Energy correlators that describe energy-weighted distances between two or three particles in a jet are measured using an event sample of $\sqrt{s}$ = 13 TeV proton-proton collisions collected by the CMS experiment and corresponding to an integrated luminosity of 36.3 fb$^{-1}$. The measured distributions are consistent with the trends in the simulation that reveal two key features of the strong interaction: confinement and asymptotic freedom. By comparing the ratio of the measured three- and two-particle energy correlator distributions with theoretical calculations that resum collinear emissions at approximate next-to-next-to-leading logarithmic accuracy matched to a next-to-leading order calculation, the strong coupling is determined at the Z boson mass: $\alpha_\mathrm{S}(m_\mathrm{Z})$ = 0.1229 $^{+0.0040}_{-0.0050}$, the most precise $\alpha_\mathrm{S}(m_\mathrm{Z})$ value obtained using jet substructure observables.

Measurements of inclusive and normalized differential cross sections of the associated production of top quark-antiquark and bottom quark-antiquark pairs, ttbb, are presented. The results are based on data from proton-proton collisions collected by the CMS detector at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. The cross sections are measured in the lepton+jets decay channel of the top quark pair, using events containing exactly one isolated electron or muon and at least five jets. Measurements are made in four fiducial phase space regions, targeting different aspects of the ttbb process. Distributions are unfolded to the particle level through maximum likelihood fits, and compared with predictions from several event generators. The inclusive cross section measurements of this process in the fiducial phase space regions are the most precise to date. In most cases, the measured inclusive cross sections exceed the predictions with the chosen generator settings. The only exception is when using a particular choice of dynamic renormalization scale, $\mu_\mathrm{R}=\frac{1}{2} \prod_{i = \mathrm{t, \bar{t}, b, \bar{b}}} m_{\mathrm{T},i}^{1/4}$, where $m_{\mathrm{T}, i}^2 = m_i^2 + p^2_{\mathrm{T}, i}$ are the transverse masses of top and bottom quarks. The differential cross sections show varying degrees of compatibility with the theoretical predictions, and none of the tested generators with the chosen settings simultaneously describe all the measured distributions.

A measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum $p_\mathrm{T}$. This observable is measured in multijet events over the range of $p_\mathrm{T}$ = 360-3170 GeV based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13 TeV, corresponding to an integrated luminosity of 134 fb$^{-1}$. The results are compared with predictions from Monte Carlo parton-shower event generator simulations, as well as with fixed-order perturbative quantum chromodynamics (pQCD) predictions at next-to-leading-order (NLO) accuracy obtained with different parton distribution functions (PDFs) and corrected for nonperturbative and electroweak effects. Data and theory agree within uncertainties. From the comparison of the measured observable with the pQCD prediction obtained with the NNPDF3.1 NLO PDFs, the strong coupling at the Z boson mass scale is $\alpha_\mathrm{S}(m_\mathrm{Z})$ = 0.1177 $\pm$ 0.0013 (exp) $_{-0.0073}^{+0.0116}$ (theo) = 0.1177 $_{-0.0074}^{+0.0117}$, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of $\alpha_\mathrm{S}(m_\mathrm{Z})$ in the TeV region shows no deviation from the expected NLO pQCD behaviour.

A measurement of the inclusive jet production in proton-proton collisions at the LHC at $\sqrt{s}$ = 13 TeV is presented. The double-differential cross sections are measured as a function of the jet transverse momentum $p_\mathrm{T}$ and the absolute jet rapidity $\lvert y \rvert$. The anti-$k_\mathrm{T}$ clustering algorithm is used with distance parameter of 0.4 (0.7) in a phase space region with jet $p_\mathrm{T}$ from 97 GeV up to 3.1 TeV and $\lvert y \rvert\lt$ 2.0. Data collected with the CMS detector are used, corresponding to an integrated luminosity of 36.3 fb$^{-1}$ (33.5 fb$^{-1}$). The measurement is used in a comprehensive QCD analysis at next-to-next-to-leading order, which results in significant improvement in the accuracy of the parton distributions in the proton. Simultaneously, the value of the strong coupling constant at the Z boson mass is extracted as $\alpha_\mathrm{S}$(Z) = 0.1170 $\pm$ 0.0019. For the first time, these data are used in a standard model effective field theory analysis at next-to-leading order, where parton distributions and the QCD parameters are extracted simultaneously with imposed constraints on the Wilson coefficient $c_1$ of 4-quark contact interactions. Note added: in the Addendum to this paper, available as Appendix B in this document, an improved value of $\alpha_\mathrm{S}$(Z) = 0.1166 $\pm$ 0.0017 has been extracted. This result supersedes the number in the above abstract of the original publication.

The observation of WW$\gamma$ production in proton-proton collisions at a center-of-mass energy of 13 TeV with an integrated luminosity of 138 fb$^{-1}$ is presented. The observed (expected) significance is 5.6 (5.1) standard deviations. Events are selected by requiring exactly two leptons (one electron and one muon) of opposite charge, moderate missing transverse momentum, and a photon. The measured fiducial cross section for WW$\gamma$ is 5.9 $\pm$ 0.8 (stat) $\pm$ 0.8 (syst) $\pm$ 0.7 (modeling) fb, in agreement with the next-to-leading order quantum chromodynamics prediction. The analysis is extended with a search for the associated production of the Higgs boson and a photon, which is generated by a coupling of the Higgs boson to light quarks. The result is used to constrain the Higgs boson couplings to light quarks.

