The inclusive cross section of top quark-antiquark pairs produced in $p\bar{p}$ collisions at $\sqrt{s}=1.96$ TeV is measured in the lepton$+$jets and dilepton decay channels. The data sample corresponds to 9.7 fb${}^{-1}$ of integrated luminosity recorded with the D0 detector during Run II of the Fermilab Tevatron Collider. Employing multivariate analysis techniques we measure the cross section in the two decay channels and we perform a combined cross section measurement. For a top quark mass of 172.5 GeV, we measure a combined inclusive top quark-antiquark pair production cross section of $\sigma_{t\bar{t}} = 7.26 \pm 0.13\,(\mathrm{stat.})\,^{+0.57}_{-0.50}\,(\mathrm{syst.})$ pb which is consistent with standard model predictions. We also perform a likelihood fit to the measured and predicted top quark mass dependence of the inclusive cross section, which yields a measurement of the pole mass of the top quark. The extracted value is $m_t = 172.8 \pm 1.1\,(\mathrm{theo.})\,^{+3.3}_{-3.1}\,(\mathrm{exp.})$ GeV.

A measurement of the Z gamma to nu nu-bar gamma production cross section in pp collisions at sqrt(s) = 8 TeV is presented, using data corresponding to an integrated luminosity of 19.6 inverse femtobarns collected with the CMS detector at the LHC. This measurement is based on the observation of events with large missing energy and with a single photon with transverse momentum above 145 GeV and absolute pseudorapidity in the range |eta| < 1.44. The measured Z gamma to nu nu-bar gamma production cross section, 52.7 +/- 2.1(stat) +/- 6.4 (syst) +/- 1.4 (lumi) fb, agrees well with the standard model prediction of 50.0 +2.4 -2.2 fb. A study of the photon transverse momentum spectrum yields the most stringent limits to date on the anomalous Z-Z-gamma and Z-gamma-gamma trilinear gauge boson couplings.

A search for an exotic decay of the Higgs boson to a pair of light pseudoscalar bosons is performed for the first time in the final state with two b quarks and two $\tau$ leptons. The search is motivated in the context of models of physics beyond the standard model (SM), such as two Higgs doublet models extended with a complex scalar singlet (2HDM+S), which include the next-to-minimal supersymmetric SM (NMSSM). The results are based on a data set of proton-proton collisions corresponding to an integrated luminosity of 35.9 fb$^{-1}$, accumulated by the CMS experiment at the LHC in 2016 at a center-of-mass energy of 13 TeV. Masses of the pseudoscalar boson between 15 and 60 GeV are probed, and no excess of events above the SM expectation is observed. Upper limits between 3 and 12% are set on the branching fraction $\mathcal{B}$(h $\to$ aa $\to$ 2$\tau$2b) assuming the SM production of the Higgs boson. Upper limits are also set on the branching fraction of the Higgs boson to two light pseudoscalar bosons in different 2HDM+S scenarios. Assuming the SM production cross section for the Higgs boson, the upper limit on this quantity is as low as 20% for a mass of the pseudoscalar of 40 GeV in the NMSSM.

A search for exotic Higgs boson decays to light pseudoscalars in the final state of two muons and two $\tau$ leptons is performed using proton-proton collision data recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV in 2016, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. Masses of the pseudoscalar boson between 15.0 and 62.5 GeV are probed, and no significant excess of data is observed above the prediction of the standard model. Upper limits are set on the branching fraction of the Higgs boson to two light pseudoscalar bosons in different types of two-Higgs-doublet models extended with a complex scalar singlet.

A search is presented for pairs of light pseudoscalar bosons, in the mass range from 4 to 15 GeV, produced from decays of the 125 GeV Higgs boson. The decay modes considered are final states that arise when one of the pseudoscalars decays to a pair of tau leptons, and the other one either into a pair of tau leptons or muons. The search is based on proton-proton collisions collected by the CMS experiment in 2016 at a center-of-mass energy of 13 TeV that correspond to an integrated luminosity of 35.9 fb${-1}$. The 2$\mu$2$\tau$ and 4$\tau$ channels are used in combination to constrain the product of the Higgs boson production cross section and the branching fraction into 4$\tau$ final state, $\sigma\mathcal{B}$, exploiting the linear dependence of the fermionic coupling strength of pseudoscalar bosons on the fermion mass. No significant excess is observed beyond the expectation from the standard model. The observed and expected upper limits at 95% confidence level on $\sigma\mathcal{B}$, relative to the standard model Higgs boson production cross section, are set respectively between 0.022 and 0.23 and between 0.027 and 0.19 in the mass range probed by the analysis.

The results of a search for a standard model-like Higgs boson in the mass range between 70 and 110 GeV decaying into two photons are presented. The analysis uses the data set collected with the CMS experiment in proton-proton collisions during the 2012 and 2016 LHC running periods. The data sample corresponds to an integrated luminosity of 19.7 (35.9) fb$^{-1}$ at $\sqrt{s} =$8 (13) TeV. The expected and observed 95% confidence level upper limits on the product of the cross section and branching fraction into two photons are presented. The observed upper limit for the 2012 (2016) data set ranges from 129 (161) fb to 31 (26) fb. The statistical combination of the results from the analyses of the two data sets in the common mass range between 80 and 110 GeV yields an upper limit on the product of the cross section and branching fraction, normalized to that for a standard model-like Higgs boson, ranging from 0.7 to 0.2, with two notable exceptions: one in the region around the Z boson peak, where the limit rises to 1.1, which may be due to the presence of Drell-Yan dielectron production where electrons could be misidentified as isolated photons, and a second due to an observed excess with respect to the standard model prediction, which is maximal for a mass hypothesis of 95.3 GeV with a local (global) significance of 2.8 (1.3) standard deviations.

