Proof of principle for template synthesis approach for the radio emission from vertical extensive air showers

The radio detection technique of cosmic ray air showers has gained renewed interest in the last two decades. While the radio experiments are very cost-effective to deploy, the Monte-Carlo simulations required to analyse the data are computationally expensive. Here we present a proof of concept for a novel way to synthesise the radio emission from extensive air showers in simulations. It is a hybrid approach which uses a single microscopic Monte-Carlo simulation, called the origin shower, to generate the radio emission from a target shower with a different longitudinal evolution, primary particle type and energy. The method employs semi-analytical relations which only depend on the shower parameters to transform the radio signals in the simulated antennas. We apply this method to vertical air showers with energies ranging from $10^{17}$ eV to $10^{19}$ eV and compare the results with CoREAS simulations in two frequency bands, namely the broad [20, 500] MHz band and a more narrow one at [30, 80] MHz. We gauge the synthesis quality using the maximal amplitude and energy fluence contained in the signal. We observe that the quality depends primarily on the difference in $X_{\text{max}}$ between the origin and target shower. After applying a linear bias correction, we find that for a shift in $X_{\text{max}}$ of less than 150 $\text{g}/\text{cm}^2$ , template synthesis has a bias of less than 2% and a scatter up to 6%, both in amplitude, on the broad frequency range. On the restricted [30, 80] MHz range the bias is similar, but the spread on amplitude drops down to 3%. These fluctuations are on the same level as the intrinsic scatter we observe in Monte-Carlo ensembles. We therefore surmise the observed scatter in amplitude to originate from intrinsic shower fluctuations we do not explicitly account for in template synthesis.