Fermion scattering on topological solitons in the $\mathbb{CP}^{N-1}$ model

TL;DR

This paper analyzes fermion scattering on topological solitons in the 2+1 dimensional $ ext{CP}^{N-1}$ model, providing exact solutions, scattering formulae, and numerical insights into phase shifts and bound states.

Contribution

It introduces analytical solutions using confluent Heun functions and explores fermion-soliton interactions, including bound states and scattering properties, in the $ ext{CP}^{N-1}$ model.

Findings

Exact fermionic wave functions expressed via confluent Heun functions

Derived general formulae for fermion scattering and phase shifts

Numerical analysis of partial phase shifts and their properties

Abstract

The scattering of Dirac fermions in the background fields of topological solitons of the $(2+1)$-dimensional $\mathbb{CP}^{N-1}$ model is studied using analytical and numerical methods. It is shown that the exact solutions for fermionic wave functions can be expressed in terms of the confluent Heun functions. The question of the existence of bound states for the fermion-soliton system is then investigated. General formulae describing fermion scattering are obtained, and a symmetry property for the partial phase shifts is derived. The amplitudes and cross-sections of the fermion-soliton scattering are obtained in an analytical form within the framework of the Born approximation, and the symmetry properties and asymptotic forms of the Born amplitudes are investigated. The dependences of the first few partial phase shifts on the fermion momentum are obtained by numerical methods, and some of their properties are investigated and discussed.