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Crucial questions about solar and supernova neutrinos remain unanswered.Super-Kamiokande has the exposure needed for progress, but detector backgroundsare a limiting factor. A leading component is the beta decays of isotopesproduced by cosmic-ray muons and their secondaries, which initiate nuclearspallation reactions. Cuts of events after and surrounding muon tracks reducethis spallation decay background by $\simeq 90\%$ (at a cost of $\simeq 20\%$deadtime), but its rate at 6--18 MeV is still dominant. A better way to cutthis background was suggested in a Super-Kamiokande paper [Bays {\it et al.},Phys.~Rev.~D {\bf 85}, 052007 (2012)] on a search for the diffuse supernovaneutrino background. They found that spallation decays above 16 MeV werepreceded near the same location by a peak in the apparent Cherenkov lightprofile from the muon; a more aggressive cut was applied to a limited sectionof the muon track, leading to decreased background without increased deadtime.We put their empirical discovery on a firm theoretical foundation. We show thatalmost all spallation decay isotopes are produced by muon-induced showers andthat these showers are rare enough and energetic enough to be identifiable.This is the first such demonstration for any detector. We detail how thephysics of showers explains the peak in the muon Cherenkov light profile andother Super-K observations. Our results provide a physical basis for practicalimprovements in background rejection that will benefit multiple studies. Forsolar neutrinos, in particular, it should be possible to dramatically reducebackgrounds at energies as low as 6 MeV.

Spallation Backgrounds in Super-Kamiokande Are Made in Muon-Induced Showers