Implications for the Standard Model and Cosmology
Neutrinos are massless in the Standard Model of particle physics by design. The Standard Model could easily be extended to include massive neutrinos via the Higgs mechanism--the phenomenon that physicists believe endows other particles with mass--but particle theorists are loath to do this. The Higgs-neutrino interaction strength would need to be a trillion times weaker than the equivalent Higgs-top quark coupling strength, which would be difficult to address naturally in a more fundamental theory. Instead, most theorists support an alternative formulation of the Higgs mechanism, called the "seesaw mechanism," which includes neutrino interactions with a very massive hypothetical particle. For the range of parameters indicated by Super-Kamiokande, that heavy mass would be within a few orders of magnitude of the scale where the strong and electroweak forces are believed to unify. Thus featherweight neutrinos might paradoxically shed light on ultraheavy dynamics.
Massive neutrinos also make some contribution to the "dark matter" of the Universe. By studying the effects of gravity on large scales, scientists have long known that visible matter makes up only a small fraction of the mass of the Universe, with the rest being some kind of matter that doesn't radiate light. Neutrinos with a mass difference as measured by Super-K could provide a significant part of that dark matter only if they have masses much larger than the tiny splitting between flavors.