Scattering of fermions on a one-dimensional Q-ball

TL;DR

This paper analytically and numerically investigates how massless fermions scatter off a one-dimensional Q-ball, deriving wave functions, transmission and reflection coefficients, and analyzing Q-ball evaporation and charge loss.

Contribution

It provides the first analytical solutions for fermion scattering states on a 1D Q-ball and explores the evaporation process and parameter dependencies numerically.

Findings

Analytical wave functions for fermion scattering states are obtained.

Transmission and reflection coefficients are derived and numerically analyzed.

Q-ball evaporation rate depends on Yukawa coupling and Noether charge.

Abstract

The scattering of massless fermions on a one-dimensional Q-ball is studied both analytically and numerically in the background field approximation. The wave functions of the fermionic scattering states are found in analytical form. General expressions are derived for the transmission and reflection coefficients and the corresponding $S$-matrix elements. General formulae describing the evaporation of the Noether charge of the one-dimensional Q-ball are given. A numerical study of the transmission and reflection coefficients along with the corresponding S-matrix elements is performed for a range of values of the model parameters. A study of the dependence of the evaporation rate of the Q-ball on the Yukawa coupling constant is carried out for several values of the Noether charge.