Two-jet Events Research Articles

Interplay between perturbative and non-perturbative effects with the ARES method

We present a new semi-numerical method to compute leading hadronisation corrections to two-jet event shapes in e+e− annihilation. The formalism we present utilises the dispersive approach, where the magnitude of power corrections is controlled by suitable moments of an effective strong coupling, but it can be adapted to other methods. We focus on observables where the interplay between perturbative and non-perturbative effects is crucial in determining the power corrections. A naive treatment of power corrections for some of these observables gives rise to an unphysical behaviour in the corresponding distributions for moderate observable values, thus considerably limiting the available range to fit the non-perturbative moments. We present a universal treatment to handle such observables, based on a suitable subtraction procedure, and compare our results to the analytic result in the case of total broadening. Finally, for the first time we present predictions for the thrust major, which cannot be handled with analytic methods.

Measurements of angular distance and momentum ratio distributions in three-jet and {text {Z}} + two-jet final states in {text {p}}{text {p}} collisions

Collinear (small-angle) and large-angle, as well as soft and hard radiations are investigated in three-jet and {text {Z}} + two-jet events collected in proton-proton collisions at the LHC. The normalized production cross sections are measured as a function of the ratio of transverse momenta of two jets and their angular separation. The measurements in the three-jet and {text {Z}} + two-jet events are based on data collected at a center-of-mass energy of 8,{text {TeV}}, corresponding to an integrated luminosity of 19.8,text {fb}^{-1}. The {text {Z}} + two-jet events are reconstructed in the dimuon decay channel of the {text {Z}} boson. The three-jet measurement is extended to include sqrt{s} = 13,{text {TeV}} data corresponding to an integrated luminosity of 2.3,text {fb}^{-1}. The results are compared to predictions from event generators that include parton showers, multiple parton interactions, and hadronization. The collinear and soft regions are in general well described by parton showers, whereas the regions of large angular separation are often best described by calculations using higher-order matrix elements.

Learning physics at future e\u2212e+ colliders with machine

Information deformation and loss in jet clustering are one of the major limitations for precisely measuring hadronic events at future e−e+ colliders. Because of their dominance in data, the measurements of such events are crucial for advancing the precision frontier of Higgs and electroweak physics in the next decades. We show that this difficulty can be well-addressed by synergizing the event-level information into the data analysis, with the techniques of deep neutral network. In relation to this, we introduce a CMB-like observable scheme, where the event-level kinematics is encoded as Fox-Wolfram (FW) moments at leading order and multi-spectra of spherical harmonics at higher orders. Then we develop a series of jet-level (w/ and w/o the FW moments) and event-level classifiers, and analyze their sensitivity performance comparatively with two-jet and four-jet events. As an application, we analyze measuring Higgs decay width at e−e+ colliders with the data of 5ab−1@240GeV. The precision obtained is significantly better than the baseline ones presented in documents. We expect this strategy to be applied to many other hadronic- event measurements at future e−e+ colliders, and to open a new angle for evaluating their physics capability.

Differential decay rates of CP-even and CP-odd Higgs bosons to top and bottom quarks at NNLO QCD

We consider the decay of a neutral Higgs boson of arbitrary CP nature to a massive quark antiquark pair at next-to-next-to-leading order in perturbative QCD. Our analysis is made at the differential level using the antenna subtraction framework. We apply our general set-up to the decays of a CP-even and CP-odd heavy Higgs boson to a top-quark top-antiquark pair and to the decay of the 125 GeV Higgs boson to a massive bottom-quark bottom-antiquark pair. In the latter case we calculate, in particular, the two-jet, three-jet, and four-jet decay rates and, for two-jet events, the energy distribution of the leading jet.

Analytic and Monte Carlo studies of jets with heavy mesons and quarkonia

We study jets with identified hadrons in which a family of jet-shape variables called angularities are measured, extending the concept of fragmenting jet functions (FJFs) to these observables. FJFs determine the fraction of energy, z, carried by an identified hadron in a jet with angularity, \tau_a. The FJFs are convolutions of fragmentation functions (FFs), evolved to the jet energy scale, with perturbatively calculable matching coefficients. Renormalization group equations are used to provide resummed calculations with next-to-leading logarithm prime (NLL') accuracy. We apply this formalism to two-jet events in e^+ e^- collisions with B mesons in the jets, and three-jet events in which a J/\psi is produced in the gluon jet. In the case of B mesons, we use a phenomenological FF extracted from e^+ e^- collisions at the Z^0 pole evaluated at the scale \mu = m_b. For events with J/\psi, the FF can be evaluated in terms of Non-Relativistic QCD (NRQCD) matrix elements at the scale \mu =2 m_c. The z and \tau_a distributions from our NLL' calculations are compared with predictions from monte carlo event generators. While we find consistency between the predictions for B mesons and the J/\psi distributions in \tau_a, we find the z distributions for J/\psi differ significantly. We describe an attempt to merge PYTHIA showers with NRQCD FFs that gives good agreement with NLL' calculations of the z distributions.

