Corrections to the Electron Spectrum of Hawking Radiation from Asteroid Mass Primordial Black Holes: Formalism and numerical evaluation of dissipative interactions

Primordial black holes (PBHs) within the mass range of 10¹⁷–10²² g are regarded as a promising dark matter candidate. In this mass range, Hawking radiation is a crucial constraint due to two main reasons: firstly, the Hawking temperatures are sufficiently high to facilitate the production of gamma rays and electron-positron pairs, and secondly, a larger number of PBHs are required to account for the observed dark matter density. In addition to constraints on PBHs arising from gamma ray photons produced by Hawking radiation, positrons originating from the PBHs Hawking radiation can contribute to the 511 keV annihilation line, which also sets constraints on the PBHs abundance. Therefore, to accurately model the signals from high-energy observations, rigorous QED calculations are needed for the spectrum of emitted electron-positron pairs from the Hawking radiation. Previously, our group has created an analytic expression for the first-order corrections to the Hawking radiation spectra from dissipative effects for Schwarzschild PBHs and demonstrated the numerical results for a range of black hole masses. This work delves into the electron spectrum resulting from Hawking radiation, applying a similar QED approach as in the previous study, to provide a comprehensive analysis both analytically and numerically.