Koide Formula

The Koide formula is an unexplained empirical relationship in particle physics, proposed by Yoshio Koide in 1981, connecting the masses of the three charged leptons: the electron, the muon and the tau. It defines a dimensionless quantity Q, equal to the sum of the three lepton masses divided by the square of the sum of their square roots, which comes out to almost exactly two thirds when calculated from the measured lepton masses, a value confirmed to close precision by measurements as of 2024. The value two thirds sits at a striking midpoint between the two theoretical extremes the formula could take, one third if all three masses were equal and one if a single mass dominated, which has led physicists such as Robert Foot to interpret it geometrically as the squared cosine of roughly a 45 degree angle between certain mass related vectors. Although extensions of the same pattern to quarks and other particles show similar regularities, no accepted theory in current physics explains why the Koide formula holds, and it remains an open puzzle. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/