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Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution. It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, αs(Q2), that varies with the energy scale Q2 characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of αs at low momentum transfers limits perturbative calculations to the high-energy region where Q2≫ΛQCD2≃ (250 MeV)2. Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large Nc-limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected qq¯ mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson, W± or Z, is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!

Inclusive jet cross section measurements from the ATLAS, CDF, CMS, D0, H1, STAR, and ZEUS experiments are explored for determinations of the strong coupling constant \\[\\alpha _{\\text {s}} (M_{\\text {Z}})\\]. Various jet cross section data sets are reviewed, their consistency is examined, and the benefit of their simultaneous inclusion in the \\[\\alpha _{\\text {s}} (M_{\\text {Z}})\\] determination is demonstrated. Different methods for the statistical analysis of these data are compared and one method is proposed for a coherent treatment of all data sets. While the presented studies are based on next-to-leading order in perturbative quantum chromodynamics (pQCD), they lay the groundwork for determinations of \\[\\alpha _{\\text {s}} (M_{\\text {Z}})\\] at next-to-next-to-leading order.

Quantum Chromodynamics, the theory of quarks and gluons, whose interactions can be described by a local SU(3) gauge symmetry with charges called “color quantum numbers”, is reviewed; the goal of this review is to provide advanced Ph.D. students a comprehensive handbook, helpful for their research. When QCD was “discovered” 50 years ago, the idea that quarks could exist, but not be observed, left most physicists unconvinced. Then, with the discovery of charmonium in 1974 and the explanation of its excited states using the Cornell potential, consisting of the sum of a Coulomb-like attraction and a long range linear confining potential, the theory was suddenly widely accepted. This paradigm shift is now referred to as the November revolution . It had been anticipated by the observation of scaling in deep inelastic scattering, and was followed by the discovery of gluons in three-jet events. The parameters of QCD include the running coupling constant, α s ( Q 2 ) , that varies with the energy scale Q 2 characterising the interaction, and six quark masses. QCD cannot be solved analytically, at least not yet, and the large value of α s at low momentum transfers limits perturbative calculations to the high-energy region where Q 2 ≫ Λ QCD 2 ≃ (250 MeV) 2 . Lattice QCD (LQCD), numerical calculations on a discretized space-time lattice, is discussed in detail, the dynamics of the QCD vacuum is visualized, and the expected spectra of mesons and baryons are displayed. Progress in lattice calculations of the structure of nucleons and of quantities related to the phase diagram of dense and hot (or cold) hadronic matter are reviewed. Methods and examples of how to calculate hadronic corrections to weak matrix elements on a lattice are outlined. The wide variety of analytical approximations currently in use, and the accuracy of these approximations, are reviewed. These methods range from the Bethe–Salpeter, Dyson–Schwinger coupled relativistic equations, which are formulated in both Minkowski or Euclidean spaces, to expansions of multi-quark states in a set of basis functions using light-front coordinates, to the AdS/QCD method that imbeds 4-dimensional QCD in a 5-dimensional deSitter space, allowing confinement and spontaneous chiral symmetry breaking to be described in a novel way. Models that assume the number of colors is very large, i.e. make use of the large N c -limit, give unique insights. Many other techniques that are tailored to specific problems, such as perturbative expansions for high energy scattering or approximate calculations using the operator product expansion are discussed. The very powerful effective field theory techniques that are successful for low energy nuclear systems (chiral effective theory), or for non-relativistic systems involving heavy quarks, or the treatment of gluon exchanges between energetic, collinear partons encountered in jets, are discussed. The spectroscopy of mesons and baryons has played an important historical role in the development of QCD. The famous X,Y,Z states – and the discovery of pentaquarks – have revolutionized hadron spectroscopy; their status and interpretation are reviewed as well as recent progress in the identification of glueballs and hybrids in light-meson spectroscopy. These exotic states add to the spectrum of expected q q ¯ mesons and qqq baryons. The progress in understanding excitations of light and heavy baryons is discussed. The nucleon as the lightest baryon is discussed extensively, its form factors, its partonic structure and the status of the attempt to determine a three-dimensional picture of the parton distribution. An experimental program to study the phase diagram of QCD at high temperature and density started with fixed target experiments in various laboratories in the second half of the 1980s, and then, in this century, with colliders. QCD thermodynamics at high temperature became accessible to LQCD, and numerical results on chiral and deconfinement transitions and properties of the deconfined and chirally restored form of strongly interacting matter, called the Quark–Gluon Plasma (QGP), have become very precise by now. These results can now be confronted with experimental data that are sensitive to the nature of the phase transition. There is clear evidence that the QGP phase is created. This phase of QCD matter can already be characterized by some properties that indicate, within a temperature range of a few times the pseudocritical temperature, the medium behaves like a near ideal liquid. Experimental observables are presented that demonstrate deconfinement. High and ultrahigh density QCD matter at moderate and low temperatures shows interesting features and new phases that are of astrophysical relevance. They are reviewed here and some of the astrophysical implications are discussed. Perturbative QCD and methods to describe the different aspects of scattering processes are discussed. The primary parton–parton scattering in a collision is calculated in perturbative QCD with increasing complexity. The radiation of soft gluons can spoil the perturbative convergence, this can be cured by resummation techniques, which are also described here. Realistic descriptions of QCD scattering events need to model the cascade of quark and gluon splittings until hadron formation sets in, which is done by parton showers. The full event simulation can be performed with Monte Carlo event generators, which simulate the full chain from the hard interaction to the hadronic final states, including the modelling of non-perturbative components. The contribution of the LEP experiments (and of earlier collider experiments) to the study of jets is reviewed. Correlations between jets and the shape of jets had allowed the collaborations to determine the “color factors” – invariants of the SU(3) color group governing the strength of quark–gluon and gluon–gluon interactions. The calculated jet production rates (using perturbative QCD) are shown to agree precisely with data, for jet energies spanning more than five orders of magnitude. The production of jets recoiling against a vector boson, W ± or Z , is shown to be well understood. The discovery of the Higgs boson was certainly an important milestone in the development of high-energy physics. The couplings of the Higgs boson to massive vector bosons and fermions that have been measured so far support its interpretation as mass-generating boson as predicted by the Standard Model. The study of the Higgs boson recoiling against hadronic jets (without or with heavy flavors) or against vector bosons is also highlighted. Apart from the description of hard interactions taking place at high energies, the understanding of “soft QCD” is also very important. In this respect, Pomeron – and Odderon – exchange, soft and hard diffraction are discussed. Weak decays of quarks and leptons, the quark mixing matrix and the anomalous magnetic moment of the muon are processes which are governed by weak interactions. However, corrections by strong interactions are important, and these are reviewed. As the measured values are incompatible with (most of) the predictions, the question arises: are these discrepancies first hints for New Physics beyond the Standard Model? This volume concludes with a description of future facilities or important upgrades of existing facilities which improve their luminosity by orders of magnitude. The best is yet to come!

