 For this reason, many physicists regard the relation as "numerology".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 in which a new gauge symmetry causes the pole masses to exactly satisfy the relation.François Goffinet's doctoral thesis gives a discussion on pole masses and how the Koide formula can be reformulated without taking the square roots of masses.