The CMS detector, including its muon system, has been operating at the CERN LHC in increasingly challenging conditions for about 15 years. The muon detector was designed to provide excellent triggering and track reconstruction for muons produced in proton–proton collisons at an instantaneous luminosity ( ℒ ) of 1 × 10^34 cm ^-2 s ^-1 . During the Run 2 data-taking period (2015–2018), the LHC achieved an instantaneous luminosity of twice its design value, resulting in larger background rates and making the efficient detection of muons more difficult. While some backgrounds result from natural radioactivity, cosmic rays, and interactions of the circulating protons with residual gas in the beam pipe, the dominant source of background hits in the muon system arises from proton–proton interactions themselves. Charged hadrons leaving the calorimeters produce energy deposits in the muon chambers. In addition, high-energy particles interacting in the hadron calorimeter and forward shielding elements generate thermal neutrons, which leak out of the calorimeter and shielding structures, filling the CMS cavern. We describe the method used to measure the background rates in the various muon subsystems. These rates, in conjunction with simulations, can be used to estimate the expected backgrounds in the High-Luminosity LHC. This machine will run for at least 10 years starting in 2029 reaching an instantaneous luminosity of ℒ = 5 ×10^34 cm^-2 s^-1 and increasing ultimately to ℒ = 7.5 ×10^34 cm^-2 s^-1 . These background estimates have been a key ingredient for the planning and design of the muon detector upgrade.

AbstractThe CMS detector, including its muon system, has been operating at the CERN LHC in increasingly challenging conditions for about 15 years. The muon detector was designed to provide excellent triggering and track reconstruction for muons produced in proton–proton collisons at an instantaneous luminosity ($$\mathcal {L}$$ L ) of $$1 \times 10^{34}$$ 1 × 10 34 cm$$^{-2}$$ - 2 s$$^{-1}$$ - 1 . During the Run 2 data-taking period (2015–2018), the LHC achieved an instantaneous luminosity of twice its design value, resulting in larger background rates and making the efficient detection of muons more difficult. While some backgrounds result from natural radioactivity, cosmic rays, and interactions of the circulating protons with residual gas in the beam pipe, the dominant source of background hits in the muon system arises from proton–proton interactions themselves. Charged hadrons leaving the calorimeters produce energy deposits in the muon chambers. In addition, high-energy particles interacting in the hadron calorimeter and forward shielding elements generate thermal neutrons, which leak out of the calorimeter and shielding structures, filling the CMS cavern. We describe the method used to measure the background rates in the various muon subsystems. These rates, in conjunction with simulations, can be used to estimate the expected backgrounds in the High-Luminosity LHC. This machine will run for at least 10 years starting in 2029 reaching an instantaneous luminosity of $$\mathcal {L} = 5 \times \text {10}^\text {34}\,\text {cm}^\text {-2}\,\text {s}^\text {-1}$$ L = 5 × 10 34 cm -2 s -1 and increasing ultimately to $$\mathcal {L} = 7.5 \times \text {10}^\text {34}\,\text {cm}^\text {-2}\,\text {s}^\text {-1}$$ L = 7.5 × 10 34 cm -2 s -1 . These background estimates have been a key ingredient for the planning and design of the muon detector upgrade.

This is a writeup, with some elaboration, of the talks by the two authors (a physicist and a statistician) at the first PHYSTAT Informal review on January 24, 2024. We discuss Bayesian and frequentist approaches to dealing with nuisance parameters, in particular, integrated versus profiled likelihood methods. In regular models, with finitely many parameters and large sample sizes, the two approaches are asymptotically equivalent. But, outside this setting, the two methods can lead to different tests and confidence intervals. Assessing which approach is better generally requires comparing the power of the tests or the length of the confidence intervals. This analysis has to be conducted on a case-by-case basis. In the extreme case where the number of nuisance parameters is very large, possibly infinite, neither approach may be useful. Part I provides an informal history of usage in high energy particle physics, including a simple illustrative example. Part II includes an overview of some more recently developed methods in the statistics literature, including methods applicable when the use of the likelihood function is problematic.