The Lambda(b) differential production cross section and the cross section ratio anti-Lambda(b)/Lambda(b) are measured as functions of transverse momentum pt(Lambda(b)) and rapidity abs(y(Lambda(b))) in pp collisions at sqrt(s) = 7 TeV using data collected by the CMS experiment at the LHC. The measurements are based on Lambda(b) decays reconstructed in the exclusive final state J/Psi Lambda, with the subsequent decays J/Psi to an opposite-sign muon pair and Lambda to proton pion, using a data sample corresponding to an integrated luminosity of 1.9 inverse femtobarns. The product of the cross section times the branching ratio for Lambda(b) to J/Psi Lambda versus pt(Lambda(b)) falls faster than that of b mesons. The measured value of the cross section times the branching ratio for pt(Lambda(b)) > 10 GeV and abs(y(Lambda(b))) < 2.0 is 1.06 +/- 0.06 +/- 0.12 nb, and the integrated cross section ratio for anti-Lambda(b)/Lambda(b) is 1.02 +/- 0.07 +/- 0.09, where the uncertainties are statistical and systematic, respectively.

Measurements of the ZZ production cross sections in proton-proton collisions at center-of-mass energies of 7 and 8 TeV are presented. Candidate events for the leptonic decay mode ZZ to 2 l 2 nu, where l denotes an electron or a muon, are reconstructed and selected from data corresponding to an integrated luminosity of 5.1 (19.6) inverse femtobarns at 7 (8) TeV collected with the CMS experiment. The measured cross sections, sigma(pp to ZZ) = 5.1 -1.4 +1.5 (stat) -1.1 +1.4 (syst) +/- 0.1 (lumi) pb at 7 TeV, and 7.2 -0.8 +0.8 (stat.) -1.5 +1.9 (syst) +/- 0.2 (lumi) pb at 8 TeV, are in good agreement with the standard model predictions with next-to-leading-order accuracy. The selected data are analyzed to search for anomalous triple gauge couplings involving the ZZ final state. In the absence of any deviation from the standard model predictions, limits are set on the relevant parameters. These limits are then combined with the previously published CMS results for ZZ in 4 l final states, yielding the most stringent constraints on the anomalous couplings.

A search for new massive particles decaying into a pair of Higgs bosons in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. Data were collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The search is performed for resonances with a mass between 0.8 and 3.5 TeV using events in which one Higgs boson decays into a bottom quark pair and the other decays into two W bosons that subsequently decay into a lepton, a neutrino, and a quark pair. The Higgs boson decays are reconstructed with techniques that identify final state quarks as substructure within boosted jets. The data are consistent with standard model expectations. Exclusion limits are placed on the product of the cross section and branching fraction for generic spin-0 and spin-2 massive resonances. The results are interpreted in the context of radion and bulk graviton production in models with a warped extra spatial dimension. These are the best results to date from searches for an HH resonance decaying to this final state, and they are comparable to the results from searches in other channels for resonances with masses below 1.5 TeV.

A search for exotic decays of the Higgs boson to a pair of light pseudoscalar particles a$_1$ is performed under the hypothesis that one of the pseudoscalars decays to a pair of opposite sign muons and the other decays to b$\overline{\mathrm{b}}$. Such signatures are predicted in a number of extensions of the standard model (SM), including next-to-minimal supersymmetry and two-Higgs-doublet models with an additional scalar singlet. The results are based on a data set of proton-proton collisions corresponding to an integrated luminosity of 35.9 fb$^{-1}$, accumulated with the CMS experiment at the CERN LHC in 2016 at a centre-of-mass energy of 13 TeV. No statistically significant excess is observed with respect to the SM backgrounds in the search region for pseudoscalar masses from 20 GeV to half of the Higgs boson mass. Upper limits at 95% confidence level are set on the product of the production cross section and branching fraction, $\sigma_{\mathrm{h}}\mathcal{B}$(h $\to$ a$_1$ a$_1$ $\to$ $\mu^+\mu^-\mathrm{b}\bar{\mathrm{b}}$), ranging from 5 to 33 fb, depending on the pseudoscalar mass. Corresponding limits on the branching fraction, assuming the SM prediction for $\sigma_{\mathrm{h}}$, are (1$-$7)$\times$ 10$^{-4}$.

A measurement is presented of the cross section for electroweak production of a Z boson and a photon in association with two jets (Z$\gamma$jj) in proton-proton collisions. The Z boson candidates are selected through their decay into a pair of electrons or muons. The process of interest, electroweak Z$\gamma$jj production, is isolated by selecting events with a large dijet mass and a large pseudorapidity gap between the two jets. The measurement is based on data collected at the CMS experiment at $\sqrt{s} =$ 13 TeV, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The observed significance of the signal is 3.9 standard deviations, where a significance of 5.2 standard deviations is expected in the standard model. These results are combined with published results by CMS at $\sqrt{s} =$ 8 TeV, which leads to observed and expected respective significances of 4.7 and 5.5 standard deviations. From the 13 TeV data, a value is obtained for the signal strength of electroweak Z$\gamma$jj production and bounds are given on quartic vector boson interactions in the framework of dimension-eight effective field theory operators.

A measurement is presented of the cross section for the electroweak production of a Z boson and a photon in association with two jets in proton-proton collisions at sqrt(s)= 8 TeV. The Z bosons are identified through their decays to electron or muon pairs. The measurement is based on data collected with the CMS detector corresponding to an integrated luminosity of 19.7 inverse femtobarns. The electroweak contribution has a significance of 3.0 standard deviations, and the measured fiducial cross section is 1.86 +0.90/-0.75 (stat) +0.34/-0.26 (syst) +/- 0.05 (lumi) fb, while the summed electroweak and quantum chromodynamic total cross section in the same region is observed to be 5.94 +1.53/-1.35 (stat) +0.43/-0.37 (syst) +/- 0.13 (lumi) fb. Both measurements are consistent with the leading-order standard model predictions. Limits on anomalous quartic gauge couplings are set based on the Z gamma mass distribution.

We determine the fraction of events with double parton (DP) scattering in a single ppbar collision at sqrt{s}=1.96 TeV in samples of photon + 3 jet and photon + b/c jet + 2 jet events collected with the D0 detector and corresponding to an integrated luminosity of about 8.7 fb^{-1}. The DP fractions and effective cross sections (sigma_eff) are measured for both event samples using the same kinematic selections. The measured DP fractions range from 0.21 to 0.17, with effective cross sections in the photon + 3 jet and photon + b/c jet + 2 jet samples of sigma_eff^incl = 12.7 +- 0.2 (stat) +- 1.3 (syst) mb and sigma_eff^HF = 14.6 +- 0.6 (stat) +- 3.2 (syst) mb, respectively.

