Anapole Dark Matter Quantum Mechanics

TL;DR

This paper investigates the quantum mechanics of anapole dark matter by solving the Schrödinger-Pauli equation with delta-function potentials, revealing bound states and matching scattering cross sections with standard model predictions.

Contribution

It introduces a novel mathematical approach to analyze anapole dark matter using delta-function potentials in quantum mechanics, which has not been previously explored.

Findings

Bound states of anapole dark matter are demonstrated.

The scattering cross section matches standard model calculations.

A direct formulation and solution of the scattering problem are provided.

Abstract

The dynamics of an anapole seen as dark matter at low energies is studied by solving the Schr\"odinger-Pauli equation in a potential involving Dirac-delta and its derivatives in three-dimensions. This is an interesting mathematical problem that, as far as we know, has not been previously discussed. We show how bound states emerge in this approach and the scattering problem is formulated (and solved) directly. The total cross section is in full agreement with independent calculations in the standard model.