Transverse momentum and angular distributions of hadrons in e+e− jets from QCD

Hadron jets in e⁺e^? annihilation will broaden at high energies due to gluon bremsstrahlung. With nonperturbative p_T effects dying out rapidly, the basic features of hadron jets can be calculated in perturbation theory. We examine the p_T distribution of secondarily produced hadrons. This is uniquely connected with the deviation from the 1 + cos²θ dependence of single particle inclusive distributions. We discuss what can be learned about the gluon fragmentation given the p_T and/or angular distributions. A sum rule is derived which establishes a relationship between the average p_T² and α_S.     

Comparison of π±, K± and p,p production in the central rapidity region in hadron-hadron collisions and in e+e− annihilation

We compare the p_T dependence of pion, kaon and proton production cross sections in the central rapidity region in e⁺e⁻ annihilation events and in proton-proton collisions at ISR energies. We find similarities both in the p_T dependence of cross sections and in the particle composition as a function of p_T, in agreement with the hypothesis of a universal mechanism of particle production.     

Jets in inclusive e+e− and leptoproduction

The assumption of jets with bounded p_T leads to the following consequences: (a) In e⁺e^? annihilation the coefficient of the cos²θ term (a) of single-particle inclusive distributions] exhibits a unique dependence on the observed particle momentum. This dependence provides a measure of 〈p_T²〉 in a jet. (b) In two-particle inclusive annihilation the average of the squared relative p_T is determined by the same parameter and by the momenta of the two particles. (c) The observation that in the current fragmentation region of leptoproduction the p_T distribution of fast hadrons is broader than that of show ones is explained.     

Indication of an onset of hard-like effects in K+p, π+p and pp collisions at 250 GeV/c: EHS/NA22 Collaboration Aachen-Antwerp/Brussel-Berlin (Zeuthen)-Helsinki-Cracow-Moscow-Nijmegen-Rio de Janeiro- Serpukhov-Warsaw-Yerevan

Similarly as in lepton-hadron scattering, but less pronounced than in e⁺e⁻ annihilation at comparable energies, we observe a rise of the “sea-gull” wings with CMS energy. The large average transverse momenta around Feynman |x_F|=0.4 are mainly due to high multiplicity events, for which also a tail develops in the multiplicity distribution. Neither of these effects can be reproduced by currently used low-p_T fragmentation models.     

Characteristics of charged particle production in relativistic heavy-ion collisions

Inclusive spectra of charged particles at midrapidity in Au+Au collisions at $\sqrt {s_{NN} } = 130$ GeV and 200 GeV were measured with the STAR detector at RHIC. The measured mean transverse momentum 〈p _T 〉 shows a characteristic dependence on charged particle multiplicity and beam energy in Au+Au collisions that is distinctly different from pp, $p\bar p$ and e⁺e^? collisions. A 32%±3%(syst) increase in 〈p _T 〉 from pp to Au+Au collisions was observed at 200 GeV. While the charged multiplicity was found to increase by 19%±5%(syst) from $\sqrt {s_{NN} } = 130$ GeV to 200 GeV, no significant difference in 〈p _T 〉 was found between the two energies. A comparison with model predictions is discussed.     

Pion production at large transverse momentum

A constituent interchange model is used to give a natural explanation of the observed energy dependence of ISR data for π° production at 90°. It is predicted that at large fixed p_T and sufficiently high energy the cross section will become constant, with a p_T dependence of (p_T²)^?2.5. It is also tentatively suggested that the e⁺e^? annihilation structure function $\text{ν}\text{W}{}_2$ should behave like ω^?1.5 near ω = 0.     

Comparison of planar features of K−p interactions with e+e− annihilations and deep inelastic μp scattering

The planar features of hadronic final states in K^?p interactions at 4.5, 5.6 and 14.3 GeV c.m. energy are compared with data from e⁺e^? annihilation and deep inelastic μp scattering. A strong energy variation of the distributions (1/σ)dσ/dp_t², 〈p_t²〉_in and Σp²_{t in} is observed over this energy range. Striking agreement is found between the K^?p data at 14.3 c.m. energy and the leptonic data at similar hadronic c.m. energies. The behaviour of these distributions from K^?p data is not well described by the simple quark fragmentation model, but shows deviations similar to those attributed to hard gluon effects in leptonic interactions.     