Two related searches for phenomena beyond the standard model (BSM) are performed using events with hadronic jets and significant transverse momentum imbalance. The results are based on a sample of proton-proton collisions at a center-of-mass energy of 13 TeV, collected by the CMS experiment at the LHC in 2016-2018 and corresponding to an integrated luminosity of 137 fb$^{-1}$. The first search is inclusive, based on signal regions defined by the hadronic energy in the event, the jet multiplicity, the number of jets identified as originating from bottom quarks, and the value of the kinematic variable $M_\mathrm{T2}$ for events with at least two jets. For events with exactly one jet, the transverse momentum of the jet is used instead. The second search looks in addition for disappearing tracks produced by BSM long-lived charged particles that decay within the volume of the tracking detector. No excess event yield is observed above the predicted standard model background. This is used to constrain a range of BSM models that predict the following: the pair production of gluinos and squarks in the context of supersymmetry models conserving $R$-parity, with or without intermediate long-lived charginos produced in the decay chain; the resonant production of a colored scalar state decaying to a massive Dirac fermion and a quark; or the pair production of scalar and vector leptoquarks each decaying to a neutrino and a top, bottom, or light-flavor quark. In most of the cases, the results obtained are the most stringent constraints to date.

The first search is presented for vector-like leptons (VLLs) in the context of the "4321 model", an ultraviolet-complete model with the potential to explain existing B physics measurements that are in tension with standard model predictions. The analyzed data, corresponding to an integrated luminosity of 96.5 fb$^{-1}$, were recorded in 2017 and 2018 with the CMS detector at the LHC in proton-proton collisions at $\sqrt{s}$ = 13 TeV. Final states with ${\geq}$ 3 b-tagged jets and two third-generation leptons ($\tau\tau$, $\tau\nu_\tau$, or $\nu_\tau\nu_\tau$) are considered. Upper limits are derived on the VLL production cross section in the VLL mass range 500-1050 GeV. The maximum likelihood fit prefers the presence of signal at the level of 2.8 standard deviations, for a representative VLL mass point of 600 GeV. As a consequence, the observed upper limits are approximately double the expected limits.

A search for new heavy resonances decaying to WW, WZ, ZZ, WH, or ZH boson pairs in the all-jets final state is presented. The analysis is based on proton-proton collision data recorded by the CMS detector in 2016-2018 at a centre-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. The search is sensitive to resonances with masses between 1.3 and 6 TeV, decaying to bosons that are highly Lorentz-boosted such that each of the bosons forms a single large-radius jet. Machine learning techniques are employed to identify such jets. No significant excess over the estimated standard model background is observed. A maximum local significance of 3.6 standard deviations, corresponding to a global significance of 2.3 standard deviations, is observed at masses of 2.1 and 2.9 TeV. In a heavy vector triplet model, spin-1 Z' and W' resonances with masses below 4.8 TeV are excluded at the 95% confidence level (CL). These limits are the most stringent to date. In a bulk graviton model, spin-2 gravitons and spin-0 radions with masses below 1.4 and 2.7 TeV, respectively, are excluded at 95% CL. Production of heavy resonances through vector boson fusion is constrained with upper cross section limits at 95% CL as low as 0.1 fb.

A search is presented for a third-generation leptoquark (LQ) coupled exclusively to a $\tau$ lepton and a b quark. The search is based on proton-proton collision data at a center-of-mass energy of 13 TeV recorded with the CMS detector, corresponding to an integrated luminosity of 138 fb$^{-1}$. Events with $\tau$ leptons and a varying number of jets originating from b quarks are considered, targeting the single and pair production of LQs, as well as nonresonant $t$-channel LQ exchange. An excess is observed in the data with respect to the background expectation in the combined analysis of all search regions. For a benchmark LQ mass of 2 TeV and an LQ-b-$\tau$ coupling strength of 2.5, the excess reaches a local significance of up to 2.8 standard deviations. Upper limits at the 95% confidence level are placed on the LQ production cross section in the LQ mass range 0.5-2.3 TeV, and up to 3 TeV for $t$-channel LQ exchange. Leptoquarks are excluded below masses of 1.22-1.88 TeV for different LQ models and varying coupling strengths up to 2.5. The study of nonresonant $\tau\tau$ production through $t$-channel LQ exchange allows lower limits on the LQ mass of up to 2.3 TeV to be obtained.

The WZ production cross section is measured by the CMS experiment at the CERN LHC in proton-proton collision data samples corresponding to integrated luminosities of 4.9 inverse femtobarns collected at sqrt(s)= 7 TeV, and 19.6 inverse femtobarns at sqrt(s)= 8 TeV. The measurements are performed using the fully-leptonic WZ decay modes with electrons and muons in the final state. The measured cross sections for 71 < m[Z] < 111 GeV are sigma(pp to WZ; sqrt(s)= 7 TeV) = 20.14 +/- 1.32 (stat) +/- 1.13 (syst) +/- 0.44 (lumi) pb and sigma(pp to WZ; sqrt(s)= 8 TeV) = 24.09 +/- 0.87 (stat) +/- 1.62 (syst) +/- 0.63 (lumi) pb. Differential cross sections with respect to the Z boson pt, the leading jet pt, and the number of jets are obtained using the sqrt(s)= 8 TeV data. The results are consistent with standard model predictions and constraints on anomalous triple gauge couplings are obtained.

A search for the exotic decay of the Higgs boson to a pair of light pseudoscalars, each of which subsequently decays into a pair of photons, is presented. The search uses data from proton-proton collisions at $\sqrt{s}$ = 13 TeV recorded with the CMS detector at the LHC that corresponds to an integrated luminosity of 132 fb$^{-1}$. The analysis probes pseudoscalar bosons with masses in the range 15-62 GeV, coming from the Higgs boson decay, which leads to four well-isolated photons in the final state. No significant deviation from the background-only hypothesis is observed. Upper limits are set on the product of the Higgs boson production cross section and branching fraction into four photons. The observed (expected) limits range from 0.80 (1.00) fb for a pseudoscalar boson mass of 15 GeV to 0.26 (0.24) fb for a mass of 62 GeV at 95% confidence level.

