Abstract
The β functions are calculated for values of the momenta of the external legs in the region of the masses of the particles in the internal loops. The effects of these β functions in an SU(2) × U(1) model of weak and electromagnetic interactions and in a grand unified model of strong, weak and electromagnetic interactions are discussed. The most significant effect is the reduction of the mass of the superheavy gauge bosons in unified theories by a factor of 6, which decreases the estimated proton lifetime by three orders of magnitude.
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