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This paper describes theCombinesoftware package used for statistical analyses by the CMS Collaboration. The package, originally designed to perform searches for a Higgs boson and the combined analysis of those searches, has evolved to become the statistical analysis tool presently used in the majority of measurements and searches performed by the CMS Collaboration. It is not specific to the CMS experiment, and this paper is intended to serve as a reference for users outside of the CMS Collaboration, providing an outline of the most salient features and capabilities. Readers are provided with the possibility to runCombineand reproduce examples provided in this paper using a publicly available container image. Since the package is constantly evolving to meet the demands of ever-increasing data sets and analysis sophistication, this paper cannot cover all details ofCombine. However, the online documentation referenced within this paper provides an up-to-date and complete user guide.

The CERN LHC provided proton and heavy ion collisions during its Run 2 operation period from 2015 to 2018. Proton-proton collisions reached a peak instantaneous luminosity of 2.1× 10³⁴cm^-2s^-1, twice the initial design value, at √(s)=13 TeV. The CMS experiment records a subset of the collisions for further processing as part of its online selection of data for physics analyses, using a two-level trigger system: the Level-1 trigger, implemented in custom-designed electronics, and the high-level trigger, a streamlined version of the offline reconstruction software running on a large computer farm. This paper presents the performance of the CMS high-level trigger system during LHC Run 2 for physics objects, such as leptons, jets, and missing transverse momentum, which meet the broad needs of the CMS physics program and the challenge of the evolving LHC and detector conditions. Sophisticated algorithms that were originally used in offline reconstruction were deployed online. Highlights include a machine-learning b tagging algorithm and a reconstruction algorithm for tau leptons that decay hadronically.

The first search for soft unclustered energy patterns (SUEPs) is performed using an integrated luminosity of$138{\mathrm{fb}}^{-1}$of proton-proton collision data at$\sqrt{s}=13\mathrm{TeV}$, collected in 2016–2018 by the CMS detector at the LHC. Such SUEPs are predicted by hidden valley models with a new, confining force with a large ’t Hooft coupling. In events with boosted topologies, selected by high-threshold hadronic triggers, the multiplicity and sphericity of clustered tracks are used to reject the background from standard model quantum chromodynamics. With no observed excess of events over the standard model expectation, limits are set on the cross section for production via gluon fusion of a scalar mediator with SUEP-like decays.

The first search for the$Z$boson decay to$\tau \tau \mu \mu$at the CERN LHC is presented, based on data collected by the CMS experiment at the LHC in proton-proton collisions at a center-of-mass energy of 13 TeV and corresponding to an integrated luminosity of$138{\mathrm{fb}}^{-1}$. The data are compatible with the predicted background. For the first time, an upper limit at the 95% confidence level of 6.9 times the standard model expectation is placed on the ratio of the$Z\to \tau \tau \mu \mu$to$Z\to 4\mu$branching fractions. Limits are also placed on the six flavor-conserving four-lepton effective-field-theory operators involving two muons and two tau leptons, for the first time testing all such operators.

A search for a new charged particle X with mass between 0.3 and 2.0 TeV decaying to a W boson and a photon is presented, using proton-proton collision data at a center-of-mass energy of 13 TeV, collected by the CMS experiment and corresponding to an integrated luminosity of 138 fb⁻¹. Particle X has electric charge ±1 and is assumed to have spin 0. The search is performed using the electron and muon decays of the W boson. No significant excess above the predicted background is observed. The upper limit at 95% confidence level on the product of the production cross section of the X and its branching fraction to a W boson and a photon is found to be 94 (137) fb for a 0.3 TeV resonance and 0.75 (0.81) fb for a 2.0 TeV resonance, for an X width-to-mass ratio of 0.01% (5%). This search presents the most stringent constraints to date on the existence of such resonances across the probed mass range. A statistical combination with an earlier study based on the hadronic decay mode of the W boson is also performed, and the upper limit at 95% confidence level for a 2.0 TeV resonance is reduced to 0.50 (0.63) fb for an X width-to-mass ratio of 0.01% (5%).

A search is described for the production of a pair of bottom-type vectorlike 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$138{\mathrm{fb}}^{-1}$collected in proton-proton collisions at$\sqrt{s}=13\mathrm{TeV}$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 the 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.