A search for new heavy resonances decaying to pairs of bosons (WW, WZ, or WH) is presented. The analysis uses data from proton-proton collisions collected with the CMS detector at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 137 fb$^{-1}$. One of the bosons is required to be a W boson decaying to an electron or muon and a neutrino, while the other boson is required to be reconstructed as a single jet with mass and substructure compatible with a quark pair from a W, Z, or Higgs boson decay. The search is performed in the resonance mass range between 1.0 and 4.5 TeV and includes a specific search for resonances produced via vector boson fusion. The signal is extracted using a two-dimensional maximum likelihood fit to the jet mass and the diboson invariant mass distributions. No significant excess is observed above the estimated background. Model-independent upper limits on the production cross sections of spin-0, spin-1, and spin-2 heavy resonances are derived as functions of the resonance mass and are interpreted in the context of bulk radion, heavy vector triplet, and bulk graviton models. The reported bounds are the most stringent to date.

A search is presented for particle dark matter produced in association with a pair of top quarks in pp collisions at a centre-of-mass energy of sqrt(s) = 8 TeV. The data were collected with the CMS detector at the LHC and correspond to an integrated luminosity of 19.7 inverse femtobarns. This search requires the presence of one lepton, multiple jets, and large missing transverse energy. No excess of events is found above the SM expectation, and upper limits are derived on the production cross section. Interpreting the findings in the context of a scalar contact interaction between fermionic dark matter particles and top quarks, lower limits on the interaction scale are set. These limits are also interpreted in terms of the dark matter-nucleon scattering cross sections for the spin-independent scalar operator and they complement direct searches for dark matter particles in the low mass region.

The consistency of the spin correlation strength in top quark pair production with the standard model (SM) prediction is tested in the muon + jets final state. The events are selected from pp collisions, collected by the CMS detector, at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 19.7 inverse femtobarns. The data are compared with the expectation for the spin correlation predicted by the SM and with the expectation of no correlation. Using a template fit method, the fraction of events that show SM spin correlations is measured to be 0.72 +/- 0.08 (stat) +0.15 -0.13 (syst), representing the most precise measurement of this quantity in the lepton + jets final state to date.

A search for the pair production of heavy fermionic partners of the top quark with charge 5/3 (X$_{5/3}$) is performed in proton-proton collisions at a center-of-mass energy of 13 TeV with the CMS detector at the CERN LHC. The data sample analyzed corresponds to an integrated luminosity of 35.9 fb$^{-1}$. The X$_{5/3}$ quark is assumed always to decay into a top quark and a W boson. Both the right-handed and left-handed X$_{5/3}$ couplings to the W boson are considered. Final states with either a pair of same-sign leptons or a single lepton are studied. No significant excess of events is observed above the expected standard model background. Lower limits at 95% confidence level on the X$_{5/3}$ quark mass are set at 1.33 and 1.30 TeV respectively for the case of right-handed and left-handed couplings to W bosons in a combination of the same-sign dilepton and single-lepton final states.

A measurement of vector boson scattering and constraints on anomalous quartic gauge couplings from events with two Z bosons and two jets are presented. The analysis is based on a data sample of proton-proton collisions at sqrt(s) = 13 TeV collected with the CMS detector and corresponding to an integrated luminosity of 35.9 inverse femtobarns. The search is performed in the fully leptonic final state ZZ to lll'l', where l, l' = e, mu. The electroweak production of two Z bosons in association with two jets is measured with an observed (expected) significance of 2.7 (1.6) standard deviations. A fiducial cross section for the electroweak production is measured to be sigma[EW](pp -> ZZjj -> lll'l'jj) = 0.40 -0.16 +0.21 (stat) -0.09 +0.13 (syst) fb, which is consistent with the standard model prediction. Limits on anomalous quartic gauge couplings are determined in terms of the effective field theory operators T0, T1, T2, T8, and T9. This is the first measurement of vector boson scattering in the ZZ channel at the LHC.

The fiducial cross section for $\Upsilon$(1S) pair production in proton-proton collisions at a center-of-mass energy of 13 TeV in the region where both $\Upsilon$(1S) mesons have an absolute rapidity below 2.0 is measured to be 79 $\pm$ 11 (stat) $\pm$ 6 (syst) $\pm$ 3 ($\mathcal{B}$) pb assuming the mesons are produced unpolarized. The last uncertainty corresponds to the uncertainty in the $\Upsilon$(1S) meson dimuon branching fraction. The measurement is performed in the final state with four muons using proton-proton collision data collected in 2016 by the CMS experiment at the LHC, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. This process serves as a standard model reference in a search for narrow resonances decaying to $\Upsilon$(1S)$\mu^+\mu^-$ in the same final state. Such a resonance could indicate the existence of a tetraquark that is a bound state of two b quarks and two $\bar{\mathrm{b}}$ antiquarks. The tetraquark search is performed for masses in the vicinity of four times the bottom quark mass, between 17.5 and 19.5 GeV, while a generic search for other resonances is performed for masses between 16.5 and 27 GeV. No significant excess of events compatible with a narrow resonance is observed in the data. Limits on the production cross section times branching fraction to four muons via an intermediate $\Upsilon$(1S) resonance are set as a function of the resonance mass.

A measurement of the production cross section of top quark pairs in association with two b jets ($\mathrm{t\bar{t}}\mathrm{b\bar{b}}$) is presented using data collected in proton-proton collisions at $\sqrt{s} =$ 13 TeV by the CMS detector at the LHC corresponding to an integrated luminosity of 35.9 fb$^{-1}$. The cross section is measured in the all-jet decay channel of the top quark pair by selecting events containing at least eight jets, of which at least two are identified as originating from the hadronization of b quarks. A combination of multivariate analysis techniques is used to reduce the large background from multijet events not containing a top quark pair, and to help discriminate between jets originating from top quark decays and other additional jets. The cross section is determined for the total phase space to be 5.5 $\pm$ 0.3 (stat)${}^{+1.6}_{-1.3}$ (syst) pb and also measured for two fiducial $\mathrm{t\bar{t}}\mathrm{b\bar{b}}$ definitions. The measured cross sections are found to be larger than theoretical predictions by a factor of 1.5-2.4, corresponding to 1-2 standard deviations.

