Analytical estimation of the signal to noise ratio efficiency in axion dark matter searches using a Savitzky-Golay filter

The signal to noise ratio efficiency ϵSNR in axion dark matter searches has been estimated using large-statistic simulation data reflecting the background information and the expected axion signal power obtained from a real experiment. This usually requires a lot of computing time even with the assistance of powerful computing resources. Employing a Savitzky-Golay filter for background subtraction, in this work, we estimated a fully analytical ϵSNR without relying on large-statistic simulation data, but only with an arbitrary axion mass and the relevant signal shape information. Hence, our work can provide ϵSNR using minimal computing time and resources prior to the acquisition of experimental data, without the detailed information that has to be obtained from real experiments. Axion haloscope searches have been observing the coincidence that the frequency independent scale factor ξ is approximately consistent with the ϵSNR. This was confirmed analytically in this work, when the window length of the Savitzky-Golay filter is reasonably wide enough, i.e., at least 5 times the signal window.