A novel approach for air shower profile reconstruction with dense radio antenna arrays using Information Field Theory

Reconstructing the longitudinal profile of extensive air showers, generated from the interaction of cosmic rays in the Earth's atmosphere, is crucial to understanding their mass composition, which in turn provides valuable insight on their possible sources of origin. Dense radio antenna arrays such as the LOw Frequency ARray (LOFAR) telescope as well as the upcoming Square Kilometre Array Observatory (SKAO) are ideal instruments to explore the potential of air shower profile reconstruction, as their high antenna density allows cosmic ray observations with unprecedented accuracy. However, current analysis approaches can only recover $X_\mathrm{max}$, the atmospheric depth at shower maximum, and heavily rely on computationally expensive simulations. As such, it is ever more crucial to develop new analysis approaches that can perform a full air shower profile reconstruction efficiently. In this work, we develop a novel framework to reconstruct the longitudinal profile of air showers using measurements from radio detectors with Information Field Theory (IFT), a state-of-the-art reconstruction framework based on Bayesian inference. Through IFT, we are able to exploit all available information in the signal (amplitude, phase, and pulse shape) at each antenna position simultaneously and explicitly utilise models that are motivated through our current understanding of air shower physics. We verify our framework on simulated datasets prepared for LOFAR, showcasing that we can not only reconstruct the air shower profile with uncertainties in each atmospheric depth bin but also recover the reconstructed trace at each antenna position. Our framework demonstrates that radio measurements with dense antenna layouts such as LOFAR and SKAO have the capability to go beyond reconstruction of $X_\mathrm{max}$ and will thus aid in our understanding of the mass composition of cosmic rays.