The influence of fragmentation models in the production of hadron jets in electron–positron annihilation

The analysis of electron–positron annihilations to hadrons at high energies shows that apart from two-jet events, there are also signs of three-jet events which are interpreted according to the QCD, as a gluon radiated by a quark. In this paper, we investigate the fragmentation of quarks and gluons to hadron jets. We show that gluon jets have a higher multiplicity compared to quark jets of the same energy. Furthermore, inclusion of different flavours in the distributions shows that quark jets are flavour-dependent, but gluon jets are not. The differences between quark and gluon jets also manifest themselves in the fragmentation functions. We observe that the fragmentation for gluon jet is softer than that for quark jet, because the radiation of soft gluons is larger for gluon jets and that gluon cannot be present as a valence parton inside a produced hadron. We provide possible explanations for these features in this paper.

EVENT SHAPES FOR HADRONIC FINAL STATE: EXPERIMENTAL REVIEW

The analysis is presented for the first moments of collective observable distributions in two-jet events for various interaction types and for wide initial energy range. These observables include sphericity, thrust, components of transverse particle momentum, alignment and planarity. Database of experimental results created in the framework of the paper includes data for all interactions. Energy dependencies of average values for collective observables except components of transverse momentum show universal behavior for various interactions. Particle transverse momentum as well as its components increase faster for e+e- interaction with growth of [Formula: see text], than that for other interactions. Empirical analytical functions are suggested for description of energy dependence for all collective observables under study with exception of infrared-stable thrust variable. Energy dependence for average thrust is compared with QCD predictions including perturbative part and analytical phenomenological corrections which account for nonperturbative effects. Dispersive model and single dressed gluon approximation are considered for description of energy dependence of first moment of thrust distribution and estimation of strong coupling constant for various interactions as well as for joint sample. The dispersive model allow to describe average thrust versus initial energy in wide range of [Formula: see text] down to strongly nonperturbative domain [Formula: see text] at qualitative level at least. Study of event shape observables allows to obtain estimations of αS(MZ) which are in reasonable agreement both with world average value and with results extracted in the framework of other methods. Using suggested analytical fitted functions some estimations of values of collective parameters under study have been obtained for present and future facilities. In TeV energy domain average values of collective observables either depend on [Formula: see text] weakly or do not depend on initial energy at all within errors. Thus, the TeV scale can be considered as an estimation of the low boundary of asymptotic region for traditional collective parameters. Usually, multiplicity dependence of collective observables under consideration agree with power function in energy domain [Formula: see text] at qualitative level at least. Behavior of sphericity versus multiplicity and comparison of experimental results with model calculations allow to suggest that the universal estimation of the low energy boundary for experimental appearance of event jet structure in multiparticle production processes is [Formula: see text].

QCD next-to-leading order predictions toW-pair production in association with a massive (anti)bottom jet at the LHC

The $W$-pair production in association with a massive (anti)bottom jet is not only an important background to a number of interesting processes, such as the single top production associated with a W boson, but also a potential background to new physics searches. We present the calculations of the total and differential cross sections for the $W^+W^-+ b(\bar{b})$ jet productions at the LHC up to the QCD next-to-leading order (NLO). Our results by adopting the QCD NLO contribution collection scheme-I show that the K factors can be 1.66 and 1.21 with the inclusive and exclusive two-jet event selection schemes respectively, when we set $m_H=120 GeV$, $\mu=m_W+m_b/2$ and take the constraints of $p_{T,b(\bar{b})}>25 GeV$, $|y_{b(\bar{b})}|<2.5$ for $b(\bar{b})$ jet. We find that the stabilization of the theoretical prediction for the integrated cross section for the $pp \to W^+W^-b(\bar b)+X$ up to the QCD NLO requires a veto on a second isolated hard jet and the inclusion of the QCD NLO contribution from the $W^+W^-b\bar{b}(bb, \bar{b}\bar{b})$ production with the final two $b(\bar{b})$ quarks being merged as one jet.

