HIGH-ENERGY PRODUCTION OF SCALAR BOSONS IN WEAK-COUPLING THEORIES

We evaluate the cross section of multiparticle production in weak-coupling lambda-phi-4 theory at high energies. By means of dispersion relations the problem is reduced to the long-standing problem of summation of perturbative series at low energies. Applying the technique and insight gained in the latter case we derive the total cross section of Higgs-boson production. The cross section is dominated by low-order terms and is small at all energies. The conclusions are in drastic variance with the tree approximation to the same cross section.