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The flux of neutrinos from annihilation of gravitationally captured darkmatter in the Sun has significant constraints from direct-detectionexperiments. However, these constraints are relaxed for inelastic dark matteras inelastic dark matter interactions generate less energetic nuclear recoilscompared to elastic dark matter interactions. In this paper, we explore thepossibility for large volume underground neutrino experiments to detect theneutrino flux from captured inelastic dark matter in the Sun. The neutrinospectrum has two components: a mono-energetic "spike" from pion and kaon decaysat rest and a broad-spectrum "shoulder" from prompt primary meson decays. Wefocus on detecting the shoulder neutrinos from annihilation of hadrophilicinelastic dark matter with masses in the range 4-100 GeV and the masssplittings in up to 300 keV. We determine the event selection criterion forDUNE to identify GeV-scale muon neutrinos and anti-neutrinos originating fromhadrophilic dark matter annihilation in the Sun, and forecast the sensitivityfrom contained events. We also map the current bounds from Super-Kamiokande andIceCube on elastic dark matter, as well as the projected limits fromHyper-Kamiokande, to the parameter space of inelastic dark matter. We find thatthere is a region of parameter space that these neutrino experiments are moresensitive to than the direct-detection experiments. For dark matterannihilation to heavy-quarks, the projected sensitivity of DUNE is weaker thancurrent (future) Super (Hyper) Kamiokande experiments. However, for thelight-quark channel, only the spike is observable and DUNE will be the mostsensitive experiment.

Neutrino constraints on inelastic dark matter captured in the Sun