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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 first observation of the concurrent production of two$J/\psi$mesons in proton-nucleus collisions is presented. The analysis is based on a proton-lead ($p\mathrm{Pb}$) data sample recorded at a nucleon-nucleon center-of-mass energy of 8.16 TeV by the CMS experiment at the CERN LHC and corresponding to an integrated luminosity of$174.6{\mathrm{nb}}^{-1}$. The two$J/\psi$mesons are reconstructed in their${\mu }^{+}{\mu }^{-}$decay channels with transverse momenta$p_{\mathrm{T}}>6.5\mathrm{GeV}$and rapidity$|y|<2.4$. Events where one of the$J/\psi$mesons is reconstructed in the dielectron channel are also considered in the search. The$p\mathrm{Pb}\to J/\psi J/\psi +X$process is observed with a significance of 5.3 standard deviations. The measured inclusive fiducial cross section, using the four-muon channel alone, is$\sigma (p\mathrm{Pb}\to J/\psi J/\psi +X)=22.0\pm 8.9(\mathrm{stat})\pm 1.5(\mathrm{syst})\mathrm{nb}$. A fit of the data to the expected rapidity separation for pairs of$J/\psi$mesons produced in single (SPS) and double (DPS) parton scatterings yields${\sigma }_{\mathrm{SPS}}^{p\mathrm{Pb}\to J/\psi J/\psi +X}=16.5\pm 10.8(\mathrm{stat})\pm 0.1(\mathrm{syst})\mathrm{nb}$and${\sigma }_{\mathrm{DPS}}^{p\mathrm{Pb}\to J/\psi J/\psi +X}=5.4\pm 6.2(\mathrm{stat})\pm 0.4(\mathrm{syst})\mathrm{nb}$, respectively. This latter result can be transformed into a lower bound on the effective DPS cross section, closely related to the squared average interparton transverse separation in the collision, of${\sigma }_{\mathrm{eff}}>1.0\mathrm{mb}$at 95% confidence level.

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.

A search for Higgs boson pair (HH) production in association with a vector boson V (W or Z boson) is presented. The search is based on proton-proton collision data at a center-of-mass energy of 13 TeV, collected with the CMS detector at the LHC, corresponding to an integrated luminosity of 138 fb⁻¹. Both hadronic and leptonic decays of V bosons are used. The leptons considered are electrons, muons, and neutrinos. The HH production is searched for in the$$ \textrm{b}\overline{\textrm{b}}\textrm{b}\overline{\textrm{b}} $$$b\overline{b}b\overline{b}$decay channel. An observed (expected) upper limit at 95% confidence level of VHH production cross section is set at 294 (124) times the standard model prediction. Constraints are also set on the modifiers of the Higgs boson trilinear self-coupling,k_λ, assumingk_2V= 1, and vice versa on the coupling of two Higgs bosons with two vector bosons,k_2V. The observed (expected) 95% confidence intervals of these coupling modifiers are−37.7 <k_λ< 37.2 (−30.1 <k_λ< 28.9) and−12.2 <k_2V< 13.5 (−7.2 <k_2V< 8.9), respectively.

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.

The effective lifetime of the$$ {\textrm{B}}_{\textrm{s}}^0 $$$B_s^0$meson in the decay$$ {\textrm{B}}_{\textrm{s}}^0\to \textrm{J}/{\uppsi \textrm{K}}_{\textrm{S}}^0 $$$B_s^0\to J/{\mathrm{\psi K}}_S^0$is measured using data collected during 2016–2018 with the CMS detector in$$ \sqrt{s} $$$\sqrt{s}$= 13 TeV proton-proton collisions at the LHC, corresponding to an integrated luminosity of 140 fb⁻¹. The effective lifetime is determined by performing a two-dimensional unbinned maximum likelihood fit to the$$ {\textrm{B}}_{\textrm{s}}^0 $$$B_s^0$meson invariant mass and proper decay time distributions. The resulting value of 1.59 ± 0.07(stat) ± 0.03(syst) ps is the most precise measurement to date and is in good agreement with the expected value.

