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 tunnelling 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 mean number of $W$ quanta $\sim 2.5/g^2$ 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 $\exp (-c{g}^{-1/3})$, and is larger than that for spontaneous decay via tunnelling in the same limit. Finally we show that in soliton decays, light $SU(2{)}_L$ 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.

64 pages, revtex, epsf, all figures included. Revised version. Section V replaced with a corrected version. Qualitative conclusions unchanged. Numerical value of one exponent has changed

References in corpus (8)

• Progress in Electroweak Baryogenesis
• Summing tree graphs at threshold
• Fermion Production in the Background of Minkowski Space Classical Solutions in Spontaneously Broken Gauge Theory
• 2 \to n threshold production at tree level
• Anomalous Violation of Conservation Laws in Minkowski Space
• Gauge Invariant Variables for Spontaneously Broken SU(2) Gauge Theory in the Spherical Ansatz
• Fermion Number Violation in the Background of a Gauge Field in Minkowski Space
• Anomalous Violation of Conservation Laws in Minkowski Space: Spontaneously Broken Gauge Theories

Cited by in corpus (8)

• Electroweak Baryogenesis
• Semilocal and Electroweak Strings
• Semiclassical Study of Baryon and Lepton Number Violation in High-Energy Electroweak Collisions
• Semi-Analytical Approaches to Local Electroweak Baryogenesis
• The Emergence of Electroweak Skyrmions through Higgs Bosons
• Collision-Induced Decay of Metastable Baby Skyrmions
• Aspects of the Electroweak Skyrmion
• Quantum effects on winding configurations in SU(2)-Higgs theory