Measurements of $W\gamma$ and $Z\gamma$ production in proton-proton collisions at $\sqrt{s}$ = 7 TeV are used to extract limits on anomalous triple gauge couplings. The results are based on data recorded by the CMS experiment at the LHC that correspond to an integrated luminosity of 5.0 inverse femtobarns. The cross sections are measured for photon transverse momenta $p_T^{\gamma} \gt$ 15 GeV, and for separations between photons and final-state charged leptons in the pseudorapidity-azimuthal plane of $\Delta R(l, \gamma) \gt$ 0.7 in $l \nu \gamma$ and $ll \gamma$ final states, where l refers either to an electron or a muon. A dilepton invariant mass requirement of $m_{ll} \gt$ 50 GeV is imposed for the Z$\gamma$ process. No deviations are observed relative to predictions from the standard model, and limits are set on anomalous WW$\gamma$, ZZ$\gamma$, and Z$\gamma\gamma$ triple gauge couplings.

A search is presented for massive narrow resonances decaying either into two Higgs bosons, or into a Higgs boson and a W or Z boson. The decay channels considered are HH$\to \mathrm{b\overline{b}}\tau^{+}\tau^{-}$ and VH$ \to \mathrm{q\overline{q}}\tau^{+}\tau^{-}$, where H denotes the Higgs boson, and V denotes the W or Z boson. This analysis is based on a data sample of proton-proton collisions collected at a center-of-mass energy of 13 TeV by the CMS Collaboration, corresponding to an integrated luminosity of 35.9 fb$^{-1}$. For the TeV-scale mass resonances considered, substructure techniques provide ways to differentiate among the hadronization products from vector boson decays to quarks, Higgs boson decays to bottom quarks, and quark- or gluon-induced jets. Reconstruction techniques are used that have been specifically optimized to select events in which the tau lepton pair is highly boosted. The observed data are consistent with standard model expectations and upper limits are set at 95% confidence level on the product of cross section and branching fraction for resonance masses between 0.9 and 4.0 TeV. Exclusion limits are set in the context of bulk radion and graviton models: spin-0 radion resonances are excluded below a mass of 2.7 TeV at 95% confidence level. In the spin-1 heavy vector triplet framework, mass-degenerate W' and Z' resonances with dominant couplings to the standard model gauge bosons are excluded below a mass of 2.8 TeV at 95% confidence level. There are the first limits for these decay channels at $\sqrt{s}=$ 13 TeV.

A search for physics beyond the standard model in final states with at least one photon, large transverse momentum imbalance, and large total transverse event activity is presented. Such topologies can be produced in gauge-mediated supersymmetry models in which pair-produced gluinos or squarks decay to photons and gravitinos via short-lived neutralinos. The data sample corresponds to an integrated luminosity of 35.9 inverse femtobarns of proton-proton collisions at sqrt(s) = 13 TeV recorded by the CMS experiment at the LHC in 2016. No significant excess of events above the expected standard model background is observed. The data are interpreted in simplified models of gluino and squark pair production, in which gluinos or squarks decay via neutralinos to photons. Gluino masses of up to 1.50-2.00 TeV and squark masses up to 1.30-1.65 TeV are excluded at 95% confidence level, depending on the neutralino mass and branching fraction.

The first observation of the electroweak (EW) production of a Z boson, a photon, and two forward jets (Z$\gamma$jj) in proton-proton collisions at a center-of-mass energy of 13 TeV is presented. A data set corresponding to an integrated luminosity of 137 fb$^{-1}$, collected by the CMS experiment at the LHC in 2016-2018 is used. The measured fiducial cross section for EW Z$\gamma$jj is $\sigma_{\mathrm{EW}}$ = 5.21 $\pm$ 0.52 (stat) $\pm$ 0.56 (syst) fb = 5.21 $\pm$ 0.76 fb. Single-differential cross sections in photon, leading lepton, and leading jet transverse momenta, and double-differential cross sections in $m_{\mathrm{jj}}$ and $\lvert\Delta\eta_{\mathrm{jj}}\rvert$ are also measured. Exclusion limits on anomalous quartic gauge couplings are derived at 95% confidence level in terms of the effective field theory operators $\mathrm{M}_{0}$ to $\mathrm{M}_{5}$, $\mathrm{M}_{7}$, $\mathrm{T}_{0}$ to $\mathrm{T}_{2}$, and $\mathrm{T}_{5}$ to $\mathrm{T}_{9}$.

Measurements of the total and differential fiducial cross sections for the Z boson decaying into two neutrinos are presented at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV. The data were collected by the CMS detector in 2016 and correspond to an integrated luminosity of 35.9 fb$^{-1}$. In these measurements, events are selected containing an imbalance in transverse momentum and one or more energetic jets. The fiducial differential cross section is measured as a function of the Z boson transverse momentum. The results are combined with a previous measurement of charged-lepton decays of the Z boson.

A search is reported for heavy resonances and quantum black holes decaying into e$\mu$, e$\tau$, and $\mu\tau$ final states in proton-proton collision data recorded by the CMS experiment at the CERN LHC during 2016-2018 at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The e$\mu$, e$\tau$, and $\mu\tau$ invariant mass spectra are reconstructed, and no evidence is found for physics beyond the standard model. Upper limits are set at 95% confidence level on the product of the cross section and branching fraction for lepton flavor violating signals. Three benchmark signals are studied: resonant $\tau$ sneutrino production in $R$ parity violating supersymmetric models, heavy Z' gauge bosons with lepton flavor violating decays, and nonresonant quantum black hole production in models with extra spatial dimensions. Resonant $\tau$ sneutrinos are excluded for masses up to 4.2 TeV in the e$\mu$ channel, 3.7 TeV in the e$\tau$ channel, and 3.6 TeV in the $\mu\tau$ channel. A Z' boson with lepton flavor violating couplings is excluded up to a mass of 5.0 TeV in the e$\mu$ channel, up to 4.3 TeV in the e$\tau$ channel, and up to 4.1 TeV in the $\mu\tau$ channel. Quantum black holes in the benchmark model are excluded up to the threshold mass of 5.6 TeV in the e$\mu$ channel, 5.2 TeV in the e$\tau$ channel, and 5.0 TeV in the $\mu\tau$ channel. In addition, model-independent limits are extracted to allow comparisons with other models for the same final states and similar event selection requirements. The results of these searches provide the most stringent limits available from collider experiments for heavy particles that undergo lepton flavor violating decays.

