WINDING TRANSITIONS AT FINITE-ENERGY AND TEMPERATURE - AN O(3) MODEL

Winding number transitions in the two-dimensional softly broken O(3) n onlinear a model are studied at finite energy and temperature. New per iodic instanton solutions which dominate the semiclassical transition amplitudes are found analytically at low energies, and numerically for all energies up to the sphaleron scale. The Euclidean period beta of these finite energy instantons increases with energy, contrary to the behavior found in the Abelian Higgs model or simple one-dimensional sy stems. This results in a sharp crossover from instanton-dominated tunn eling to sphaleron-dominated thermal activation ata certain critical t emperature. Since this behavior is traceable to the soft breaking of c onformal invariance by the mass term in the a model, semiclassical win ding number transition amplitudes in the electroweak theory in 3+1 dim ensions should exhibit a similar sharp crossover. We argue that this i s indeed the case in the standard model for M(H)<4M(W).