Abstract The CMS detector, including its muon system, has been operating at the CERN LHC in increasingly challenging conditions for about 15 years. The muon detector was designed to provide excellent triggering and track reconstruction for muons produced in proton–proton collisons at an instantaneous luminosity ( $$\mathcal {L}$$ L ) of $$1 \times 10^{34}$$ 1 × 10 34 cm $$^{-2}$$ - 2 s $$^{-1}$$ - 1 . During the Run 2 data-taking period (2015–2018), the LHC achieved an instantaneous luminosity of twice its design value, resulting in larger background rates and making the efficient detection of muons more difficult. While some backgrounds result from natural radioactivity, cosmic rays, and interactions of the circulating protons with residual gas in the beam pipe, the dominant source of background hits in the muon system arises from proton–proton interactions themselves. Charged hadrons leaving the calorimeters produce energy deposits in the muon chambers. In addition, high-energy particles interacting in the hadron calorimeter and forward shielding elements generate thermal neutrons, which leak out of the calorimeter and shielding structures, filling the CMS cavern. We describe the method used to measure the background rates in the various muon subsystems. These rates, in conjunction with simulations, can be used to estimate the expected backgrounds in the High-Luminosity LHC. This machine will run for at least 10 years starting in 2029 reaching an instantaneous luminosity of $$\mathcal {L} = 5 \times \text {10}^\text {34}\,\text {cm}^\text {-2}\,\text {s}^\text {-1}$$ L = 5 × 10 34 cm -2 s -1 and increasing ultimately to $$\mathcal {L} = 7.5 \times \text {10}^\text {34}\,\text {cm}^\text {-2}\,\text {s}^\text {-1}$$ L = 7.5 × 10 34 cm -2 s -1 . These background estimates have been a key ingredient for the planning and design of the muon detector upgrade.

Using a data sample of $$\sqrt{s}=13\,\text {TeV}$$ proton-proton collisions collected by the CMS experiment at the LHC in 2017 and 2018 with an integrated luminosity of $$103\text {~fb}^{-1}$$ , the $$\text {B}^{0}_{\mathrm{s}} \rightarrow \uppsi (\text {2S})\text {K}_\mathrm{S}^{0}$$ and $$\text {B}^{0} \rightarrow \uppsi (\text {2S})\text {K}_\mathrm{S}^{0} \uppi ^+\uppi ^-$$ decays are observed with significances exceeding 5 standard deviations. The resulting branching fraction ratios, measured for the first time, correspond to $${\mathcal {B}}(\text {B}^{0}_{\mathrm{s}} \rightarrow \uppsi (\text {2S})K_\mathrm{S}^{0})/{\mathcal {B}}(\text {B}^{0}\rightarrow \uppsi (\text {2S})K_\mathrm{S}^{0}) = (3.33 \pm 0.69 (\text {stat})\, \pm 0.11\,(\text {syst}) \pm 0.34\,(f_{\mathrm{s}}/f_{\mathrm{d}})) \times 10^{-2}$$ and $${\mathcal {B}}(\text {B}^{0} \rightarrow \uppsi (\text {2S})\text {K}_\mathrm{S}^{0} \uppi ^{+} \uppi ^{-})/ {\mathcal {B}}(\text {B}^{0} \rightarrow \uppsi (\text {2S})\text {K}^{0}_{\mathrm{S}}) = 0.480 \pm 0.013\,(\text {stat}) \pm 0.032\,(\text {syst})$$ , where the last uncertainty in the first ratio is related to the uncertainty in the ratio of production cross sections of $$\hbox {B}^{0}_{\mathrm{s}}$$ and $$\hbox {B}^{0}$$ mesons, $$f_{\mathrm{s}}/f_{\mathrm{d}}$$ .

The B$^0_s$ and B$^+$ production yields are measured in PbPb collisions at a center-of-mass energy per nucleon pair of 5.02 TeV. The data sample, collected with the CMS detector at the LHC, corresponds to an integrated luminosity of 1.7 nb$^{-1}$. The mesons are reconstructed in the exclusive decay channels B$^0_s$ $\to$ J/$\psi(\mu^+\mu^-)\phi($K$^+$K$^-)$ and B$^+$ $\to$ J/$\psi(\mu^+\mu^-)$K$^+$, in the transverse momentum range 7-50 GeV/c and absolute rapidity 0-2.4. The B$^0_s$ meson is observed with a statistical significance in excess of five standard deviations for the first time in nucleus-nucleus collisions. The measurements are performed as functions of the transverse momentum of the B mesons and of the PbPb collision centrality. The ratio of production yields of B$^0_s$ and B$^+$ is measured and compared to theoretical models that include quark recombination effects.

