Towards a Cosmic-Ray Energy Scale with the Auger Engineering Radio Array

Radio detection of cosmic-ray (CR) induced extensive air showers with digital antenna arrays is
a matured technique by now. At the Pierre Auger Observatory, the Auger Engineering Radio
Array (AERA) has been measuring air-shower signals in conjunction with the particle detectors
of the surface detector (SD) for over ten years. For an absolute determination of the CR energy
with the Auger baseline detectors, the shower size estimator from the SD is calibrated with the
energy scale of the fluorescence detector (FD). However, AERA has an independent access to the
energy scale through the reconstructed radio signals. The hybrid detectors at the Pierre Auger
Observatory offer the unique opportunity to compare the two independent energy scales. In this
contribution, we present our envisaged methodology for cross-checking the agreement between
the energy scales of the FD and AERA using hybrid SD-AERA shower data and simulations.
We show individual steps of our radio signal reconstruction and highlight the key ingredients for
calibrated energy measurements