A bstract A search for a standard model Higgs boson decaying into a pair of τ leptons is performed using events recorded by the CMS experiment at the LHC in 2011 and 2012. The dataset corresponds to an integrated luminosity of 4.9 fb −1 at a centre-of-mass energy of 7 TeV and 19.7 fb −1 at 8 TeV. Each τ lepton decays hadronically or leptonically to an electron or a muon, leading to six different final states for the τ -lepton pair, all considered in this analysis. An excess of events is observed over the expected background contributions, with a local significance larger than 3 standard deviations for m H values between 115 and 130 GeV. The best fit of the observed H → τ τ signal cross section times branching fraction for m H = 125 GeV is 0 . 78 ± 0 . 27 times the standard model expectation. These observations constitute evidence for the 125 GeV Higgs boson decaying to a pair of τ leptons.

From the manner of its discovery in 2012, it was apparent that the 125 GeV Higgs boson couples to bosons, but does it couple to fermions too? Yes, says the CMS Collaboration at CERN, who present combined evidence of Higgs decay to pairs of bottom quarks and pairs of tau leptons. The discovery of a new boson with a mass of approximately 125 GeV in 2012 at the Large Hadron Collider 1 , 2 , 3 has heralded a new era in understanding the nature of electroweak symmetry breaking and possibly completing the standard model of particle physics 4 , 5 , 6 , 7 , 8 , 9 . Since the first observation in decays to γγ , WW and ZZ boson pairs, an extensive set of measurements of the mass 10 , 11 and couplings to W and Z bosons 11 , 12 , 13 , as well as multiple tests of the spin-parity quantum numbers 10 , 11 , 13 , 14 , have revealed that the properties of the new boson are consistent with those of the long-sought agent responsible for electroweak symmetry breaking. An important open question is whether the new particle also couples to fermions, and in particular to down-type fermions, as the current measurements mainly constrain the couplings to the up-type top quark. Determination of the couplings to down-type fermions requires direct measurement of the corresponding Higgs boson decays, as recently reported by the Compact Muon Solenoid (CMS) experiment in the study of Higgs decays to bottom quarks 15 and τ leptons 16 . Here, we report the combination of these two channels, which results in strong evidence for the direct coupling of the 125 GeV Higgs boson to down-type fermions, with an observed significance of 3.8 standard deviations, when 4.4 are expected.