A search for the nonresonant production of Higgs boson pairs (HH) via gluon-gluon and vector boson fusion processes in final states with two bottom quarks and two tau leptons is presented. The search uses data from proton-proton collisions at a center-of-mass energy of $\sqrt{s}$ = 13 TeV recorded with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb$^{-1}$. Events in which at least one tau lepton decays hadronically are considered and multiple machine learning techniques are used to identify and extract the signal. The data are found to be consistent, within uncertainties, with the standard model (SM) predictions. Upper limits on the HH production cross section are set to constrain the parameter space for anomalous Higgs boson couplings. The observed (expected) upper limit at 95% confidence level corresponds to 3.3 (5.2) times the SM prediction for the inclusive HH cross section and to 124 (154) times the SM prediction for the vector boson fusion HH cross section. At 95% confidence level, the Higgs field self-coupling is constrained to be within -1.7 and 8.7 times the SM expectation, and the coupling of two Higgs bosons to two vector bosons is constrained to be within -0.4 and 2.6 times the SM expectation.

A search for physics beyond the Standard Model inducing periodic signals in the dielectron and diphoton invariant mass spectra is presented using 139 fb$^{-1}$ of $\sqrt{s}=13$ TeV $pp$ collision data collected by the ATLAS experiment at the LHC. Novel search techniques based on continuous wavelet transforms are used to infer the frequency of periodic signals from the invariant mass spectra and neural network classifiers are used to enhance the sensitivity to periodic resonances. In the absence of a signal, exclusion limits are placed at the 95% confidence level in the two-dimensional parameter space of the clockwork gravity model. Model-independent searches for deviations from the background-only hypothesis are also performed.

We report on a CDF measurement of the total cross section and rapidity distribution, $d\sigma/dy$, for $q\bar{q}\to \gamma^{*}/Z\to e^{+}e^{-}$ events in the $Z$ boson mass region ($66<M_{ee}<116$GeV/c$^2$) produced in $p\bar{p}$ collisions at $\sqrt{s}=1.96$TeV with 2.1fb$^{-1}$ of integrated luminosity. The measured cross section of $257\pm16$pb and $d\sigma/dy$ distribution are compared with Next-to-Leading-Order(NLO) and Next-to-Next-to-Leading-Order(NNLO) QCD theory predictions with CTEQ and MRST/MSTW parton distribution functions (PDFs). There is good agreement between the experimental total cross section and $d\sigma/dy$ measurements with theoretical calculations with the most recent NNLO PDFs.

Measurements are presented of the t-channel single-top-quark production cross section in proton-proton collisions at sqrt(s) = 8 TeV. The results are based on a data sample corresponding to an integrated luminosity of 19.7 inverse femtobarns recorded with the CMS detector at the LHC. The cross section is measured inclusively, as well as separately for top (t) and antitop (t-bar), in final states with a muon or an electron. The measured inclusive t-channel cross section is sigma[t-ch] = 83.6 +/- 2.3 (stat.) +/- 7.4 (syst.) pb. The single t and t-bar cross sections are measured to be sigma[t-ch,t] = 53.8 +/- 1.5 (stat.) +/- 4.4 (syst.) pb and sigma[t-ch,t-bar] = 27.6 +/- 1.3 (stat.) +/- 3.7 (syst.) pb, respectively. The measured ratio of cross sections is R[t-ch] = sigma[t-ch,t]/sigma[t-ch,t-bar] = 1.95 +/- 0.10 (stat.) +/- 0.19 (syst.), in agreement with the standard model prediction. The modulus of the Cabibbo-Kobayashi-Maskawa matrix element Vtb is extracted and, in combination with a previous CMS result at sqrt(s) = 7 TeV, a value abs(Vtb) = 0.998 +/- 0.038 (exp.) +/- 0.016 (theo.) is obtained.

The first measurement of the cross section ratio $\sigma_\mathrm{ t \bar{t} b \bar{b}} / \sigma_\mathrm{ t \bar{t} jj }$ is presented using a data sample corresponding to an integrated luminosity of 19.6 fb$^{-1}$ collected in pp collisions at $\sqrt{s}$ = 8 TeV with the CMS detector at the LHC. Events with two leptons ($\mathrm{e}$ or $\mu$) and four reconstructed jets, including two identified as b quark jets, in the final state are selected. The ratio is determined for a minimum jet transverse momentum $p_\mathrm{T}$ of both 20 and 40 GeV/$c$. The measured ratio is 0.022 $\pm$ 0.003 (stat) $\pm$ 0.005 (syst) for $p_\mathrm{T}$ greater than 20 GeV/$c$. The absolute cross sections $\sigma_\mathrm{ t \bar{t} b \bar{b}}$ and $\sigma_\mathrm{ t \bar{t} jj }$ are also measured. The measured ratio for $p_\mathrm{T}$ greater than 40 GeV/$c$ is compatible with a theoretical quantum chromodynamics calculation at next-to-leading order.

We present a measurement of the $W$-boson-pair production cross section in $p\bar{p}$ collisions at 1.96 TeV center-of-mass energy and the first measurement of the differential cross section as a function of jet multiplicity and leading-jet energy. The $W^{+}W^{-}$ cross section is measured in the final state comprising two charged leptons and neutrinos, where either charged lepton can be an electron or a muon. Using data collected by the CDF experiment corresponding to $9.7~\rm{fb}^{-1}$ of integrated luminosity, a total of $3027$ collision events consistent with $W^{+}W^{-}$ production are observed with an estimated background contribution of $1790\pm190$ events. The measured total cross section is $\sigma(p\bar{p} \rightarrow W^{+}W^{-}) = 14.0 \pm 0.6~(\rm{stat})^{+1.2}_{-1.0}~(\rm{syst})\pm0.8~(\rm{lumi})$ pb, consistent with the standard model prediction.

