Inverse Problem of Cosmic-Ray Electron/Positron from Dark Matter

TL;DR

This paper presents an analytic method to reconstruct the source spectrum of cosmic-ray electrons and positrons originating from dark matter, using observed flux data, with applications to recent Fermi and HESS measurements.

Contribution

It introduces simple analytic formulas for solving the inverse problem of cosmic-ray electron/positron spectra from dark matter sources, enabling direct reconstruction from observational data.

Findings

Successfully applied formulas to Fermi and HESS data

Demonstrated feasibility of reconstructing dark matter source spectra

Provided a new analytical approach for cosmic-ray analysis

Abstract

We discuss the possibility of solving the inverse problem of the cosmic-ray electron/positron from decaying/annihilating dark matter, and show simple analytic formulae to reconstruct the source spectrum of the electron/positron from the observed flux. We also illustrate our approach by applying the obtained formula to the just released Fermi data as well as the new HESS data.