Large-pT protons from constituent diquark scattering

Recent data from the CERN ISR on the fractional proton yield in pp collisions are explained within the Stockholm diquark model. Describing the proton as a u(ud)₀ system, the observed high magnitude and fall-off _pT, θ and $\text{s}$ of the proton yield are natural consequences of constituent diquark elastic scattering. The _pT and θ dependence favour a value of around 10 GeV²/c² for the size parameter in the diquark form factor, corresponding to a diquark rms radius of around 0.2 fm. This is consistent with earlier results of the model applied to deep inelastic lepton-nucleon scattering and e⁺e^? annihilation.     

Two-photon exchange in p⊆)p→ℓ+ℓ−X and a comparison with QCD

A thorough study of lepton-pair production from two-photon annihilation in p?)p collisions is presented. The differential cross section is calculated over a large range of energies (27?√s?800 GeV as a function of the dilepton mass M as well as the dilepton transverse momentum Q_T and the Feynman variable x_F. No kinematical approximations (such as the equivalent photon approximation) are made. For Q_T ≈ 0 the two-photon mechanism represents an important fraction of the pp→e⁺e^?X cross section already at ISR energies, whereas at ISABELLE energies it dramatically dominates in the interval 0?Q_T?1 GeV. At ISR energies these conclusions follow from a direct comparison of the two-photon contribution with pp→e⁺e^?X data. For the ISABELLE energy range the expected O(α_s) QCD contribution to pp→?⁺?^?X, corrected for soft gluon radiation to all orders (in leading bilogarithmic approximation), was taken as a reference. At larger Q_T and ISR energies the γγ contribution is negligible, whereas at √s = 800 GeV γγ/QCD? 10–20% almost everywhere. Furthermore, two-photon candidate events from the ISR are shown to be in reasonable agreement with theory. A decomposition of the γγ cross section into contributions from both proton vertices being elastic, inelastic and of mixed configuration is given. The results provide important clues for a future isolation of the two-photon mechanism.     

Large corrections to high-pT hadron-hadron scattering in QCD

We have computed the first non-trivial QCD corrections to the quark-quark scattering process which contributes to the production of hadrons at large p_T in hadron-hadron collisions. Using quark distribution functions defined in deep inelastic scattering and fragmentation functions defined in one particle inclusive e⁺e^? annihilation, we find that the corrections are large. This implies that QCD perturbation theory may not be reliable for large-p_T haron physics.     

Strong forward-backward multiplicity correlations in hadron-hadron collisions and their absence in electron-positron annihilation

In high-energypp ( \((\bar pp)\) ) collisions, the average value of backward produced charged particles, taken at fixed number of forward produced particlesn _F, depends significantly uponn _F. This correlation is absent ine ⁺ e ^? annihilation at present energies. We relate these facts using the picture of the broadpp multiplicity distribution which arises from the incoherent superposition of narrow distributions from all impact parameters.     

Two- and three-point energy correlations in Hadronice + e − annihilation

Correlations between the energies incident on two or three detectors arounde ⁺ e ^? annihilation events are considered as a probe of the QCD structure of the events. Practical methods for deducing two-detector energy correlations (which give the mean product of energies incident on two detectors as a function of their angular separation) from measured events are devised. Analytical formulae for energy correlations from QCD perturbation theory are given, but it is found that large corrections from hadron formation obscure these symptotic predictions at available energies. Correlations between the final state and the incominge ^± beam direction are discussed, and observables are presented which measure the angular distributions of planes of final particles with respect to the beam axis (but do not require explicit determination of the planes). Finally, three-detector energy correlatons and their moments are treated, and methods for investigating planar structures ine ⁺ e ^? annihilation events are devised.     

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.     

Equilibrium temperature of hadrons

The temperatureT of hadrons frome ⁺ e ^? annihilation is analyzed using the SPEAR and the PLUTO data. Thermal equilibrium is found for π,K and ρ andT～E _c.m ^α with α=0.31±0.05. A discussion is given on the equipartition of energy between broad resonances and particles from their strong decay, and its application to estimate the quark mass difference:m _s?m_u=0.11 andm _c?m_u=1.60 GeV.     