A combination of searches for top squark pair production using proton-proton collision data at a center-of-mass energy of 13 TeV at the CERN LHC, corresponding to an integrated luminosity of 137 fb(-1) collected by the CMS experiment, is presented. Signatures with at least 2 jets and large missing transverse momentum are categorized into events with 0, 1, or 2 leptons. New results for regions of parameter space where the kinematical properties of top squark pair production and top quark pair production are very similar are presented. Depending on themodel, the combined result excludes a top squarkmass up to 1325 GeV for amassless neutralino, and a neutralinomass up to 700 GeV for a top squarkmass of 1150 GeV. Top squarks with masses from 145 to 295 GeV, for neutralino masses from 0 to 100 GeV, with a mass difference between the top squark and the neutralino in a window of 30 GeV around the mass of the top quark, are excluded for the first time with CMS data. The results of theses searches are also interpreted in an alternative signal model of dark matter production via a spin-0 mediator in association with a top quark pair. Upper limits are set on the cross section for mediator particle masses of up to 420 GeV.

The second-order Fourier coefficients (v(2)) characterizing the azimuthal distributions of Y(1S) and Y(2S) mesons produced in PbPb collisions at root s(NN) = 5.02 TeV are studied. The Y mesons are reconstructed in their dimuon decay channel, as measured by the CMS detector. The collected data set corresponds to an integrated luminosity of 1.7 nb(-1). The scalar product method is used to extract the v2 coefficients of the azimuthal distributions. Results are reported for the rapidity range vertical bar y vertical bar < 2.4, in the transverse momentum interval 0 < pT < 50 GeV/c, and in three centrality ranges of 10-30%, 30-50% and 50-90%. In contrast to the J/psi mesons, the measured v(2) values for the Y mesons are found to be consistent with zero. (C) 2021 The Author(s). Published by Elsevier B.V.

The first measurement of the dependence of $\\gamma\\gamma \\to \\mu^{+}\\mu^{-}$ production on the multiplicity of neutrons emitted very close to the beam direction in ultraperipheral heavy ion collisions is reported. Data for lead-lead interactions at $\\sqrt{s_\\mathrm{NN}} =$ 5.02 TeV, with an integrated luminosity of approximately 1.5 nb$^{-1}$, were collected using the CMS detector at the LHC. The azimuthal correlations between the two muons in the invariant mass region 8 $\\lt m_{\\mu\\mu} \\lt$ 60 GeV are extracted for events including zero, one, or at least two neutrons detected in the forward pseudorapidity range $|\\eta| \\lt$ 8.3. The back-to-back correlation structure from leading-order photon-photon scattering is found to be significantly broader for events with a larger number of emitted neutrons from each nucleus, corresponding to interactions with a smaller impact parameter. This observation provides a data-driven demonstration that the average transverse momentum of photons emitted from relativistic heavy ions has an impact parameter dependence. These results provide new constraints on models of photon-induced interactions in ultraperipheral collisions. They also provide a baseline to search for possible final-state effects on lepton pairs caused by traversing a quark-gluon plasma produced in hadronic heavy ion collisions.

Likelihood functions are ubiquitous in data analyses at the LHC and elsewhere in particle physics. Partly because "probability" and "likelihood" are virtual synonyms in everyday English, but crucially distinct in data analysis, there is great potential for confusion. Furthermore, each of various approaches to statistical inference (likelihoodist, Neyman-Pearson, Bayesian) uses the likelihood function in different ways. This note is intended to provide a brief introduction at the advanced undergraduate or beginning graduate student level, citing a few papers giving examples and containing numerous pointers to the vast literature on likelihood. The Likelihood Principle (routinely violated in particle physics analyses) is mentioned as an unresolved issue in the philosophical foundations of statistics.

A measurement is presented of electroweak (EW) production of a W boson in association with two jets in proton-proton collisions at s = 13 Te . The data sample was recorded by the CMS Collaboration at the LHC and corresponds to an integrated luminosity of 35.9 fb - 1 . The measurement is performed for the l ν jj final state (with l ν indicating a lepton-neutrino pair, and j representing the quarks produced in the hard interaction) in a kinematic region defined by invariant mass m jj \u003e 120 Ge and transverse momenta p T j \u003e 25 Ge . The cross section of the process is measured in the electron and muon channels yielding σ EW ( W jj ) = 6.23 ± 0.12 (stat) ± 0.61 (syst) pb per channel, in agreement with leading-order standard model predictions. The additional hadronic activity of events in a signal-enriched region is studied, and the measurements are compared with predictions. The final state is also used to perform a search for anomalous trilinear gauge couplings. Limits on anomalous trilinear gauge couplings associated with dimension-six operators are given in the framework of an effective field theory. The corresponding 95% confidence level intervals are - 2.3 c W W W / Λ 2 2.5 Te - 2 , - 8.8 c W / Λ 2 16 Te - 2 , and - 45 c B / Λ 2 46 Te - 2 . These results are combined with the CMS EW Zjj analysis, yielding the constraint on the c W W W coupling: - 1.8 c W W W / Λ 2 2.0 Te - 2 .