Abstract A search is presented for a new scalar resonance, X, decaying to a standard model Higgs boson and another new scalar particle, Y, in the final state where the Higgs boson decays to a $$\\text{b}\\overline{\\text{b} }$$ pair, while the Y particle decays to a pair of photons. The search is performed in the mass range 240–1000 GeV for the resonance X, and in the mass range 70–800 GeV for the particle Y, using proton-proton collision data collected by the CMS experiment at $$\\sqrt{s}=13$$ TeV, corresponding to an integrated luminosity of 132 fb −1. In general, the data are found to be compatible with the standard model expectation. Observed (expected) upper limits at 95% confidence level on the product of the production cross section and the relevant branching fraction are extracted for the X → YH process, and are found to be within the range of 0.05–2.69 (0.08–1.94) fb, depending on m X and m Y. The most significant deviation from the background-only hypothesis is observed for X and Y masses of 300 and 77 GeV, respectively, with a local (global) significance of 3.33 (0.65) standard deviations.

Several new physics models including versions of supersymmetry (SUSY) characterized by R-parity violation (RPV) or with additional hidden sectors predict the production of events with top quarks, low missing transverse momentum, and many additional quarks or gluons. The results of a search for top squarks decaying to two top quarks and six additional light-flavor quarks or gluons are reported. The search employs a novel machine learning method for background estimation from control samples in data using decorrelated discriminators. The search is performed using events with 0, 1, or 2 electrons or muons in conjunction with at least six jets. No requirement is placed on the magnitude of the missing transverse momentum. The result is based on a sample of proton-proton collisions at $\\sqrt{s}=13$ TeV corresponding to 138 fb−1 of integrated luminosity collected with the CMS detector at the LHC in 2016–2018. With no statistically significant excess of events observed beyond the expected contributions from the standard model, the data are used to determine upper limits on the top squark pair production cross section in the frameworks of RPV and stealth SUSY. Models with top squark masses less than 700 (930) GeV are excluded at 95% confidence level for RPV (stealth) SUSY scenarios.

A first study is presented of the cross section for the scattering of same-sign W boson pairs via the detection of a τ lepton. The data from proton-proton collisions at the center-of-mass energy of 13 TeV were collected by the CMS detector at the LHC, and correspond to an integrated luminosity of 138 fb−1. Events were selected that contain two jets with large pseudorapidity and large invariant mass, one τ lepton, one light lepton (e or μ), and significant missing transverse momentum. The measured cross section for electroweak same-sign WW scattering is $1.44^{+0.63}_{-0.56}$ times the standard model prediction. In addition, a search is presented for the indirect effects of processes beyond the standard model via the effective field theory framework, in terms of dimension-6 and dimension-8 operators.

Despite the f (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 ( ) meson, a tetraquark ( ) exotic state, a kaon-antikaon ( ) molecule, or a quark-antiquark-gluon ( ) hybrid. This paper reports strong evidence that the f (980) state is an ordinary meson, inferred from the scaling of elliptic anisotropies (v ) with the number of constituent quarks (n ), as empirically established using conventional hadrons in relativistic heavy ion collisions. The f (980) state is reconstructed via its dominant decay channel f (980) → π π , in proton-lead collisions recorded by the CMS experiment at the LHC, and its v is measured as a function of transverse momentum (p ). It is found that the n = 2 ( state) hypothesis is favored over n = 4 ( or states) by 7.7, 6.3, or 3.1 standard deviations in the p < 10, 8, or 6 GeV/c ranges, respectively, and over n = 3 ( hybrid state) by 3.5 standard deviations in the p < 8 GeV/c range. This result represents the first determination of the quark content of the f (980) state, made possible by using a novel approach, and paves the way for similar studies of other exotic hadron candidates.

Measurements of light-by-light scattering (LbL, γγ → γγ) and the Breit-Wheeler process (BW, γγ →e$^{+}$e$^{−}$) are reported in ultraperipheral PbPb collisions at a centre-of-mass energy per nucleon pair of 5.02 TeV. The data sample, corresponding to an integrated luminosity of 1.7 nb$^{−1}$, was collected by the CMS experiment at the CERN LHC in 2018. Events with an exclusively produced γγ or e$^{+}$e$^{−}$ pair with invariant masses m$^{γγ,ee}$> 5 GeV, along with other fiducial criteria, are selected. The measured BW fiducial production cross section, σ$_{fid}$(γγ → e$^{+}$e$^{−}$) = 263.5 ± 1.8(stat) ± 17.8(syst) μb, as well as the differential distributions for various kinematic observables, are in agreement with leading-order quantum electrodynamics predictions complemented with final-state photon radiation. The measured differential BW cross sections allow discrimination between different theoretical descriptions of the photon flux of the lead ion. In the LbL final state, 26 exclusive diphoton candidate events are observed compared with 12.0 ± 2.9 expected for the background. Combined with previous results, the observed significance of the LbL signal with respect to the background-only hypothesis is above five standard deviations. The measured fiducial LbL scattering cross section, σ$_{fid}$(γγ → γγ) = 107 ± 24(stat) ± 13(syst) nb, is in agreement with next- to-leading-order predictions. Limits on the production of axion-like particles coupled to photons are set over the mass range 5–100 GeV, including the most stringent limits to date in the range of 5–10 GeV. [graphic not available: see fulltext]