A study of jets in electron positron annihilation into hadrons in the energy range 3.1 to 9.5 GeV

From an analysis of data taken with the detector PLUTO and the DORIS storage rings we have obtained evidence for jet structure in e⁺e^? annihilation with hadrons. Results for mean sphericity, mean thrust, the angular dependence of the jet axis and for 〈p_t〉 and 〈p_∥〉 with respect to the jet axis are presented. At 9.4 GeV we also discuss the angular dependence of the charged and neutral deposited energy with respect to the jet axis.     

Renormalization group approach to Sterman-Weinberg jets

A renormalization group approach is developed for single-jet Sterman-Weinberg cross sections. For small δ², but large Q²δ², the complete δ², Q² and ? dependence of the cross section for e⁺e^? annihilation is shown to be calculable in QCD systematically in powers of α(Q²). ? is not assumed to be small.     

Comments on the Sterman-Weinberg jet formula

A simple derivation of the Sterman-Weinberg jet formula (the QCD perturbation theory formula for the 2-jet cross section) is described. Conditions on the jet parameters ? and δ for this formula to be applicable are discussed and the corrections to the formula up to O(?²), O(δ²) are presented.     

Some comments on jet fragmentation models andα s determinations

A number of interrelated topics on jet properties ine ⁺ e ^? annihilation is discussed. The need for differentα _s values in different fragmentation models is explained, with particular emphasis on the sensitivity to the choice of momentum conservation scheme in independent fragmentation models. Also other factors leading to a broad range of experimentalα _s values are discussed. Old and new methods to distinguish different fragmentation models are presented, with particular emphasis on gluon jet fragmentation properties.     

Single jet structure ine + e − annihilation

By using JETSET 7.2 ase ⁺ e ^? event generator at different c.m. energies, we studiedsingle jet multiplicity distributions in different rapidity andp _T intervals. Good NB behavior is found and related clan structure analysis is performed. Observed differences in the behavior of the 2-and 3-jet samples can be understood in terms of the relative contribution of single quark and gluon jet to the 3-jet sample, which are obtained by selecting event by event in this sample the highest and the lowest energy jet respectively.     

The transverse momentum profile of a quark jet

The first and second moments of the transverse momentum distribution of pions ine ⁺ e ^?-annihilation at fixed longitudinal momentum with respect to the jet axis are discussed, treating the hadronic final state evolving from the 2-quark system in the framework of a fireball-model. Good agreement with the published data is found. A comparison with thep _T -distribution of electroproduction is made, showing qualitative agreement. This casts serious doubts on previous conclusions favoring a large partonk _T inside the proton.     

Energy cone distribution around the jet axis in e+e− annihilation

We study the hadronic energy-weighted angular cross section inside (or outside) a pair of back-to-back cones around the thrust axis in e⁺e^? annihilation. The relevant cross sections. both on and off a quarkonium state (i.e., with three-gluon or quark-antiquark-gluon final states), are calculated in the leading order in perturbative QCD. Our method employs only one variable, viz., the half-radius of the cones, to measure the jet-likeness of events. The usefulness of this “energy-cone” distribution is discussed and compared to the Sterman-Weinberg formula and the energy-correlation distribution.     

Observation of planar three-jet events in e+e− annihilation and evidence for gluon bremsstrahlung

Topological distributions of charged and neutral hadrons from the reaction e⁺e^? → multihadrons are studied at √s of about 30 GeV. An excess of planar events is observed at a rate which cannot be explained by statistical fluctuations in the standard two-jet process. The planar events, mostly consisting of a slim jet on one side and a broader jet on the other, are shown actually to possess three-jet structure by demonstrating that the broader jet itself consists of two collinear jets in its own rest system. Detailed agreement between data and predictions is obtained if the process $\text{e}{}^{\mathrm{+}}\text{e}{}^{\mathrm{?}}\text{→q}\text{q}\text{?}\text{g}$ is taken into account. This strongly suggests gluon bremsstrahlung as the origin of the planar three-jet events. By comparison of the data with the qq?g-model we obtain a value for the strong coupling constant of α_S(q² = 0.17 ± 0.04.     

Semi-classical models for gluon jets and leptoproduction based on the massless relativistic string

Based upon the dynamics of a massless relativistic string we propose a semi-classical model for a gluon jet. We also show a close but non-trivial similarity between a jet obtained in a leptoproduction event and the quark jets frome ⁺ e ^?-annihilation.     

Multijet events in soft and semihard hadronic collisions

Various phenomena suggest the importance of a hard component in soft hadronic collisions with large cross sections already at moderate energies below \(\sqrt s \sim 30 GeV\) which involve the valence quarks. We consider Born term models based on one gluon exchange and hadron quark couplings either pointlike or with additional largep _T damping. A resolution dependent multijet analysis-performed in a way similar toe ⁺ e ^?-annihilation-can yield important information about the elements of a perturbative approach. Predictions are presented for multijet rates and properties of 2 and 3 jet events in the low resolution regime. Some results for 2 jet events do also apply for higher energies and high resolution.     

