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We give a self-contained (though sketchy) derivation of the charged multiplicity distribution of final hadrons in a simplified (only pions) version of the statistical bootstrap model (SBM). The analytical form of this distribution is determined by two prominent features of SBM: a singularity at some temperatureT0 (related to the phase transition hadrons → quark-gluon plasma) and the production of Poisson-distributed hadron clusters with well-defined decay structure. The multiplicity distribution of final hadrons has two free parameters: an average temperatureT and the mean number\(\bar N\) of clusters, both depending on the collision energy √s such that for √s→∞, the temperature tends to the limitT0 while\(\bar N\) may grow (very slowly) without bound. With these two free parameters we obtain reasonable to good fits to experimental data at energies ranging from √s=7.87 to 900 GeV (full and in some cases cut pseudorapidity). The average cluster sizes found in our fits are compatible with those inferred from (pseudo) rapidity correlations in the data. We discuss the relation of this model to the negative binomial distribution (NBD).

It is shown that a gauge theory of self-interacting massless spin-3 particles which is analogous to Yang-Mills or the theory of gravity does not exist. A way out may be the existence of an interacting infinite family of massless particles of various spins. The first-order interactions which are possible between such particles show a remarkable structure. This is established by explicit construction. Detailed results are obtained for the possible algebraic structures which one may obtain for gauge theories which are induced from the gauge invariance of free lagrangians.

A complete two-loop O( α 2 ) initial state radiative correction to the Z-resonance shape is presented. The correction is compared with those expressions where only the soft-photon effects are resummed in all orders of perturbation theory. Our result shows that the soft-photon part constitutes the bulk of the radiative correction near the top of the Z-peak. The effect of non-photonic QED processes on the Z-resonance is found to be very small. The above results have been obtained by means of a standard Feynman diagram calculation. In addition we have also computed the cross sections by using the renormalization group method, where besides the leading logs ln( s / m 2 ), the next-to-leading ones also have been taken into account.

The standard model prediction for the shape of the Z resonance in e + e − collisions is calculated. The initial-state radiation and the boson self-energies are taken into account. This is both necessary and sufficient to match the experimental precision of SLC and LEP. The dependence of the resonance shape on the top mass and the Higgs mass is studied.

The effect of the initial-state QED radiative corrections to the Z resonance shape is considered. A complete O(α 2 ) correction is carried out and compared to calculations, where higher-order effects are obtained by some form of exponentiation of the first-order correction. The results also apply to the shape of the radiative tail far above resonance, for which some examples are shown.

The one-loop QED corrections to e+e− → Zγ production are presented. In contrast to γγ production, the result contains no anomalous large double logarithms. It is pointed out that our results can also be applied to processes like e+e− → μ+μ− γ and e + e − → v v λ .

In this paper we start the construction of a self interacting massless spin three field theory. The first order self interaction is constructed. The free field gauge invariance is modified by a term of first order in the coupling constant. Finally the abelian gauge transformation of the free Lagrangian is shown to become non-abelian.

We present a detailed calculation of the process e + e − →ν ν γ . For the lowest order, the calculation is done keeping a finite mass for the W boson and the results apply for unpolarized as well as longitudinally polarized beams. One-loop QED corrections are calculated and, together with the hard bremsstrahlung process e + e − →ν ν γγ , are implemented in an unweighted Monte Carlo generator of events. Results for a realistic experimental set-up are presented, amounting to corrections of the order of 17%.

We give an explicit construction of conserved currents for massless fields of arbitrary spin. These currents are gauge invariant and conserved on shell. Also they allow for the construction of a large class of trilinear interaction terms for the interaction between a massless spin-s1 field and two spin-s2 fields. The class is restricted only to 2s2⩽s1. In case s1 = 4 and s2 = 2, the current is the linearized Bel-Robinson tensor. To these conserved currents corresponds an infinite dimensional Lie algebra of global infinitesimal invariances of the action of a free massless field of arbitrary spin.

Charged multiplicity distributions calculated in the framework of the statistical bootstrap model (SBM) describe the shape of the experimentally observed distributions rather well. The SBM distribution is fairly close to the negative binomial distribution. It has two parameters, the average number N of clusters and the temperature T. Their dependence on s and on rapidity cuts is intuitively obvious. The behaviour of SBM multiplicity distributions is governed by the existence of a singularity of the model at some critical temperature T0 where the phase transition from hadrons to a quark-gluon plasma is expected

A simple and accurate expression for the high energy limit of the two-loop QED vertex correction is presented. Also the two-loop QED contribution to the electron form factor due to the diagram where in the electron-photon vertex the vacuum polarization of another fermion species is inserted is calculated. These expressions are required for order α2 corrections to electron-positron collisions.

We study the formulation of QCD on anisotropic lattices with different couplings in space and time directions of a four-dimensional hypercube. A non-perturbative determination of the ratio of lattice spacings, ξ = aσ/aτ, as well as the ratio of Λ-parameters has been performed in the scaling regime of SU(3) gauge theory. We apply these results to the thermodynamics of QCD on anisotropic lattices.

We present results for the ratio of lattice spacings, ξ = a a τ , and the ratio of Λ-parameters, Λ ξ Λ 1 , anisotropic lattices with different couplings in spatial and temporal directions.