A search is conducted for a low-mass charged Higgs boson produced in a top quark decay and subsequently decaying into a charm and a strange quark. The data sample was recorded in proton-proton collisions at $\\sqrt{s}=$ 13 TeV by the CMS experiment at the LHC and corresponds to an integrated luminosity of 35.9 fb$^{-1}$. The search is performed in the process of top quark pair production, where one top quark decays to a bottom quark and a charged Higgs boson, and the other to a bottom quark and a W boson. With the W boson decaying to a charged lepton (electron or muon) and a neutrino, the final state comprises an isolated lepton, missing transverse momentum, and at least four jets, of which two are tagged as b jets. To enhance the search sensitivity, one of the jets originating from the charged Higgs boson is required to satisfy a charm tagging selection. No significant excess beyond standard model predictions is found in the dijet invariant mass distribution. An upper limit in the range 1.68-0.25% is set on the branching fraction of the top quark decay to the charged Higgs boson and bottom quark for a charged Higgs boson mass between 80 and 160 GeV.

Anisotropies in the initial energy density distribution of the quark-gluon plasma created in high energy heavy ion collisions lead to anisotropies in the azimuthal distributions of the final-state particles known as collective anisotropic flow. Fourier harmonic decomposition is used to quantify these anisotropies. The higher-order harmonics can be induced by the same order anisotropies (linear response) or by the combined influence of several lower order anisotropies (nonlinear response) in the initial state. The mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles are measured as functions of transverse momentum and centrality in collisions at nucleon-nucleon center-of-mass energies and 5.02 with the CMS detector. The results are compared with viscous hydrodynamic calculations using several different initial conditions, as well as microscopic transport model calculations. None of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients.

Events with no charged particles produced between the two leading jets are studied in proton-proton collisions at

Anisotropies in the initial energy density distribution of the quark-gluon plasma created in high energy heavy ion collisions lead to anisotropies in the azimuthal distributions of the final-state particles known as collective anisotropic flow. Fourier harmonic decomposition is used to quantify these anisotropies. The higher-order harmonics can be induced by the same order anisotropies (linear response) or by the combined influence of several lower order anisotropies (nonlinear response) in the initial state. The mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles are measured as functions of transverse momentum and centrality in PbPb collisions at nucleon-nucleon center-of-mass energies $\\sqrt{S}$$_{NN}$=2.76 and 5.02TeV with the CMS detector. The results are compared with viscous hydrodynamic calculations using several different initial conditions, as well as microscopic transport model calculations. None of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients.

Abstract Anisotropies in the initial energy density distribution of the quark-gluon plasma created in high energy heavy ion collisions lead to anisotropies in the azimuthal distributions of the final-state particles known as collective anisotropic flow. Fourier harmonic decomposition is used to quantify these anisotropies. The higher-order harmonics can be induced by the same order anisotropies (linear response) or by the combined influence of several lower order anisotropies (nonlinear response) in the initial state. The mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles are measured as functions of transverse momentum and centrality in $$\mathrm {PbPb}$$ PbPb collisions at nucleon-nucleon center-of-mass energies $$\sqrt{\smash [b]{s_{_{\mathrm {NN}}}}} = 2.76$$ sNN=2.76 and 5.02$$\,\text {TeV}$$ TeV with the CMS detector. The results are compared with viscous hydrodynamic calculations using several different initial conditions, as well as microscopic transport model calculations. None of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients.

Central exclusive and semiexclusive production of [see pdf] pairs is measured with the CMS detector in proton-proton collisions at the LHC at center-of-mass energies of 5.02 and 13TeV. The theoretical description of these nonperturbative processes, which have not yet been measured in detail at the LHC, poses a significant challenge to models. The two pions are measured and identified in the CMS silicon tracker based on specific energy loss, whereas the absence of other particles is ensured by calorimeter information. The total and differential cross sections of exclusive and semiexclusive central [see pdf] production are measured as functions of invariant mass, transverse momentum, and rapidity of the [see pdf] system in the fiducial region defined as transverse momentum [see pdf] and pseudorapidity [see pdf] . The production cross sections for the four resonant channels , [see pdf] , , and are extracted using a simple model. These results represent the first measurement of this process at the LHC collision energies of 5.02 and 13TeV.