Statistical research on determining sensitivity of neutrinoless double beta decays

TL;DR

This work addresses how to quantify sensitivity for neutrinoless double beta decay and compares counting within a RoI to full-spectrum fitting. It provides analytic derivations of discovery and exclusion sensitivities and validates them with toy Monte Carlo simulations. The main result is that method performance hinges on energy resolution and exposure, with fitting yielding tighter sensitivity at high exposure, while counting can be advantageous at lower exposure and/or better resolution. The study also highlights the informative role of background information outside the RoI and demonstrates that the approach generalizes across detector types, offering practical guidance for future experiments.

Abstract

The determination of experimental sensitivity is a key step in the search for neutrinoless double beta decay ($0νββ$), providing a quantitative benchmark for detector design. Two commonly used statistical approaches are the counting method, which estimates sensitivity from the number of events in a predefined region of interest, and the fitting method, which extracts the signal contribution by fitting the full energy spectrum. In this work, we investigate both discovery sensitivity and exclusion sensitivity within these two approaches. Through statistical derivation and simulation verification, we show that the relative performance of the methods depends on both energy resolution and exposure, while at higher exposures the fitting method consistently yields more stringent sensitivity. These results provide guidance for selecting the optimal statistical method in future $0νββ$ experiments.

Figures (8)

• Figure 1: Simple examples of calculating (a) discovery sensitivity and (b) exclusion sensitivity. The figures shows the test statistic distributions, which is defined differently in the two cases ($\Delta \chi^2(0)$ for discovery and $\Delta \chi^2(s_0)$ for exclusion); see Section \ref{['subsec:Counting']} for details. The blue curve shows the $\Delta \chi^2$ probability densities under the null hypothesis $H_0$, which is background-only for discovery sensitivity and signal+background for exclusion sensitivity. The red curve shows the $\Delta \chi^2$ probability densities under the alternative hypothesis $H_1$, which is signal+background for discovery sensitivity and background-only for exclusion sensitivity. The blue shaded area denotes the type-I error $\alpha$. The red shaded area denotes the type-II error $\beta$, which is fixed at 0.5 in both cases.
• Figure 2: The 3$\sigma$ discovery sensitivity analysis process of the fitting method. The figure is obtained from a liquid scintillator detector doped $^{130}$Te with an energy resolution of 3$\%$. The blue dashed line corresponds to $\Delta \chi^2_{\alpha}(S=0\mid S=0)$, and the black dots are $\Delta \chi^2_{\mathrm{median}}(S=0\mid s_0)$ at different $s_0$ values. The red curve shows a cubic spline interpolation of $\Delta \chi^2_{\mathrm{median}}(S=0\mid s_0)$. The green star represents the crossover point of $\Delta \chi^2_{\alpha}(S=0\mid S=0)$ and $\Delta \chi^2_{\mathrm{median}}(S=0\mid s_0)$, which indicates the discovery sensitivity $s_{\mathrm{disc}}$ result.
• Figure 3: The 90$\%$ C.L. exclusion sensitivity analysis process of the fitting method. The figure is obtained from a liquid scintillator detector doped $^{130}$Te with an energy resolution of 3$\%$. The blue dashed curve corresponds to $\Delta \chi^2_{\alpha}(S=s_0\mid s_0)$, and the black dots are $\Delta \chi^2_{\mathrm{median}}(S=s_0\mid S=0)$ at different $s_0$ values. The red curve shows a cubic spline interpolation of $\Delta \chi^2_{\mathrm{median}}(S=s_0\mid S=0)$. The green star represents the crossover point of $\Delta \chi^2_{\alpha}(S=s_0\mid s_0)$ and $\Delta \chi^2_{\mathrm{median}}(S=s_0\mid S=0)$, which indicates the exclusion sensitivity $s_{\mathrm{excl}}$ result.
• Figure 4: The (a) 3$\sigma$ discovery sensitivities and (b) 90$\%$ C.L. exclusion sensitivities of $0\nu\beta\beta$ half-life obtained with $^{130}$Te by two methods. The detector run time is set to one year, corresponding to a $^{130}$Te exposure of 1.71 ton-year. The energy resolution ranges from 0.1$\%$ to 7$\%$.
• Figure 5: Evolution of the $3\sigma$ discovery sensitivity of the $0\nu\beta\beta$ half-life in $^{130}$Te as a function of detector live time for an energy resolution of 3%. Red markers show the counting method (using an RoI optimized at this resolution) and blue markers show the spectrum-fitting method. This plot complements Fig. \ref{['fig:crossover']} by illustrating the ordering reversal with increasing exposure.