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We describe the physics potential of e + e − linear colliders in this report. These machines are planned to operate in the first phase at a center-of-mass energy of 500 GeV, before being scaled up to about 1 TeV. In the second phase of the operation, a final energy of about 2 TeV is expected. The machines will allow us to perform precision tests of the heavy particles in the Standard Model, the top quark and the electroweak bosons. They are ideal facilities for exploring the properties of Higgs particles, in particular in the intermediate mass range. New vector bosons and novel matter particles in extended gauge theories can be searched for and studied thoroughly. The machines provide unique opportunities for the discovery of particles in supersymmetric extensions of the Standard Model, the spectrum of Higgs particles, the supersymmetric partners of the electroweak gauge and Higgs bosons, and of the matter particles. High precision analyses of their properties and interactions will allow for extrapolations to energy scales close to the Planck scale where gravity becomes significant. In alternative scenarios, like compositeness models, novel matter particles and interactions can be discovered and investigated in the energy range above the existing colliders up to the TeV scale. Whatever scenario is realized in Nature, the discovery potential of e + e − linear colliders and the high-precision with which the properties of particles and their interactions can be analysed, define an exciting physics programme complementary to hadron machines.

We show that the data on γp and γγ interactions can be derived from the pp andpp forward scattering amplitudes using vector meson dominance and the additive quark model. The nucleon-nucleon data are parameterized using a model where high energy cross sections rise with energy as a consequence of the increasing numbers of soft partons populating the colliding particles. We present detailed descriptions of the data on the total and elastic cross sections, the ratio of the real to imaginary part of the forward scattering amplitude, and on the slope of the differential cross sections for pp,pp, γp, γγ, γp → γV and γγ → V i V j reactions, where V = ρ, ω, φ. We make a wide range of predictions for future HERA and LHC experiments and for γγ measurements at LEP. *

We present the achievements of the last years of the experimental and theoretical groups working on hadronic cross section measurements at the low-energy e + e − colliders in Beijing, Frascati, Ithaca, Novosibirsk, Stanford and Tsukuba and on τ decays. We sketch the prospects in these fields for the years to come. We emphasise the status and the precision of the Monte Carlo generators used to analyse the hadronic cross section measurements obtained as well with energy scans as with radiative return, to determine luminosities and τ decays. The radiative corrections fully or approximately implemented in the various codes and the contribution of the vacuum polarisation are discussed.

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High energy photon colliders (γγ,γe) are based on e-e-linear colliders where high energy photons are produced using Compton scattering of laser light on high energy electrons just before the interaction point. This paper is a part of the Technical Design Report of the linear collider TESLA.1Physics program, possible parameters and some technical aspects of the photon collider at TESLA are discussed.

An impact parameter representation for soft gluon radiation is applied to obtain both the initial decrease of the total cross-section (σ tot ) for proton-proton collisions as well as the later rise of σ tot with energy for both pp and pp. The non-perturbative soft part of the eikonal includes only limited low energy gluon emission and leads to the initial decrease in the proton-proton cross-section. On the other hand, the rapid rise in the hard, perturbative jet part of the eikonal is tamed into the experimentally observed mild increase by soft gluon radiation whose maximum energy rises slowly with energy.