This paper describes the Combine software 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 run Combine and 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 of Combine. 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× 10³⁴ cm^-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.

Measurements of the polarization and spin correlation in top quark pairs ($t\overline{t}$) are presented using events with a single electron or muon and jets in the final state. The measurements are based on proton-proton collision data from the LHC at $\sqrt{s}=13\text{ }\text{ }\mathrm{TeV}$ collected by the CMS experiment, corresponding to an integrated luminosity of $138\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$. All coefficients of the polarization vectors and the spin correlation matrix are extracted simultaneously by performing a binned likelihood fit to the data. The measurement is performed inclusively and in bins of additional observables, such as the mass of the $t\overline{t}$ system and the top quark scattering angle in the $t\overline{t}$ rest frame. The measured polarization and spin correlation are in agreement with the standard model. From the measured spin correlation, conclusions on the $t\overline{t}$ spin entanglement are drawn by applying the Peres-Horodecki criterion. The standard model predicts entangled spins for $t\overline{t}$ states at the production threshold and at high masses of the $t\overline{t}$ system. Entanglement is observed for the first time in events at high $t\overline{t}$ mass, where a large fraction of the $t\overline{t}$ decays are spacelike separated, with an expected and observed significance of above 5 standard deviations.

The traditional quark model ^1,2 accounts for the existence of baryons, such as protons and neutrons, which consist of three quarks, as well as mesons, composed of a quark–antiquark pair. Only recently has substantial evidence started to accumulate for exotic states composed of four or five quarks and antiquarks ³ . The exact nature of their internal structure remains uncertain ^4–29 . Here we report the first measurement of quantum numbers of the recently discovered family of three all-charm tetraquarks ^30–32 , using data collected by the CMS experiment at the Large Hadron Collider from 2016 to 2018 (refs. ^33,34 ). The angular analysis techniques developed for the discovery and characterization of the Higgs boson ^35–37 have been applied to the new exotic states. Here we show that the quantum numbers for parity P and charge conjugation C symmetries are found to be +1. The spin J of these exotic states is determined to be consistent with 2 ħ , while 0 ħ and 1 ħ are excluded at 95% and 99% confidence levels, respectively. The J ^{P C} = 2 ⁺⁺ assignment implies particular configurations of constituent spins and orbital angular momenta, which constrain the possible internal structure of these tetraquarks.