Jets containing a prompt J$/\psi$ meson are studied in lead-lead collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV, using the CMS detector at the LHC. Jets are selected to be in the transverse momentum range of 30 $\lt$$p_\mathrm{T}$$\lt$ 40 GeV. The J$/\psi$ yield in these jets is evaluated as a function of the jet fragmentation variable $z$, the ratio of the J$/\psi$$p_\mathrm{T} $ to the jet $p_\mathrm{T}$. The nuclear modification factor, $R_\mathrm{AA}$, is then derived by comparing the yield in lead-lead collisions to the corresponding expectation based on proton-proton data, at the same nucleon-nucleon center-of-mass energy. The suppression of the J$/\psi$ yield shows a dependence on $z$, indicating that the interaction of the J$/\psi$ with the quark-gluon plasma formed in heavy ion collisions depends on the fragmentation that gives rise to the J$/\psi$ meson.

The differential cross sections of $\Lambda_\mathrm{c}^+$ baryon production are measured via the exclusive decay channel $\Lambda_\mathrm{c}^+ \to $pK$^-\pi^+$, as a function of transverse momentum ($p_\mathrm{T}$) in proton-proton (pp) and lead-lead (PbPb) collisions at a nucleon-nucleon center-of-mass energy of 5.02 TeV with the CMS detector at the LHC. The measurement is performed within the $\Lambda_\mathrm{c}^+$ rapidity interval $|y|<$1.0 in the $p_\mathrm{T}$ range of 5-20 GeV/$c$ in pp and 10-20 GeV/$c$ in PbPb collisions. The observed yields of $\Lambda_\mathrm{c}^+$ for $p_\mathrm{T}$ of 10-20 GeV/$c$ suggest a possible suppression in central PbPb collisions compared to pp collisions. The $\Lambda_\mathrm{c}^+/$D$^0$ production ratio in pp collisions is compared to theoretical models. In PbPb collisions, this ratio is consistent with the result from pp collisions in their common $p_\mathrm{T}$ range.

Differential cross sections for the Drell-Yan process, including Z boson production, using the dimuon decay channel are measured in proton-lead (pPb) collisions at a nucleon-nucleon centre-of-mass energy of 8.16 TeV. A data sample recorded with the CMS detector at the LHC is used, corresponding to an integrated luminosity of 173 nb$^{-1}$. The differential cross section as a function of the dimuon mass is measured in the range 15-600 GeV, for the first time in proton-nucleus collisions. It is also reported as a function of dimuon rapidity over the mass ranges 15-60 GeV and 60-120 GeV, and ratios for the p-going over the Pb-going beam directions are built. In both mass ranges, the differential cross sections as functions of the dimuon transverse momentum $p_\mathrm{T}$ and of a geometric variable $\phi^*$ are measured, where $\phi^*$ highly correlates with $p_\mathrm{T}$ but is determined with higher precision. In the Z mass region, the rapidity dependence of the data indicate a modification of the distribution of partons within a lead nucleus as compared to the proton case. The data are more precise than predictions based upon current models of parton distributions.

Measurements at $\sqrt{s}$ = 13.6 TeV of the opposite-sign W boson pair production cross section in proton-proton collisions are presented. The data used in this study were collected with the CMS detector at the CERN LHC in 2022, and correspond to an integrated luminosity of 34.8 fb$^{-1}$. Events are selected by requiring one electron and one muon of opposite charge. A maximum likelihood fit is performed on signal- and background-enriched data categories defined by the flavour and charge of the leptons, the number of jets, and number of jets originating from b quarks. An inclusive W$^+$W$^-$ production cross section of 125.7 $\pm$ 5.6 pb is measured, in agreement with standard model predictions. Cross sections are also reported in a fiducial region close to that of the detector acceptance, both inclusively and differentially, as a function of the jet multiplicity in the event. For first time in proton-proton collisions, WW events with at least two reconstructed jets are studied and compared with recent theoretical predictions.

Using a data sample corresponding to an integrated luminosity of $2.0\,fb^{-1}$, collected by the LHCb experiment, the production of the $\eta_c(1S)$ state in proton-proton collisions at a centre-of-mass energy of $\sqrt{s}=13 \text{ TeV}$ is studied in the rapidity range ${2.0 < y < 4.5}$ and in the transverse momentum range ${6.5 < p_{T} < 14.0\text{ GeV}}$. The cross-section for prompt production of $\eta_c(1S)$ mesons relative to that of the $J/\psi$ meson is measured using the ${p\bar{p}}$ decay mode and is found to be ${\sigma_{\eta_c(1S)}/\sigma_{J/\psi} = 1.69 \pm 0.15 \pm 0.10 \pm 0.18}$. The quoted uncertainties are, in order, statistical, systematic and due to uncertainties on the branching fractions of the ${J/\psi\to p \bar{p}}$ and ${\eta_c\to p \bar{p}}$ decays. The prompt $\eta_c(1S)$ production cross-section is determined to be ${\sigma_{\eta_c(1S)} = 1.26 \pm 0.11\pm 0.08 \pm 0.14 \,\mu b}$, where the last uncertainty includes that on the ${J/\psi}$ meson cross-section. The ratio of the branching fractions of $b$-hadron decays to the $\eta_c(1S)$ and ${J/\psi}$ states is measured to be ${\mathcal{B}_{b\to\eta_c X}/\mathcal{B}_{b\to J/\psi X} = 0.48 \pm 0.03 \pm 0.03 \pm 0.05}$, where the last uncertainty is due to those on the branching fractions of the ${J/\psi \to p \bar{p}}$ and ${\eta_c\to p \bar{p}}$ decays. The difference between the ${J/\psi}$ and $\eta_c(1S)$ masses is also determined to be ${113.0 \pm 0.7 \pm 0.1\text{ MeV}}$, which is the most precise single measurement of this quantity to date.