Collision-induced decays of electroweak solitons: Fermion number violation with two and few initial particles.

Abstract

We consider a variant of the standard electroweak theory in which the Higgs sector has been modified so that there is a classically stable weak scale soliton. We explore fermion-number-violating processes which involve soliton decay. A soliton can decay by tunneling under the sphaleron barrier, or the decay can be collision induced if the energy is sufficient for the barrier to be traversed. We present a classical solution to the Minkowski space equations of motion in which a soliton is kicked over the barrier by an incoming pulse. This pulse corresponds to a quantum coherent state with a mean number of $W$ quanta $\ensuremath{\sim}\frac{2.5}{{g}^{2}}$ where $g$ is the SU(2) gauge coupling constant. We also give a self-contained treatment of the relationship between classical solutions, including those in which solitons are destroyed, and tree-level quantum amplitudes. Furthermore, we consider a limit in which we can reliably estimate the amplitude for soliton decay induced by collision with a single $W$ boson. This amplitude depends on $g$ like $\mathrm{exp}(\ensuremath{-}c{g}^{\ensuremath{-}\frac{1}{3}})$, and is larger than that for spontaneous decay via tunneling in the same limit. Finally, we show that in soliton decays light $\mathrm{SU}{(2)}_{L}$ doublet fermions are anomalously produced. Thus we have a calculation of a two-body process with energy above the sphaleron barrier in which fermion number is violated.