Novel approach to assess the impact of the Fano factor on the sensitivity of low-mass dark matter experiments

Abstract

As first suggested by U. Fano in the 1940s, the statistical fluctuation of the number of pairs produced in an ionizing interaction is known to be sub-Poissonian. The dispersion is reduced by the so-called "Fano factor," which empirically encapsulates the correlations in the process of ionization. In modeling the energy response of an ionization measurement device, the effect of the Fano factor is commonly folded into the overall energy resolution. While such an approximate treatment is appropriate when a significant number of ionization pairs are expected to be produced, the Fano factor needs to be accounted for directly at the level of pair creation when only a few are expected. To do so, one needs a discrete probability distribution of the number of pairs created N with independent control of both the expectation µ and Fano factor F . Although no distribution P (N |µ, F ) with this convenient form exists, we propose the use of the COM-Poisson distribution together with strategies for utilizing it to effectively fulfill this need. We then use this distribution to assess the impact that the Fano factor may have on the sensitivity of low-mass WIMP search experiments.

Ionization yield in silicon for eV-scale electron-recoil processes

“…In contrast to the treatment in Ref. [44], in which the Fano distribution is used to model charge yield down to the ionization threshold, we find that both eh and F are inadequate to accurately capture low-energy ionization yield. This is in large part due to the solid-state nature of Si; for processes close to the gap, where the phase space is restricted by the band-structure, we observe non-trivial departures from this simple two-parameter model.…”

Precision laser-based measurements of the single electron response of spherical proportional counters for the NEWS-G light dark matter search experiment

“…where P com (N |µ(E d ), F (E d )) is derived from the COM-Poisson distribution [21,22], a discrete distribution function well-suited to model ionization statistics as it allows for an independent control -and hence fitting - of the mean value µ(E d ) = E d /W (E d ) and Fano factor F (E d ) [23]. The energy scale of the 37 Ar spectrum shown in Fig.…”

“…Furthermore, these are evidence of the excellent agreement between our model and the energy response of the detector. It is also worth emphasizing that this study allowed for an assessment of the COM-Poisson distribution as a model for primary ionization statistics [23].…”

The search for Light Dark Matter with NEWS-G

“…This allows for confirmation of the linearity of the detector energy response over this energy regime, and modelling of the detector response in energy and risetime (a PSD variable proportional to radii). To fit this data, the detector's energy response was modeled using the COM-Poisson distribution for primary ionization [18], and the Polya distribution for avalanche ionization [14]. Electronegative contaminants in the gas (such as O 2 and H 2 O) preferentially reduce the amplitude of events originating farther from the sensor (at higher risetimes), which is modeled using binomial statistics for the number of un-trapped primary electrons, with the survival probability varying linearly with risetime.…”