Branching ratios for deexcitation processes of daughter nuclei following invisible dinucleon decays in $^{16}$O

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 unles s its ground state is directly populated. In this paper, we estimate branching ratios for processes associated with dinucleon decays of the $^{16}$O nucleus. To this end, we use a simple shell model for the ground state of $^{16}$O. For dinucleon decays from the 1$p_{1/2}$ and 1$p_{3/2}$ configurations in $^{16}$O, we take into account the pairing cor relation using the hole-hole Tamm-Dancoff approximation. For decays from the 1$s_{1/2}$ configuration, which result in highly excited states in the daughter nucleus, we employ a statistical model with the Hauser-Feschbach 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 2.42\%, 51.7\%, and 2.64\% for the $nn$, $pp$, and $pn$ decays in $^{16}$O, respectively. In particular, emission of 6.09~MeV gamma-ray from $^{14}$C originated from the diproton decay of $^{16}$O has a branchi ng ratio of as large as 48.6\%.