Some evidences of multiple particle sources from nuclear matter jets in He+AT collisions at relativistic energies

Searching for interesting variables which contains information about the compression stage of a relativistic A + A collision, the concept of “nuclear matter jets” is an interesting tool for selecting different event structures as: single-jet events, two-jet events, three-jet events, and non-jet events. We found a relation between the number of jets and the centrality of the collision. The analysis of the jet properties allowed us to make assumptions about their origin. The founded jets in these interactions have a hadronic origin and not a partonic one.

Test of the τ-model of Bose–Einstein correlations and reconstruction of the source function in hadronic Z-boson decay at LEP

Bose-Einstein correlations of pairs of identical charged pions produced in hadronic Z decays are analyzed in terms of various parametrizations. A good description is achieved using a L\'evy stable distribution in conjunction with a model where a particle's momentum is correlated with its space-time point of production, the \taumodel. Using this description and the measured rapidity and transverse momentum distributions, the space-time evolution of particle emission in two-jet events is reconstructed. However, the elongation of the particle emission region previously observed is not accommodated in the \taumodel, and this is investigated using an \adhoc/ modification.

Factorization ofe+e−event shape distributions with hadronic final states in soft collinear effective theory

We present a new analysis of two-jet event shape distributions in soft collinear effective theory. Extending previous results, we observe that a large class of such distributions can be expressed in terms of vacuum matrix elements of operators in the effective theory. We match these matrix elements to the full theory in the two-jet limit without assuming factorization of the complete set of hadronic final states into independent sums over partonic collinear and soft states. We also briefly discuss the relationship of this approach to diagrammatic factorization in the full theory.

UNIVERSAL NONPERTURBATIVE EFFECTS IN EVENT SHAPES FROM SOFT-COLLINEAR EFFECTIVE THEORY

Two-jet event shape distributions, traditionally studied in the language of perturbative QCD, can be described naturally in soft-collinear effective theory. In this language, we demonstrate factorization of event shape distributions into perturbatively-calculable hard and jet functions and nonperturbative soft functions, and show how the latter contribute universal shifts to the mean values of various event shape distributions. Violations of universality in shifts of higher moments can give information on correlations of energy flow in soft radiation.

Momentum flow correlations from event shapes: Factorized soft gluons and soft-collinear effective theory

The distributions of two-jet event shapes contain information on hadronization in QCD. Near the two-jet limit, these distributions can be described by convolutions of nonperturbative event shape functions with the same distributions calculated in resummed perturbation theory. The shape functions, in turn, are determined by correlations of momentum flow operators with each other and with lightlike Wilson lines, which describe the coupling of soft, wide-angle radiation to jets. We observe that leading power corrections to the mean values of event shapes are determined by the correlation of a single momentum flow operator with the relevant Wilson lines. This generalizes arguments for the universality of leading power corrections based on the low-scale behavior of the running coupling or resummation. We also show how a study of the angularity event shapes can provide information on correlations involving multiple momentum flow operators, giving a window to the system of QCD dynamics that underlies the variety of event shape functions. In deriving these results, we review, develop and compare factorization techniques in conventional perturbative QCD and soft-collinear effective theory (SCET). We give special emphasis to the elimination of double counting of momentum regions in these two formalisms.

Coherent soft particle production in Z decays into three jets

Low-energy particle production perpendicular to the event plane in three-jet events produced in Z decays in e+e− annihilation is measured and compared to that perpendicular to the event axis in two-jet events. The topology dependence of the hadron production ratio is found to agree with a leading-order QCD prediction. This agreement and especially the need for the presence of a destructive interference term gives evidence for the coherent nature of gluon radiation. Hadron production in three-jet events is found to be directly proportional to a single topological scale function of the inter-jet angles. The slope of the dependence of the multiplicity with respect to the topological scale was measured to be 2.211±0.014(stat.)±0.053(syst.) in good agreement with the expectation given by the colour-factor ratio CA/CF=9/4. This result strongly supports the assumption of local parton–hadron duality, LPHD, at low hadron momentum.

Real radiation at next-to-next-to-leading order in QCD: e+e- --> 2 jets through O(alpha2s).

