CONSTRAINED INSTANTON AND BARYON NUMBER NONCONSERVATION AT HIGH-ENERGIES

The total cross-section for baryon number violating processes at high energies is usually parametrized as sigma(total) is-proportional-to exp((4pi/alpha)F(epsilon)), where epsilon = square-root S/E0, E0 = square-root 6pim(w)/alpha. Only a few terms are known for the expansion of the function F(epsilon) at small epsilon. In the present work we investigate the case of sufficiently heavy Higgs boson (m(h)/M(w))2 much greater than 1. The third nontrivial term of the expansion F(epsilon) = -1 + 9/8 epsilon4/3 - 9/16 epsilon2 - 9/32 (m(h)/m(w))2 epsilon8/3 log (1/3epsilon (2m(w)/gammam(h))2) + O(epsilon8/3) is obtained. The unknown corrections to F(epsilon) are expected to be also of the order of epsilon8/3, but with no (m(h)/m(w))2 enhancement. The above formula is valid if both epsilon much less than 1 and epsilon(m(h)/m(w))3/2 much less than 1. For sufficiently heavy Higgs boson the p-dependent part of the instanton action is changed drastically. In this case even the leading contribution to F(epsilon), responsible for a growth of cross-section due to the multiple production of classical W-bosons, is changed: F(epsilon) = -1 + 9/8 (2/3)2/3 epsilon4/3 + ... epsilon much less than 1 much less than epsilon (m(h)/m(w))3/2.