Partial virial theorems for atomic-molecular systems

New virial relations for three-and four-particle atomic-molecular systems are proposed. Using operators of extension or squeezing of interparticle distances, it is shown that, for all pairs of j and k particles in S states of these systems, the following partial virial relations are valid: 〈2T _jk 〉+〈 V _jk 〉=0, where 〈V _jk 〉 is the average Coulomb interaction energy for a pair of particles and 〈T _jk 〉 is a part of the average kinetic energy of the system. There are three and six such relations for three-and four-particle systems, respectively. The conventional virial theorem (〈 2T〉+〈V〉=0) for the average total kinetic and potential energies of the system (〈 T〉 and 〈V〉, respectively) corresponds to the summation of partial virial relations over all pairs of particles. It is shown by an example of variational calculations of the helium atom ⁴He²⁺ e ^? e ^? and the helium muon-electron mesoatom ⁴He²⁺μ^? e ^? that partial virial relations are a highly sensitive indicator of the accuracy of wave functions.     

Low-energy gluon to the vacuum polarization of heavy quarks

We calculate a correction to the effective electromagnetic current at low energies, induced by a heavy-quark loop, and determine the analytic structure of the vacuum polarization function at small q ², for which an explicit expression is given to the O(α _s ³ ) order of perturbation theory. Implications to the high-precision analysis of experimental data on heavy-quark production in e ⁺ e ^? annihilation are discussed.     

Measurement of inelastic J/ψ photoproduction at HERA

We present a measurement of the inelastic, non diffractive J/ψ photoproduction cross section in the reaction e ⁺ p → e ⁺J/ψ X with the ZEUS detector at HERA. The J/ψ was identified using both the μ ⁺ μ ^- and e ⁺ e ^- decay channels and events were selected within the range 0.4 < z < 0.9 (0.5 < z < 0.9) for the muon (electron) decay mode, where z is the fraction of the photon energy carried by the J/ψ in the proton rest frame. The cross section, the p _T ² and the z distributions, after having subtracted the contributions from resolved photon and diffractive proton dissociative processes, are given for the photon-proton centre of mass energy range 50 < W < 180 GeV; p _T ² is the square of the J/ψ transverse momentum with respect to the incoming proton beam direction. In the kinematic range 0.4 < z < 0.9 and p _T ² > 1 GeV², NLO calculations of the photon-gluon fusion process based on the colour-singlet model are in good agreement with the data. The predictions of a specific leading order colour-octet model, as formulated to describe the CDF data on J/ψ hadroproduction, are not consistent with the data.     

SU(2)×U(1) effects in e+e− annihilation: Generalized charge asymmetry

The observability of the SU(2)×U(1) electroweak charge asymmetry effects in e⁺e^? annihilation at $\text{s}\text{=29}\text{GeV}$ is addressed in the context of a Feynman-Field type fragmentation model. We assume three colors of five flavored quarks and one heavy lepton τ. We neglect, at this time, the hard gluon bremsstrahlung events. We take b→c+X as the b-decay mode and we assume all τ's and heavy hadrons decay within the resolution of the detector so thatonly light hadrons and leptons are detected. Allowing all these decays to occur, we then compute the expected front-back asymmetry of negatively charged particles weighted with zⁿ for z?0.0175, where n = 0.5, 1…, 7, 10, and z is the light-cone momentum fraction. We find, for example, that such an asymmetry is ≈5% for n=2for sin²θ_w=0.236 and Λ_{QCD=0.34 GeV}. In other words, due to the large number of charge particles produced per event, this SU(2)×U(1) charge asymmetry may be accessible experimentally in e⁺e^? → X already at PEP and PETRA energies.     

A method of three-jet analysis ine + e − annihilation

For three-jet events ine ⁺ e ^? annihilation, a procedure is described to determine all three jet axes by minimizing the sum of squares of transverse momenta. Computations with this procedure show that at high energies the result is quite insensitive to missing particles, such as neurals.     

Nonlinear supersymmetry at HERA-energies

Some consequences of a model whereN=1 supersymmetry is realized nonlinearly are worked out forep-collisions at HERA-energies. The model contains in addition to the standard particles one Goldstone-fermion λ, a neutrino-like Majoranaparticle. The existence of such a particle would be signalled by events with large missing energy and momentum. We present detailed predictions for the following special kinematic regions: (1) events with a tagged small angle electron and a largeE _T jet, (2) events with a large angle electron and a small angle tagged exclusive proton, (3) events with a tagged small angle electron and a tagged small angle exclusive proton. We indicate the region in coupling constant and mass of the Goldstone-fermion which can be explored at HERA and compare with the limits obtainable from existing data one ⁺ e ^? and \(p\bar p\) collisions at high energies.