Branching ratios for de-excitation processes of daughter nuclei following invisible dinucleon decays in ¹⁶O

Various theories beyond the standard model of particle physics predict the existence of baryon number violating processes resulting in nucleon decay. When occurring within an atomic nucleus, such a decay will be followed by secondary decays of the daughter nucleus unless its ground state is directly populated. In this paper, we estimate branching ratios for processes associated with dinucleon decays of the ¹⁶O nucleus. To this end, we use a simple shell model for the ground state of ¹⁶O. For decays from the configuration, which result in highly excited states in the daughter nucleus, we employ a statistical model with the Hauser-Feshbach theory. Our analysis indicates that the branching ratio for gamma-ray emission in the energy range between 5 and 9 MeV, which is relevant to low-threshold water Cherenkov experiments such as SNO+, is 4.53%, 35.7%, and 20.2% for the nn, pp, and pn decays in ¹⁶O, respectively. In particular, emission of 6.09 and 7.01 MeV gamma-rays from ¹⁴C, and 6.45 and 7.03 MeV gamma-rays from ¹⁴N, have branching ratios of as large as 10.9%, 20.1%, 7.73% and 8.90%, respectively.