Fermion-soliton scattering in a modified ${\mathbb{CP}}^1$ model

Abstract

The scattering of fermions in the background field of a topological soliton of the modified $(2+1)$-dimensional ${\mathbb{CP}}^1$ model is studied here both analytically and numerically. Unlike the original ${\mathbb{CP}}^1$ model, the Lagrangian of the modified model contains a potential term. Due to this, a dilatation zero mode of the topological soliton disappears, which results in stability of the fermion-soliton system. The symmetry properties of the fermion-soliton system are established, and the asymptotic forms of fermionic radial wave functions are studied. Questions related to the bound states of the fermion-soliton system are then discussed. General formulae describing the scattering of fermions are presented. The amplitudes of the fermion-soliton scattering are obtained in an analytical form within the framework of the Born approximation, and their symmetry properties and asymptotic forms are studied. The energy levels of the fermionic bound states and the partial phase shifts of fermionic scattering are obtained by numerical methods, and the ultrarelativistic limits of the partial phase shifts are found.

arXiv comment17 pages, 5 figures

References in corpus (8)

• Vortices, Instantons and Branes
• Nonabelian Superconductors: Vortices and Confinement in $\mathcal{N}=2$ SQCD
• Vortex Strings and Four-Dimensional Gauge Dynamics
• Non-Abelian String Junctions as Confined Monopoles
• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Quantum Vortex Strings: A Review
• Soliton Dynamics in a Novel Discrete O(3) Sigma Model in (2+1) Dimensions
• Fermion scattering on topological solitons in the ${\mathbb{CP}}^{N-1}$ model