Neutrino constraints on inelastic dark matter captured in the Sun

The flux of neutrinos from annihilation of gravitationally captured dark matter in the Sun has significant constraints from direct-detection experiments. However, these constraints are relaxed for inelastic dark matter as inelastic dark matter interactions generate less energetic nuclear recoils compared to elastic dark matter interactions. In this paper, we explore the possibility for large volume underground neutrino experiments to detect the neutrino flux from captured inelastic dark matter in the Sun. The neutrino spectrum has two components: a mono-energetic "spike" from pion and kaon decays at rest and a broad-spectrum "shoulder" from prompt primary meson decays. We focus on detecting the shoulder neutrinos from annihilation of hadrophilic inelastic dark matter with masses in the range 4-100 GeV and the mass splittings in up to 300 keV. We determine the event selection criterion for DUNE to identify GeV-scale muon neutrinos and anti-neutrinos originating from hadrophilic dark matter annihilation in the Sun, and forecast the sensitivity from contained events. We also map the current bounds from Super-Kamiokande and IceCube on elastic dark matter, as well as the projected limits from Hyper-Kamiokande, to the parameter space of inelastic dark matter. We find that there is a region of parameter space that these neutrino experiments are more sensitive to than the direct-detection experiments. For dark matter annihilation to heavy-quarks, the projected sensitivity of DUNE is weaker than current (future) Super (Hyper) Kamiokande experiments. However, for the light-quark channel, only the spike is observable and DUNE will be the most sensitive experiment.