a new gauge symmetry causes the pole masses to exactly satisfy the relation. Koide has published his opinions concerning Sumino's model. François Goffinet's doctoral thesis gives a discussion on pole masses and how the Koide formula can be reformulated to avoid needing the square roots of masses. See also References Further reading (See the article's references links to "The lepton masses" and "Recent results from the MINOS experiment".) External links Wolfram Alpha, link solves for the predicted tau mass from the Koide formula. Leptons Unsolved problems in physics Empirical laws 1980s in science