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Analytical expressions for the cross section including all the one-loop radiative corrections in the context of the Weinberg model are presented. The systematic calculation of one-loop diagrams has been carried out using a recently proposed scheme. Numerical results are shown in a region from 40-200 GeV c.m. energy and different values of the scattering angle; they indicate that the percentage corrections are mainly due to soft photons. The only departure from QED-like corrections can be seen in a region where the lowest-order cross section is lowered by weak-e.m. interference. In that region hard photon contributions are relatively prominent and perhaps within experimental possibilities.

Massive and mass-less Yang-Mills and gravitational fields are considered.It is found that there is a discrete difference between the zero-mass theories and the very small, but non-zero mass theories. In the oase of gravitation, comparison of massive and mass-less theories with experiment, in particular the perihelion movement of Mercury, leads to exclusion of the massive theory. It is concluded that the graviton mass must be rigorously zero.

The completely general one-loop scalar one-, two-, three-and four-point functions are studied. Also an integral occurring in connection with soft bremsstrahlung is considered. Formulas in terms of Spence functions are given. An expansion for Spence functions with complex argument is presented. The whole forms a basis for the calculation of one-loop radiative corrections in the general case, including unstable particles and particles with spin.

Within the Weinberg model mass differences between members of a multiplet generate further mass differences between the neutral and charged vector bosons. The experimental situation on the Weinberg model leads to an upper limit of about 800 GeV on mass differences within a multiplet. No limit on the average mass can be deduced.

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The two-loop correction to the o-parameter in lhe limit of the large l-tiggs mass is calculated. Numerically it is found that the two-loop contribution is equal in magnitude, but of opposite sign to the one-kw, p correction if the tliggs mass is about 137 times the vector boson mass. The calculation suggest a breakdown of perturbation theory if the tliggs mass is larger than 3 TeV. There is no direct correspondence between our results and the poles at n = 3 of the simple non-linear o-model at the two-loop level. * For an unknown reason these terms were misrepresented in ref. [5].

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