A method to define the energy threshold depending on noise level for rare event searches

Solid state detectors and low-temperature calorimeters are widely employed in rare event searches, because of their excellent sensitivity and consequent low energy threshold. A common procedure to establish the energy threshold is to define the trigger level at a fixed number of baseline standard deviations (sigmas) above the baseline level, typically 3σ or 5σ. This is not an ideal option when the threshold becomes a critical parameter for the detectors, requiring an optimised definition of the trigger. Recorded events with a small amplitude-to-noise ratio likely survive the selection criteria of the analysis chain contributing to the experiment background. We present a method to quantify the lowest trigger threshold achievable as a function of the acceptable amount of noise events triggered for the physics case under investigation. We then apply this novel method to existing experimental and simulated data to validate the model we presented.