We present a calculation of the differential two-jet cross section in e(+)e(-) annihilation through next-to-next-to-leading order (NNLO) in the strong coupling constant alpha(s). The calculation is performed using a new method for dealing with real radiation suggested recently by us. For the first time, the two-jet event rate is computed directly, without any reference to the inclusive cross section e(+)e(-)-->hadrons. We also calculate the energy distribution of the leading jet in e(+)e(-)-->2 jets and find significant modifications of the shape of this distribution at NNLO.

Enhanced nonperturbative effects in jet distributions.

We consider the triple differential distribution d Gamma/dE(J)dm(2)(J)d Omega(J) for two-jet events at center of mass energy M, smeared over the end-point region m(2)(J)<<M2, absolute value 2E(J)-M approximately Delta, Lambda(QCD)<<Delta<<M. The leading nonperturbative correction, suppressed by Lambda(QCD)/Delta, is given by the matrix element of a single operator. A similar analysis is performed for three-jet events, and the generalization to any number of jets is discussed. At order Lambda(QCD)/Delta, nonperturbative effects in four or more jet events are completely determined in terms of two matrix elements which can be measured in two- and three-jet events.

A MONTE CARLO STUDY ON THE DYNAMICAL FLUCTUATIONS INSIDE QUARK AND ANTIQUARK JETS

The dynamical fluctuations inside the quark and antiquark jets are studied using Monte Carlo method. Quark and antiquark jets are identified from the two-jet events in e+e- collisions at 91.2 GeV by checking them at parton level. It is found that the transition point exists inside both of these two kinds of jets. At this point the jets are circular in the transverse plane with respect to the property of dynamical fluctuations. The results are consistent with the fact that the third jet (gluon jet) was historically first discovered in e+e- collisions in the energy region 17–30 GeV.

Energy flow in interjet radiation

We study the distribution of transverse energy, Q_Omega, radiated into an arbitrary interjet angular region, Omega, in high-p_T two-jet events. Using an approximation that emphasizes radiation directly from the partons that undergo the hard scattering, we find a distribution that can be extrapolated smoothly to Q_Omega=Lambda_QCD, where it vanishes. This method, which we apply numerically in a valence quark approximation, provides a class of predictions on transverse energy radiated between jets, as a function of jet energy and rapidity, and of the choice of the region Omega in which the energy is measured. We discuss the relation of our approximation to the radiation from unobserved partons of intermediate energy, whose importance was identified by Dasgupta and Salam.

Inclusive production of $\mathrm{\pi^0}$ , $\eta$ , ${\rm \eta^{\prime}(958)}$ , ${\rm K^0_{\rm S}}$ and ${\rm \Lambda}$ in two- and three-jet events from hadronic Z decays

The production rates and the inclusive cross sections of the isovector meson ${\rm \pi^0}$ , the isoscalar mesons $\eta$ and ${\rm \eta^{\prime}(958)}$ , the strange meson ${\rm K^0_{\rm S}}$ and the ${\rm \Lambda}$ baryon have been measured as functions of scaled energy in hadronic events, two-jet events and each jet of three-jet events from hadronic Z decays and compared to Monte Carlo models. The analysis is based on 3.7 million hadronic events collected with the ALEPH detector at LEP at a centre-of-mass energy of $\sqrt{s}=91.2$ GeV. The JETSET modelling of the gluon fragmentation into isoscalar mesons is found to be in agreement with the experimental results. HERWIG fails to describe the ${\mathrm{K^0_S}}$ spectra in gluon-enriched jets and the ${\rm \Lambda}$ spectra in quark jets.

Bose-Einstein correlations in ${\mathrm K^{\pm}}{\mathrm K^{\pm}}$ pairs from $\mathrm{Z}^0$ decays into two hadronic jets

Bose-Einstein correlations in pairs of charged kaons produced in a sample of 3.9 million hadronic \(\mathrm{Z}^0\) decays have been measured with the OPAL experiment at LEP. Charged kaons were identified in the central tracking detector using their specific energy loss in the drift chamber gas. The correlation function was studied in two-jet events using a double ratio, formed by the number of like-sign pairs normalised by a reference sample in the data, divided by the same ratio in a Monte Carlo simulation. The enhancement at small values of the four-momentum difference of the pair was parametrised using a Gaussian function. The parameters of the Bose-Einstein correlations were measured to be \(\lambda = 0.82 \pm 0.22^{+0.17}_{-0.12}\) for the strength and \(R_0 = 0.56 \pm 0.08^{+0.08}_{-0.06}\) fm for the kaon source radius, where the first errors are statistical and the second systematic. Corrections for final-state interactions are discussed.