Understanding the impact of nuclear effects on proton decay searches with the GiBUU model

Proton decay searches in the next generation of water Cherenkov detectors, such as Hyper-Kamiokande, are expected to probe the $10^{35}$-year lifetime regime where atmospheric neutrino backgrounds and systematic uncertainties begin to play an increasingly important role. In this study, we employ the GiBUU framework and reevaluate the proton decay search sensitivity for the $\textrm{p}\rightarrow\textrm{e}^{+}π^{0}$ channel by incorporating a typical event reconstruction performance in water Cherenkov detectors. Using sophisticated models implemented in GiBUU -- most notably the mean-field potential and Boltzmann transport -- which have been benchmarked against accelerator neutrino scattering data, in particular pion production, we find that the resulting proton decay signal detection efficiency and atmospheric neutrino background rate are comparable to those previously evaluated for the current and near future water Cherenkov experiments using $\textit{ad hoc}$ nuclear models. In addition to pion final-state interactions, we evaluate the impact of differences in the Fermi momentum distribution of nucleons in the nucleus, as a source of systematic uncertainty, on the signal detection efficiency and the expected background event rate. We find that the uncertainty associated with pion final-state interactions is moderate, whereas the choice of Fermi momentum distribution can significantly affect the estimated atmospheric neutrino background rate and constitutes the dominant contribution. Our study provides an independent and complementary characterisation of nuclear effects on proton decay searches and helps to refine sensitivity estimates in the regime where systematic uncertainties become more relevant.