Existence of a new instanton in constrained Yang-Mills-Higgs theory

Our goal is to discover possible new four-dimensional euclidean solutions (instantons) in fundamental SU(2) Yang-Mills-Higgs theory, with a constraint added to prevent collapse of the scale. We show that, most likely, there exists one particular new constrained instanton (I*) with vanishing Pontryagin index. This is based on a topological argument that involves the construction of a non-contractible loop of four-dimensional configurations with a certain upper bound on the action, which we establish numerically. We expect I* to be the lowest action non-trivial solution in the vacuum sector of the theory. There also exists a related static, but unstable, solution, the new sphaleron S*. Possible applications of I* to the electroweak interactions include the asymptotics of perturbation theory and the high-energy behaviour of the total cross section. (orig.)