Applying template synthesis to the radio emission from air showers with generic geometries

Studying high-energy cosmic-ray air showers through the radio emission produced by their secondary particles is a well-established technique. However, due to the increasing size and density of the radio arrays, analyses are running into computational limits, as these rely on Monte Carlo simulations to model the emission. To address this, we have been developing template synthesis, a new approach to simulate the radio emission from air showers. With template synthesis, we use semi-analytical expressions to describe how the radio emission from an air shower depends on the shower age and the position of the antenna with respect to the shower. These expressions are extracted from a set of microscopic simulations, thus benefiting from their accuracy. Once obtained, we can use these relations to synthesise the emission from an air shower with any longitudinal profile, by using a single Monte Carlo simulation as an input. Previously we have demonstrated that this hybrid approach can synthesise the radio emission from air showers and agrees with results from microscopic simulations within 10\%. The method was however limited to a specific geometry. Here we present our first step towards generalising template synthesis across geometries. We found a set of scaling relations which correct for the shower geometry as well as the viewing angle under which the radiation is observed. This allows us to reformulate the semi-analytical relations in a way that does not longer depend on the geometry, significantly reducing the number of parameters that need to be fitted. We apply these scaling relations to a simulation library of CORSIKA showers with a zenith angle of 50 degrees, with primary energies between $10^{17} \; \text{eV}$ and $10^{19} \; \text{eV}$. We then extract the semi-analytical expressions required for template synthesis, and use them to synthesise the emission from air showers with lower zenith angles. We investigate the accuracy by comparing both to microscopic simulations as well as the single geometry version of template synthesis.