However, the Japanese physicist Yukinari Sumino has proposed mechanisms to explain origins of the charged lepton spectrum as well as the Koide formula, e.g., by constructing an effective field theory with a new gauge symmetry that 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 using square roots for the masses.