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

Abstract

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.

Figures (24)

• Figure 1: Schematic of the free proton decay, $\textrm{p} \to \textrm{e}^+ \pi^0$, in a water Cherenkov detector. The positron, as well as the two photons from the $\pi^{0}$ decay, generate electromagnetic cascades in water and emit radially distributed Cherenkov light.
• Figure 2: Momentum ($p_{\textrm{e}^+{\gamma\gamma}}$) vs. invariant mass ($M_{\textrm{e}^+{\gamma\gamma}}$) of the proton decay candidates. True events from different sources---free proton decay, bound proton decay in oxygen, and atmospheric neutrino interactions---are considered. All atmospheric neutrino events are simulated for interactions on a water target. The nuclear initial state is modeled with local Fermi gas (LFG). The box size corresponds to the normalized event population, shown on a linear scale. The treatment of nuclear effects in GiBUU is described in Sec. \ref{['sec:gibuu']}. Detector effects (det.) are modeled based on the Super-Kamiokande reconstruction performance as described in Sec. \ref{['sec:detector_modeling']} with secondary interactions (SIs) to be discussed in Sec. \ref{['sec:eventgen_atm']}. The signal region defined in the latest Super-Kamiokande analysis, which is also adopted in the present analysis (see C5 and C6 in Sec. \ref{['sec:signal_definition']}), is indicated by the black dotted rectangle. The concentration of events near $0.13MeV/\textit{c}^{2}$ in $M_{\textrm{e}^+{\gamma\gamma}}$ for atmospheric neutrinos originates from single neutral pion production processes.
• Figure 3: Probability density function (p.d.f.) of $\log_{10} P_\textrm{atmo}$, where $P_\textrm{atmo}$ denotes the probability classifier that is defined by Eq. (\ref{['eq:categoryprob']}). Underflow events are merged into the first bin.
• Figure 4: Ternary classification of proton decay candidates. Each point inside the triangle corresponds to a unique combination of the probability classifiers, $P_\textrm{free}$, $P_\textrm{bound}$, and $P_\textrm{atmo}$, defined by Eq. (\ref{['eq:categoryprob']}). As an example, the star marker indicates $P_\textrm{free} = 0.1$, $P_\textrm{bound} = 0.3$, and $P_\textrm{atmo} = 0.6$. The size of each box is proportional to the event population, shown on a linear scale. Individual plots for each event type are shown in Appendix \ref{['app:dec']}.
• Figure 5: Similar to Fig. \ref{['fig:3sample']}, but restricted to true bound proton decay events. In the legends, FM, SRC, and FSI denote Fermi motion, short-range correlation, and final-state interaction, respectively.