Secular Equilibrium Assessment in a ${\mathrm{C}\mathrm{a}\mathrm{W}\mathrm{O}}_4$ Target Crystal from the Dark Matter Experiment CRESST using Bayesian Likelihood Normalisation

CRESST is a leading direct detection sub-${\mathrm{G}\mathrm{e}\mathrm{V}\mathrm{c}}^{-2}$ dark matter experiment. During its second phase, cryogenic bolometers were used to detect nuclear recoils off the ${\mathrm{C}\mathrm{a}\mathrm{W}\mathrm{O}}_4$ target crystal nuclei. The previously established electromagnetic background model relies on secular equilibrium (SE) assumptions. In this work, a validation of SE is attempted by comparing two likelihood-based normalisation results using a recently developed spectral template normalisation method based on Bayesian likelihood. We find deviations from SE; further investigations are necessary to determine their origin.