given. Events generated with greater than the number of NLO partons have LO accuracy. If no matching scheme is listed the comparison was done directly to the parton-level cross section predictions after applying a correction for NP effects. For the 7 and 8 TeV results the SHERPA with BLACKHAT ( SHERPA 1/2, BH) NLO comparison was done only for lower parton multiplicities. The MADGRAPH 5 or MadGraph-5_aMC@NLO (denoted MG5_aMC) comparisons are shown for higher jet multiplicities. |
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Table 12:
Measurements of W and Z boson production in association with heavy-flavour quarks. The table lists the measured production cross sections, pp collision energy, heavy-flavour tagging technique, source of theory cross section calculation used for comparison, and other results of interest produced by the analysis. In several cases, ratios of production cross sections are measured including $ R_{\mathrm{W^+}\overline{\mathrm{c}}/\mathrm{W^-}\mathrm{c}} = \sigma(\mathrm{W^+}\overline{\mathrm{c}})/\sigma(\mathrm{W^-}\mathrm{c}) $, $ R_{\mathrm{W}\mathrm{c}/ \mathrm{Z}\mathrm{b}} = \sigma(\mathrm{W}\mathrm{c})/\sigma( \mathrm{Z}\mathrm{b}) $, $ R_{ \mathrm{Z}\mathrm{b}/ \mathrm{Z}\mathrm{q}} = \sigma( \mathrm{Z}\mathrm{b})/\sigma( \mathrm{Z}\mathrm{q}) $ and $ R_{ \mathrm{Z}\ge 2\mathrm{b}/ \mathrm{Z}\ge 1\mathrm{b}} = \sigma( \mathrm{Z}\ge 2\mathrm{b})/\sigma( \mathrm{Z}\ge 1\mathrm{b}) $. Parton-level MCFM NLO and NNLO predictions are corrected for NP effects. All predictions are computed at NLO QCD accuracy except for the W+c 13 TeV analysis, where the prediction is done at NNLO QCD and NLO EW accuracy [266,267]. |
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Table 13:
Diboson production cross section measurements. Listed in the table are the final states studied, pp collision energy, theory cross section calculation used for comparison, and selected additional results of interest from each paper. |
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Table 14:
Summary of measurements of diboson production in association with jets. Listed are the diboson state, number of jets measured, generator(s) used with perturbative QCD order and $ K $-factors used to scale the result to a higher order, total number of additional partons generated, number of partons generated at NLO, parton shower MC, and ME-PS jet merging scheme. The total number of partons includes additional real-emission partons generated by NLO or NNLO QCD matrix element calculations. The highest bin in the jet multiplicity includes events with a higher number of jets as well. |
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Table 15:
Triboson production cross section measurements. Listed in the table are signatures studied, pp collision energy, theory cross section calculation used for comparison, and selected additional results of interest from each measurement. |
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Table 16:
Purely EW production cross section measurements. Listed in the table are signatures studied, pp collision energy, theory cross section calculation used for comparison, and selected additional results of interest from each paper. |
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Table 17:
Summary of final states covered experimentally in associated top quark and neutral boson production by CMS. For each process listed in column (a), column (b) quotes the theoretical prediction at 13 TeV. Columns (c) and (d) summarize the different final states generated by the top quark (s) and boson decays with the corresponding branching fraction (B) listed in column (f). The combined results for the W and Z boson Bs include the propagation of $ \tau $-leptonic decays. The nomenclature assigned to these channels is shown in column (e) with SS (OS) used as a shorthand for same- (opposite-) charge lepton pairs. The CMS measurements of these channels are listed in column (g). The theoretical uncertainties include the PDF+$ \alpha_\mathrm{S} $ and scale choice. Symbols provide additional information: ($ \dagger $) predicted at NLO accuracy using MadGraph-5_aMC@NLO v2.6.5, and corresponding to the fiducial region [437]; ($ \bullet $) the quoted fiducial $ \mathrm{t}\gamma $ cross section is predicted at NLO QCD accuracy [70] corresponding to the selection of Ref. [436]; ($ \ast $) - computed at NLO including QCD+EW effects and NNLL QCD effects [438]; ($ \star $) - computed at NLO QCD and EW accuracy [439,440,441]; ($ \diamond $) - computed at NLO QCD accuracy in the 5FS [70], in the phase space of [442]. ($ \delta $) - computed at NLO QCD accuracy [440,243]. |
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Table 18:
Summary of final states covered experimentally in associated $ {\mathrm{t}\overline{\mathrm{t}}} \mathrm{W} $ production. The structure of the table is similar to that of Table 17. The cross section column cites the prediction at 13 TeV computed at NLO including QCD (up to two jets) and EW contributions [452]. |
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Table 19:
Measured inclusive cross sections for the main Higgs boson production modes. At 7 and 8 TeV, the measured cross sections are derived by scaling the theoretical cross sections of Ref. [523] by the signal strengths published in Ref. [522]. At $ \sqrt{s} = $ 13 TeV, the cross sections are obtained from a global fit, as described in the text. The results are in good agreement with the predictions from Ref. [523] and Ref. [439], respectively. |
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Table 20:
Measurements of the fiducial cross sections of Higgs boson production in various decay modes published by CMS using pp data at a centre-of-mass energy of 13 TeV and an integrated luminosity of 138 fb$^{-1}$. The reference Higgs boson mass is 125.38 GeV. Isolation ($ \mathcal{I} $) represents the sum of scalar $ p_{\mathrm{T}} $ of all stable particles within $ \Delta R= $ 0.3 of the lepton or photon. Additional details on the fiducial phase space variables and on the calculation of the reference SM cross section are presented in the original references. |
png pdf |
Table 21:
Measurements of the various fiducial cross sections of the Higgs boson for different decay modes published by CMS using proton-proton data at a centre-of-mass energy of 13 TeV. Previous results at 7 and 8 TeV or with a partial data sample are not included in the table. The list of Higgs boson kinematic variables targeted in each case are listed. |
| Summary |
| A wide selection of cross section measurements has been presented from the CMS programme of the quantum chromodynamics, electroweak, top quark, and Higgs physics. Summary plots of electroweak (Fig. 62), electroweak with jets (Fig. 63), top quark (Fig. 64), and Higgs boson (Fig. 65) production cross sections are shown below. No significant deviations from the standard-model (SM) predictions have been found in total or fiducial cross section measurements. Some deviations from the best predictions based on SM physics are found in differential measurements of difficult-to-model areas of phase space in events where multiple SM particles are produced including both light-flavour QCD jets and massive SM bosons or quarks. There is an expectation that improvements in the modelling of QCD and electroweak physics would result in better agreement in these measurements. These discrepancies present a challenge to improve our ability to model SM physics, rather than a sign of beyond-the-SM physics. Of particular note among the CMS cross section measurements are: the SM single W boson production cross section determined with 1.9% uncertainty; the ratios of W to Z production cross sections measured with 0.35% accuracy; the measurement of the WZ diboson cross section with 3.4% precision; the measurement of the top quark pair production cross section with 3.2% uncertainty; and the measurement of the inclusive Higgs boson production cross section with an uncertainty of 5.7%. The achievement of sub-2% level accuracy in production cross section measurements of massive SM particles is unprecedented at hadron colliders. The exploration of the Higgs boson through cross section measurements with high precision is one of the CMS physics programme's most exciting aspects, and the study of the Higgs boson, currently unique to the LHC, is one of our best prospects for finding signs of new physics. These CMS cross section measurements are an enduring legacy in particle physics. |
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