A measurement of electroweak-induced production of W gamma and two jets is performed, where the W boson decays leptonically. The data used in the analysis correspond to an integrated luminosity of 19.7 inverse femtobarns collected by the CMS experiment in sqrt(s) = 8 TeV proton-proton collisions produced at the LHC. Candidate events are selected with exactly one muon or electron, missing transverse momentum, one photon, and two jets with large rapidity separation. An excess over the hypothesis of the standard model without electroweak production of W gamma with two jets is observed with a significance of 2.7 standard deviations. The cross section measured in the fiducial region is 10.8 +/- 4.1 (stat) +/- 3.4 (syst) +/- 0.3 (lumi) fb, which is consistent with the standard model electroweak predictions. The total cross section for W gamma production in association with 2 jets in the same fiducial region is measured to be 23.2 +/- 4.3 (stat) +/- 1.7 (syst) +/- 0.6 (lumi) fb, which is consistent with the standard model prediction from the combination of electroweak- and quantum chromodynamics-induced processes. No deviations are observed from the standard model predictions and experimental limits on anomalous quartic gauge couplings f[M, 0-7] / Lambda^4, f[T, 0-2] / Lambda^4, and f[T, 5-7] / Lambda^4 are set at 95% confidence level.

Measurements of the differential jet cross section are presented as a function of jet mass in dijet events, in bins of jet transverse momentum, with and without a jet grooming algorithm. The data have been recorded by the CMS Collaboration in proton-proton collisions at the LHC at a center-of-mass energy of 13 TeV and correspond to an integrated luminosity of 2.3 fb$^{-1}$. The absolute cross sections show slightly different jet transverse momentum spectra in data and Monte Carlo event generators for the settings used. Removing this transverse momentum dependence, the normalized cross section for ungroomed jets is consistent with the prediction from Monte Carlo event generators for masses below 30% of the transverse momentum. The normalized cross section for groomed jets is measured with higher precision than the ungroomed cross section. Semi-analytical calculations of the jet mass beyond leading logarithmic accuracy are compared to data, as well as predictions at leading order and next-to-leading order, which include parton showering and hadronization. Overall, in the normalized cross section, the theoretical predictions agree with the measured cross sections within the uncertainties for masses from 10 to 30% of the jet transverse momentum.

A search is described for the production of a pair of bottom-type vector-like quarks (B VLQs) with mass greater than 1000 GeV. Each B VLQ decays into a b quark and a Higgs boson, a b quark and a Z boson, or a t quark and a W boson. This analysis considers both fully hadronic final states and those containing a charged lepton pair from a Z boson decay. The products of the H $to$ bb boson decay and of the hadronic Z or W boson decays can be resolved as two distinct jets or merged into a single jet, so the final states are classified by the number of reconstructed jets. The analysis uses data corresponding to an integrated luminosity of 138 fb$^{-1}$ collected in proton-proton collisions at $\sqrt{s}$ = 13 TeV with the CMS detector at the LHC from 2016 to 2018. No excess over the expected background is observed. Lower limits are set on the B VLQ mass at 95% confidence level. These depend on the B VLQ branching fractions and are 1570 and 1540 GeV for 100% B $\to$ bH and 100% B $\to$ bZ, respectively. In most cases, the mass limits obtained exceed previous limits by at least 100 GeV.

The results of a search for Higgs boson pair (HH) production in the WW*WW*, WW*$\tau\tau$, and $\tau\tau\tau\tau$ decay modes are presented. The search uses 138 fb$^{-1}$ of proton-proton collision data recorded by the CMS experiment at the LHC at a center-of-mass energy of 13 TeV from 2016 to 2018. Analyzed events contain two, three, or four reconstructed leptons, including electrons, muons, and hadronically decaying tau leptons. No evidence for a signal is found in the data. Upper limits are set on the cross section for nonresonant HH production, as well as resonant production in which a new heavy particle decays to a pair of Higgs bosons. For nonresonant production, the observed (expected) upper limit on the cross section at 95% confidence level (CL) is 21.3 (19.4) times the standard model (SM) prediction. The observed (expected) ratio of the trilinear Higgs boson self-coupling to its value in the SM is constrained to be within the interval $-$6.9 to 11.1 ($-$6.9 to 11.7) at 95% CL, and limits are set on a variety of new-physics models using an effective field theory approach. The observed (expected) limits on the cross section for resonant HH production range from 0.18 to 0.90 (0.08 to 1.06) pb at 95% CL for new heavy-particle masses in the range 250-1000 GeV.

This paper presents the measurement of fiducial and differential cross sections for both the inclusive and electroweak production of a same-sign $W$-boson pair in association with two jets ($W^\pm W^\pm jj$) using 139 fb$^{-1}$ of proton-proton collision data recorded at a centre-of-mass energy of $\sqrt{s}=13$ TeV by the ATLAS detector at the Large Hadron Collider. The analysis is performed by selecting two same-charge leptons, electron or muon, and at least two jets with large invariant mass and a large rapidity difference. The measured fiducial cross sections for electroweak and inclusive $W^\pm W^\pm jj$ production are $2.92 \pm 0.22\, \text{(stat.)} \pm 0.19\, \text{(syst.)}$ fb and $3.38 \pm 0.22\, \text{(stat.)} \pm 0.19\, \text{(syst.)}$ fb, respectively, in agreement with Standard Model predictions. The measurements are used to constrain anomalous quartic gauge couplings by extracting 95% confidence level intervals on dimension-8 operators. A search for doubly charged Higgs bosons $H^{\pm\pm}$ that are produced in vector-boson fusion processes and decay into a same-sign $W$ boson pair is performed. The largest deviation from the Standard Model occurs for an $H^{\pm\pm}$ mass near 450 GeV, with a global significance of 2.5 standard deviations.

A measurement of the differential cross sections for a W boson produced in association with jets in the muon decay channel is presented. The measurement is based on 13 TeV proton-proton collision data corresponding to an integrated luminosity of 2.2 inverse femtobarns, recorded by the CMS detector at the LHC. The cross sections are reported as functions of jet multiplicity, jet transverse momentum pT, jet rapidity, the scalar pT sum of the jets, and angular correlations between the muon and the jet for different jet multiplicities. The measured cross sections are in agreement with predictions that include multileg leading-order (LO) and next-to-LO matrix element calculations interfaced with parton showers, as well as a next-to-next-to-LO calculation for the W boson and one jet production.

