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Abstract Despite the f₀(980) hadron having been discovered half a century ago, the question about its quark content has not been settled: it might be an ordinary quark-antiquark ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$) meson, a tetraquark ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$) exotic state, a kaon-antikaon ($${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$) molecule, or a quark-antiquark-gluon ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$) hybrid. This paper reports strong evidence that the f₀(980) state is an ordinary$${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$meson, inferred from the scaling of elliptic anisotropies (v₂) with the number of constituent quarks (n_q), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f₀(980) state is reconstructed via its dominant decay channel f₀(980) →π⁺π⁻, in proton-lead collisions recorded by the CMS experiment at the LHC, and itsv₂is measured as a function of transverse momentum (p_T). It is found that then_q= 2 ($${{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}$state) hypothesis is favored overn_q= 4 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{q}}}\overline{{{\rm{q}}}}$$ $q\overline{q}q\overline{q}$or$${{\rm{K}}}\overline{{{\rm{K}}}}$$ $K\overline{K}$states) by 7.7, 6.3, or 3.1 standard deviations in thep_T< 10, 8, or 6 GeV/cranges, respectively, and overn_q= 3 ($${{\rm{q}}}\overline{{{\rm{q}}}}{{\rm{g}}}$$ $q\overline{q}g$hybrid state) by 3.5 standard deviations in thep_T< 8 GeV/crange. This result represents the first determination of the quark content of the f₀(980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates. 

Abstract 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. 

Abstract A measurement is presented of a ratio observable that provides a measure of the azimuthal correlations among jets with large transverse momentum$$p_{\textrm{T}}$$ $p_{\text{T}}$. This observable is measured in multijet events over the range of$$p_{\textrm{T}} = 360$$ $p_{\text{T}}=360$–$$3170\,\text {Ge}\hspace{-.08em}\text {V} $$ $3170\text{Ge}\text{V}$based on data collected by the CMS experiment in proton-proton collisions at a centre-of-mass energy of 13$$\,\text {Te}\hspace{-.08em}\text {V}$$ $\text{Te}\text{V}$, corresponding to an integrated luminosity of 134$$\,\text {fb}^{-1}$$ ${\text{fb}}^{-1}$. 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$$\alpha _\textrm{S} (m_{{\textrm{Z}}}) =0.1177 \pm 0.0013\, \text {(exp)} _{-0.0073}^{+0.0116} \,\text {(theo)} = 0.1177_{-0.0074}^{+0.0117}$$ ${\alpha }_{\text{S}}\left(m_{\text{Z}}\right)=0.1177\pm 0.0013{\text{(exp)}}_{-0.0073}^{+0.0116}\text{(theo)}=0.{1177}_{-0.0074}^{+0.0117}$, where the total uncertainty is dominated by the scale dependence of the fixed-order predictions. A test of the running of$$\alpha _\textrm{S}$$ ${\alpha }_{\text{S}}$in the$$\,\text {Te}\hspace{-.08em}\text {V}$$ $\text{Te}\text{V}$region shows no deviation from the expected NLO pQCD behaviour. 

Abstract A search for$${\text {Z}{}{}} {\text {Z}{}{}} $$ $\text{Z}\text{Z}$and$${\text {Z}{}{}} {\text {H}{}{}} $$ $\text{Z}\text{H}$production in the$${\text {b}{}{}} {\bar{{\text {b}{}{}}}{}{}} {\text {b}{}{}} {\bar{{\text {b}{}{}}}{}{}} $$ $\text{b}\overline{\text{b}}\text{b}\overline{\text{b}}$final state is presented, where H is the standard model (SM) Higgs boson. The search uses an event sample of proton-proton collisions corresponding to an integrated luminosity of 133$$\,\text {fb}^{-1}$$ ${\text{fb}}^{-1}$collected at a center-of-mass energy of 13$$\,\text {Te}\hspace{-.08em}\text {V}$$ $\text{Te}\text{V}$with the CMS detector at the CERN LHC. The analysis introduces several novel techniques for deriving and validating a multi-dimensional background model based on control samples in data. A multiclass multivariate classifier customized for the$${\text {b}{}{}} {\bar{{\text {b}{}{}}}{}{}} {\text {b}{}{}} {\bar{{\text {b}{}{}}}{}{}} $$ $\text{b}\overline{\text{b}}\text{b}\overline{\text{b}}$final state is developed to derive the background model and extract the signal. The data are found to be consistent, within uncertainties, with the SM predictions. The observed (expected) upper limits at 95% confidence level are found to be 3.8 (3.8) and 5.0 (2.9) times the SM prediction for the$${\text {Z}{}{}} {\text {Z}{}{}} $$ $\text{Z}\text{Z}$and$${\text {Z}{}{}} {\text {H}{}{}} $$ $\text{Z}\text{H}$production cross sections, respectively.