Phenomenological Modeling of the $^{163}$Ho Calorimetric Electron Capture Spectrum from the HOLMES Experiment

TL;DR

This paper develops a detailed phenomenological model of the $^{163}$Ho electron capture spectrum from the HOLMES experiment, aiding neutrino mass measurements by accurately describing spectral features and backgrounds.

Contribution

It introduces a comprehensive phenomenological approach to model the $^{163}$Ho spectrum, including instrumental effects and spectral features, supporting future neutrino mass experiments.

Findings

Good agreement with ab initio calculations for main peaks and tails

Accurate modeling of the spectral endpoint region

Framework for systematic uncertainty analysis

Abstract

We present a comprehensive phenomenological analysis of the calorimetric electron capture (EC) decay spectrum of $^{163}$Ho as measured by the HOLMES experiment. Using high-statistics data, we unfold the instrumental energy resolution from the measured spectrum and model it as a sum of Breit-Wigner resonances and shake-off continua, providing a complete set of parameters for each component. Our approach enables the identification and tentative interpretation of all observed spectral features, including weak and overlapping structures, in terms of atomic de-excitation processes. We compare our phenomenological model with recent ab initio theoretical calculations, finding good agreement for both the main peaks and the spectral tails, despite the limitations of current theoretical and experimental precision. The model delivers an accurate description of the endpoint region, which is crucial for neutrino mass determination, and allows for a realistic treatment of backgrounds such as pile-up and tails of low-energy components. Furthermore, our decomposition facilitates the generation of Monte Carlo toy spectra for sensitivity studies and provides a framework for investigating systematic uncertainties related to solid-state and detector effects. This work establishes a robust foundation for future calorimetric neutrino mass experiments employing $^{163}$Ho, supporting both data analysis and experimental design.