The Homestake experiment was designed to detect solar neutrinos. In order to shield it from the background, it was set up in a deep underground mine. It was found that the only one third of expected neutrinos were detected, leading to the solar neutrino problem. What I wonder is why neutrinos created in the upper atmosphere by cosmic rays were not detected?
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The experiment detected more than just solar neutrinos, it also detected those produced by interactions with muons from cosmic rays, radioactive decays in the rocks surrounding the mine, internal radioactive contaminants in their tetracholorethylene fluid, and atmospheric argon decay production, but like any good experiment they controlled and subtracted all of these backgrounds.
The full paper is actually available for free here and in Section 6 of the paper (Nonsolar production of ${}^{37}$Ar) there is a full discussion of all of their background subtraction methods and calibration measurements. In particular, section 6.1 (Cosmic Rays) discusses how they subtracted the cosmic ray background from direct depth intensity measurements.