Using proton–proton collision data corresponding to an integrated luminosity of$$140\hbox { fb}^{-1}$$$140{\text{fb}}^{-1}$collected by the CMS experiment at$$\sqrt{s}= 13\,\text {Te}\hspace{-.08em}\text {V} $$$\sqrt{s}=13\text{Te}\text{V}$, the$${{{\Lambda }} _{\text {b}}^{{0}}} \rightarrow {{\text {J}/\uppsi }} {{{\Xi }} ^{{-}}} {{\text {K}} ^{{+}}} $$${\Lambda }_{\text{b}}^0\to \text{J}/\psi {\Xi }^{-}{\text{K}}^{+}$decay is observed for the first time, with a statistical significance exceeding 5 standard deviations. The relative branching fraction, with respect to the$${{{\Lambda }} _{\text {b}}^{{0}}} \rightarrow {{{\uppsi }} ({2\textrm{S}})} {{\Lambda }} $$${\Lambda }_{\text{b}}^0\to \psi \left(2\text{S}\right)\Lambda$decay, is measured to be$$\mathcal {B}({{{\Lambda }} _{\text {b}}^{{0}}} \rightarrow {{\text {J}/\uppsi }} {{{\Xi }} ^{{-}}} {{\text {K}} ^{{+}}} )/\mathcal {B}({{{\Lambda }} _{\text {b}}^{{0}}} \rightarrow {{{\uppsi }} ({2\textrm{S}})} {{\Lambda }} ) = [3.38\pm 1.02\pm 0.61\pm 0.03]\%$$$B({\Lambda }_{\text{b}}^0\to \text{J}/\psi {\Xi }^{-}{\text{K}}^{+})/B({\Lambda }_{\text{b}}^0\to \psi \left(2\text{S}\right)\Lambda )=[3.38\pm 1.02\pm 0.61\pm 0.03]\%$, where the first uncertainty is statistical, the second is systematic, and the third is related to the uncertainties in$$\mathcal {B}({{{\uppsi }} ({2\textrm{S}})} \rightarrow {{\text {J}/\uppsi }} {{{\uppi }} ^{{+}}} {{{\uppi }} ^{{-}}} )$$$B(\psi \left(2\text{S}\right)\to \text{J}/\psi {\pi }^{+}{\pi }^{-})$and$$\mathcal {B}({{{\Xi }} ^{{-}}} \rightarrow {{\Lambda }} {{{\uppi }} ^{{-}}} )$$$B({\Xi }^{-}\to \Lambda {\pi }^{-})$.

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 for collective effects inside jets produced in proton-proton collisions is performed via correlation measurements of charged particles using the CMS detector at the CERN LHC. The analysis uses data collected at a center-of-mass energy of$\sqrt{s}=13\mathrm{TeV}$, corresponding to an integrated luminosity of$138{\mathrm{fb}}^{-1}$. Jets are reconstructed with the anti-$k_{\mathrm{T}}$algorithm with a distance parameter of 0.8 and are required to have transverse momentum greater than 550 GeV and pseudorapidity$|{\eta }^{\text{jet}}|<1.6$. Two-particle correlations among the charged particles within the jets are studied as functions of the particles’ azimuthal angle and pseudorapidity separations ($\mathrm{\Delta }{\varphi }^{*}$and$\mathrm{\Delta }{\eta }^{*}$) in a jet coordinate basis, where particles’${\eta }^{*}$,${\varphi }^{*}$are defined relative to the direction of the jet. The correlation functions are studied in classes of in-jet charged-particle multiplicity up to$N_{\mathrm{ch}}^{\mathrm{j}}\approx 100$. Fourier harmonics are extracted from long-range azimuthal correlation functions to characterize azimuthal anisotropy for$|\mathrm{\Delta }{\eta }^{*}|>2$. For low-$N_{\mathrm{ch}}^{\mathrm{j}}$jets, the long-range elliptic anisotropic harmonic,$v_2^{*}$, is observed to decrease with$N_{\mathrm{ch}}^{\mathrm{j}}$. This trend is well described by Monte Carlo event generators. However, a rising trend for$v_2^{*}$emerges at$N_{\mathrm{ch}}^{\mathrm{j}}\gtrsim 80$, hinting at a possible onset of collective behavior, which is not reproduced by the models tested. This observation yields new insights into the dynamics of jet evolution in the vacuum.