The cross section of top quark pair production is measured in the $\mathrm{t\bar{t}}\to (\ell\nu_{\ell})(\tau_\mathrm{h}\nu_{\tau})\mathrm{b\bar{b}}$ final state, where $\tau_\mathrm{h}$ refers to the hadronic decays of the $\tau$ lepton, and $\ell$ is either an electron or a muon. The data sample corresponds to an integrated luminosity of 35.9 fb$^{-1}$ collected in proton-proton collisions at $\sqrt{s}=$ 13 TeV with the CMS detector. The measured cross section is $\sigma_{\mathrm{t\bar{t}}} =$ 781 $\pm$ 7 (stat) $\pm$ 62 (syst) $\pm$ 20 (lum) pb, and the ratio of the partial width $\Gamma($t$\to\tau\nu_{\tau}$b) to the total decay width of the top quark is measured to be 0.1050 $\pm$ 0.0009 (stat) $\pm$ 0.0071 (syst). This is the first measurement of the $\mathrm{t\bar{t}}$ production cross section in proton-proton collisions at $\sqrt{s}=$ 13 TeV that explicitly includes $\tau$ leptons. The ratio of the cross sections in the $\ell\tau_\mathrm{h}$ and $\ell\ell$ final states yields a value $R_{\ell\tau_\mathrm{h}/\ell\ell}=$ 0.973 $\pm$ 0.009 (stat) $\pm$ 0.066 (syst), consistent with lepton universality.

A search is described for the production of a pair of bottom-type vector-like quarks (VLQs), each decaying into a b or $\mathrm{\bar{b}}$ quark and either a Higgs or a Z boson, with a mass greater than 1000 GeV. The analysis is based on data from proton-proton collisions at a 13 TeV center-of-mass energy recorded at the CERN LHC, corresponding to a total integrated luminosity of 137 fb$^{-1}$. As the predominant decay modes of the Higgs and Z bosons are to a pair of quarks, the analysis focuses on final states consisting of jets resulting from the six quarks produced in the events. Since the two jets produced in the decay of a highly Lorentz-boosted Higgs or Z boson can merge to form a single jet, nine independent analyses are performed, categorized by the number of observed jets and the reconstructed event mode. No signal in excess of the expected background is observed. Lower limits are set on the VLQ mass at 95% confidence level equal to 1570 GeV in the case where the VLQ decays exclusively to a b quark and a Higgs boson, 1390 GeV for when it decays exclusively to a b quark and a Z boson, and 1450 GeV for when it decays equally in these two modes. These limits represent significant improvements over the previously published VLQ limits.

Many new physics models, including versions of supersymmetry characterized by $R$-parity violation (RPV), compressed mass spectra, long decay chains, or additional hidden sectors, predict the production of events with top quarks, low missing transverse momentum, and many additional quarks or gluons. The results of a search for new physics in events with two top quarks and additional jets are reported. The search is performed using events with at least seven jets and exactly one electron or muon. No requirement on missing transverse momentum is imposed. The study is based on a sample of proton-proton collisions at $\sqrt{s} =$ 13 TeV corresponding to 137 fb$^{-1}$ of integrated luminosity collected with the CMS detector at the LHC in 2016-2018. The data are used to determine best fit values and upper limits on the cross section for pair production of top squarks in scenarios of RPV and stealth supersymmetry. Top squark masses up to 670 (870) GeV are excluded at 95% confidence level for the RPV (stealth) scenario, and the maximum observed local signal significance is 2.8 standard deviations for the RPV scenario with top squark mass of 400 GeV.

The strange quark content of the proton is probed through the measurement of the production cross section for a W boson and a charm (c) quark in proton-proton collisions at a center-of-mass energy of 13 TeV. The analysis uses a data sample corresponding to a total integrated luminosity of 138 fb$^{-1}$ collected with the CMS detector at the LHC. The W bosons are identified through their leptonic decays to an electron or a muon, and a neutrino. Charm jets are tagged using the presence of a muon or a secondary vertex inside the jet. The W+c production cross section and the cross section ratio $R^\pm_\text{c}$ = $\sigma$(W$^+$+$\bar{\text{c}}$) / $\sigma$(W$^-$+$\text{c}$) are measured inclusively and differentially as functions of the transverse momentum and the pseudorapidity of the lepton originating from the W boson decay. The precision of the measurements is improved with respect to previous studies, reaching 1% in $R^\pm_\text{c}$. The precision of the measurements is improved with respect to previous studies, reaching 1% in $R^\pm_\text{c}$ = 0.950 $\pm$ 0.005 (stat) $\pm$ 0.010 (syst). The measurements are compared with theoretical predictions up to next-to-next-to-leading order in perturbative quantum chromodynamics.

A search for supersymmetry in events with two or three low-momentum leptons and missing transverse momentum is performed. The search uses proton-proton collisions at $\sqrt{s} =$ 13 TeV collected in the three-year period 2016-2018 by the CMS experiment at the LHC and corresponding to an integrated luminosity of up to 137 fb$^{-1}$. The data are found to be in agreement with expectations from standard model processes. The results are interpreted in terms of electroweakino and top squark pair production with a small mass difference between the produced supersymmetric particles and the lightest neutralino. For the electroweakino interpretation, two simplified models are used, a wino-bino model and a higgsino model. Exclusion limits at 95% confidence level are set on $\widetilde{\chi}^0_2 / \widetilde{\chi}^\pm_1$ masses up to 275 GeV for a mass difference of 10 GeV in the wino-bino case, and up to 205 (150) GeV for a mass difference of 7.5 (3) GeV in the higgsino case. The results for the higgsino are further interpreted using a phenomenological minimal supersymmetric standard model, excluding the higgsino mass parameter $\mu$ up to 180 GeV with the bino mass parameter $M_1$ at 800 GeV. In the top squark interpretation, exclusion limits are set at top squark masses up to 540 GeV for four-body top squark decays and up to 480 GeV for chargino-mediated decays with a mass difference of 30 GeV.

A measurement is presented of the production of Z bosons that decay into two electrons or muons in association with jets, in proton-proton collisions at a centre-of-mass energy of 13 TeV. The data were recorded by the CMS Collaboration at the LHC with an integrated luminosity of 35.9 fb$^{-1}$. The differential cross sections are measured as a function of the transverse momentum ($p_\mathrm{T}$) of the Z boson and the transverse momentum and rapidities of the five jets with largest $p_\mathrm{T}$. The jet multiplicity distribution is measured for up to eight jets. The hadronic activity in the events is estimated using the scalar sum of the $p_\mathrm{T}$ of all the jets. All measurements are unfolded to the stable particle-level and compared with predictions from various Monte Carlo event generators, as well as with expectations at leading and next-to-leading orders in perturbative quantum chromodynamics.