On non-perturbative effects in the jet physics

We consider quark scattering off nonperturbative gluonic fields in the vacuum and its impact on the hadronic final state in thee ⁺ e ^?—annihilation. A conservative estimate gives a nonperturbativep _⊥?1GeV. The modification of the final state survives even at an arbitrary high energy, where the corrections to the total cross-section die away. We also argue that the coupling constant extracted from the perturbative treatment of the jet phenomenology can well be different from that governing the correction toσ _tot.     

Recombination dependence of theO(α s 2 ) three-jet cross section ine + e − annihilation

TheO(α _s ² ) QCD corrections to the thrust distribution for three-jet production ine ⁺ e ^? annihilation are found to depend on the algorithm for recombining four partons into three jets. Several recombination schemes are discussed and results are compared. Results of the recombination approach are compared also to recent direct calculations of three-jet thrust distributions. The importance of terms proportional to jet resolution parameters is stressed.     

The topology dependence of charged particle multiplicities in three-jet events

A study of individual jet and whole-event charged particle multiplicities in three-jet events measured in e ⁺ e ^? annihilation at the Z reveals a significant topology dependence. Mean jet multiplicities are inadequately described by jet energies; interjet angles must also be specified. Quantitative tests suggest that it is necessary to use transversemomentum- like scales to describe the data.     

Higher order QCD corrections to the energy-energy correlation function

We calculate theO(α _s ² correction to the energy-energy correlation cross section using a Sterman-Weinberg type resolution criterion to account for higher-order/nonperturbative effects. We find that the energy-energy correlation function as well as the asymmetry is sensitive to the choice of resolution parameters.     

The correlation between charge and energy flow within cascade models for quark and hadron jets

We consider the ratio \(\frac{{\Delta Q}}{{\Delta \varepsilon }}\) of the charge and energy fraction carried by particles in the angular interval ΔΩ with respect to the jet axis, where we assume a recursive scheme for the hadron cascade. A measurement of this ratio inep andvp collisions determines the quark chargeQ _q at any angle ΔΩ and ine ⁺ e ^?-annihilations alsoQ _q ⁴ can be obtained. In hadron hadron collisions this ratio discriminates in a very direct way between different production models. We consider the “stopping quark” model, the “two dual sheet” model, and finally a leading cluster model. More data on \(\frac{{\Delta Q}}{{\Delta \varepsilon }}\) would be desirable at higher energies in particular for meson beams.     

Large logarithm behaviour ofe + e − jet cross sections and event shape distributions inO(α s 2 )

We have calculated the leading and next-to-leading logarithm coefficients ofO(α _s ² )e ⁺ e ^? annihilation jet cross sections, thrust distribution and energy-energy correlation in the two-jet limit when the jet resolution and the event shape variables vanish. We have compared our results with expectations based on leading logarithm approximations used to resum the pertubative cross sections where this is possible. There is good agreement for the leading and next-to-leading coefficients of jet cross sections in the Durham scheme. Also for the thrust distribution and energy-energy correlation we find results which are consistent with the leading logarithm predictions.     

e + e −-Annihilation with polarized beams in the standard model and extended electroweak gauge models

We derive the general expressions for the differential cross section and final state polarization ine ⁺ e ^?→γ,Z ₁ ⁰ ,Z ₂ ⁰ , ...→ff (f: leptons and quarks) with several neutral bosons and with polarized beams. From this also the jet axis distributions ine ⁺ e ^? → 2 jets are obtained. The general formulas are applied to the standard model and extended gauge models of electroweak interactions with one neutral boson lighter than the standard modelZ ⁰. The models differ from each other in the coefficients of angular distributions at energies around the firstZ ⁰ resonance and beyond. Observable effects are expected in certain models already at energies up to 60 GeV if the firstZ ⁰ is not too heavy.     

Baryon production in lepton-nucleon scattering and diquark fragmentation

We study baryon production in deep inelastic scattering using an extended version of the Lund jet model. There are two contributing sources. The first is baryon production in the target fragmentation. In a scheme related to our earlier work on lowp _hu baryon fragmentation we present some details of the fragmentation of a diquark into baryons and mesons. A non-negligible baryon-antibaryon production is observed ine ⁺ e ^? annihilation. In a previous paper we developed a model for this production, and the same mechanism should also give fast baryons in leptoproduction. In this paper we discuss those features of baryon production which can be more easily studied in a leptoproduction experiment.     

Simple model for spin-crisis

Starting from the additive quarkSU(6) model and taking into account the pion and kaon (η) emission during the initial stage of evolution (fromq ²～m _quark ² toq ²～1 GeV²) we convert the main fraction of the proton spin into the orbital momentum of the pseudoscalar mesons. The results are in a good agreement with the experimental data. We get ∫g ₁(x)dx=0.152 for proton and +0.007 for the Λ hyperon (i.e. the quarks carry out only about 39% of the Λ spin). In the same model we explain the violation of the Gottfried sum rule ?∫(F ₂ ^p(x)?F ₂ ⁿ(x))dx=0.23 due to the charged meson exchanges at the beginning of the evolution. The Gribov-Lipatov relation between the polarized structure functions in DIS ande ⁺ e ^?-annihilation is discussed. It gives the possibility to study the spin structure of Λ hyperon produced through the decay of the jet originated by a polarized quark ine ⁺ e ^?-annihilation or in DIS.