[Paper Review] High-Dimensional Bayesian Likelihood Normalisation for CRESST's Background Model

G. Angloher, S. Banik+60 more|arXiv (Cornell University)|Jul 19, 2023

Dark Matter and Cosmic PhenomenaPhysics and Astronomy3 citations

TL;DR

This paper introduces a high-dimensional Bayesian likelihood normalization method for CRESST’s electromagnetic background model, improving spectral fitting without assuming secular equilibrium. By fitting Geant4-simulated spectra to experimental data via Bayesian inference, the method explains up to 82.7% of the background in [1 keV, 40 keV], representing an 18.6% improvement over previous methods, with enhanced robustness through full covariance handling and reduced reliance on prior assumptions.

ABSTRACT

Using CaWO$_4$ crystals as cryogenic calorimeters, the CRESST experiment searches for nuclear recoils caused by the scattering of potential Dark Matter particles. A reliable identification of a potential signal crucially depends on an accurate background model. In this work we introduce an improved normalisation method for CRESST's model of the electromagnetic backgrounds. Spectral templates, based on Geant4 simulations, are normalised via a Bayesian likelihood fit to experimental background data. Contrary to our previous work, no assumption of partial secular equilibrium is required, which results in a more robust and versatile applicability. Furthermore, considering the correlation between all background components allows us to explain 82.7% of the experimental background within [1 keV, 40 keV], an improvement of 18.6% compared to our previous method.

Motivation & Objective

• To develop a more robust and accurate normalization method for CRESST’s electromagnetic background model in the context of low-energy dark matter searches.
• To eliminate the need for an explicit secular equilibrium assumption in background normalization, enhancing model flexibility and reliability.
• To improve spectral agreement between simulated and experimental background data across multiple isotopic components.
• To enable a more comprehensive and extendable background model by properly accounting for correlations between background components.

Proposed method

• A Bayesian likelihood framework is used to normalize Geant4-simulated spectral templates to experimental background data.
• The method employs a likelihood model that accounts for correlations between all background components through a full covariance matrix.
• Priors are assigned to contamination levels and nuisance parameters, with marginalization performed over nuisance parameters to improve robustness.
• The normalization is performed via maximum a posteriori estimation, allowing for systematic uncertainty propagation.
• The approach avoids explicit secular equilibrium assumptions by letting the data constrain relative activities through the likelihood function.
• The method is implemented using Markov Chain Monte Carlo (MCMC) sampling to explore the posterior distribution and assess uncertainties.

Experimental results

Research questions

• RQ1 Can a Bayesian likelihood normalization method improve spectral agreement between simulated and experimental background data without assuming secular equilibrium?
• RQ2 How does the inclusion of full covariance between background components affect the accuracy and robustness of the normalization?
• RQ3 To what extent can the new method explain the observed experimental background in the [1 keV, 40 keV] energy range compared to previous approaches?
• RQ4 How do the derived contamination activities compare across different background components, and what insights do they provide into residual radioactivity?

Key findings

• The new Bayesian likelihood normalization method explains up to 82.7% of the experimental background in the [1 keV, 40 keV] energy range, representing a maximum improvement of 18.6% over the previous Gaussian fitting method.
• The method reduces reliance on the secular equilibrium assumption, resulting in a more robust and versatile background model applicable across diverse detector modules.
• For the internal radiogenic background, the method yields consistent activity estimates with small uncertainties, e.g., 238U at 1110 ± 10 µBq/kg, and improves constraints on low-activity components like 214Bi and 210Po.
• The method successfully accounts for correlations between similar contaminants, such as those in the 238U and 235U decay chains, leading to more coherent and physically plausible activity estimates.
• For near-external and additional external radiogenic backgrounds, the method provides tighter constraints, with many components reduced to sub-µBq/kg levels, indicating effective suppression of high-background components.
• The method demonstrates improved spectral agreement, particularly in the 1–10 keV range, where electromagnetic and nuclear recoil discrimination degrades, enhancing sensitivity to potential dark matter signals.