On the Aharonov-Casher scattering in a CPT-odd Lorentz-violating background

TL;DR

This paper investigates how a Lorentz-violating background affects Aharonov-Casher scattering, revealing new bound states and non-conservation of helicity, using self-adjoint extension methods.

Contribution

It introduces a novel analysis of Aharonov-Casher scattering in a Lorentz-violating background, deriving explicit expressions for bound states and scattering parameters.

Findings

Additional scattering occurs for all self-adjoint extension parameters.

Negative energy bound states exist for certain parameter values.

Helicity is not conserved in the Lorentz-violating scenario.

Abstract

The effects of a Lorentz symmetry violating background vector on the Aharonov-Casher scattering in the nonrelativistic limit is considered. By using the self-adjoint extension method we found that there is an additional scattering for any value of the self-adjoint extension parameter and non-zero energy bound states for negative values of this parameter. Expressions for the energy bound states, phase-shift and the scattering matrix are explicitly determined in terms of the self-adjoint extension parameter. The expression obtained for the scattering amplitude reveals that the helicity is not conserved in this scenario.