Determination of the absolute energy scale of extensive air showers via radio emission: Systematic uncertainty of underlying first-principle calculations

Recently, the energy determination of extensive air showers using radio emission has been shown to be both precise and accurate. In particular, radio detection offers the opportunity for an independent measurement of the absolute energy scale of cosmic rays, since the radiation energy (the energy radiated in the form of radio signals) can be predicted using first-principle calculations involving no free parameters, and the measurement of radio waves is not subject to any significant absorption or scattering in the atmosphere. To quantify the uncertainty associated with such an approach, we collate the various contributions to the uncertainty, and we verify the consistency of radiation-energy calculations from microscopic simulation codes by comparing Monte Carlo simulations made with the two codes CoREAS and ZHAireS. We compare a large set of simulations with different primary energies and shower directions and observe differences in the radiation energy prediction for the 30 - 80 MHz band of 5.2 %. This corresponds to an uncertainty of 2.6 % for the determination of the absolute cosmic-ray energy scale. Our result has general validity and can be built upon directly by experimental efforts for the calibration of the cosmic-ray energy scale on the basis of radio emission measurements.
22 pages, 3 figures, accepted for publication in Astroparticle Physics