A Statistical Analysis of Background Contributions for Experiments Measuring Neutrinoless Double Beta Decay

Large-scale experiments are underway to observe the neutrinoless double-beta decay of $^{\mathrm{76}}$Ge with a respective energy of 2039.0-keV. A 2040.7-keV $\gamma $ ray from the 69$^{\mathrm{th}}$ excited state of $^{\mathrm{76}}$Ge could create false signals in the $^{\mathrm{76}}$Ge-enriched detectors used in these experiments. It is therefore crucial to estimate the background contribution of this 2040.7-keV $\gamma $-line. A recent experiment performed at the National Superconducting Cyclotron Laboratory was able to populate the energy state of interest and observe the 2040.7-keV $\gamma $-line. The present work focuses on the statistical analysis of this experiment in order to determine the branching ratio of the 2040.7-keV $\gamma $ ray from the 69$^{\mathrm{th}}$ excited state of $^{\mathrm{76}}$Ge. This branching ratio is to be applied to experiments attempting to observe 0$\nu \beta \beta $ events. Successful observations of 0$\nu \beta \beta $ events would be the best way to obtain the mass of the neutrino and determine its nature as a Dirac or Majorana fermion.