End-to-end reconstruction of ultra-high energy particle observables from radio detection of extensive air showers

Abstract The radio detection of very inclined air showers offers a promising avenue for studying ultra-high-energy cosmic rays (UHECRs) and neutrinos. Accurate reconstruction methods are essential for investigating the properties of primary particles. Recently, we developed an analytical $$\chi ^2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>χ</mml:mi> <mml:mn>2</mml:mn> </mml:msup> </mml:math> minimization method to reconstruct the electric field using three polarization components. The reconstruction yields no bias, with a 68% confidence interval of [ $$-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>-</mml:mo> </mml:math> 0.02, 0.02], and a standard deviation of 0.04 in the reconstruction of the peak envelope amplitude. In this paper, we perform a realistic reconstruction of the properties of primary particles using this reconstructed electric field. We employ a spherical wave model combined with an angular distribution function for arrival direction reconstruction, achieving an angular resolution of $$0.04^\circ $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>0</mml:mn> <mml:mo>.</mml:mo> <mml:msup> <mml:mn>04</mml:mn> <mml:mo>∘</mml:mo> </mml:msup> </mml:mrow> </mml:math> . We also present an energy reconstruction after accounting for the change in radio emission mechanisms in inclined air showers. We implement a new air-density correction factor, resulting in a 10% energy resolution. These results match the precision obtained when using simulated electric fields. These findings demonstrate the reliability and effectiveness of the recently developed electric field reconstruction methodology for its application on a typical event reconstruction chain. This ensures that the critical step of computing the electric field from the measure voltage at the antenna does not affect our ability to infer the properties of the primary particles, paving the way for future applications in radio experiments.