Is the Koide formula correct?

The Koide formula is (m_e + m_mu + m_tau)/(sqrt(m_e) + sqrt(m_mu) + sqrt(m_tau))^2 = 2/3, where m_e, m_mu and m_tau are the masses of the electron, the muon and of the tau lepton respectively. (This is halfway between the lowest and the highest possible value of (a+b+c)/(sqrt(a)+sqrt(b)+sqrt(c))^2, namely 1/3 and 1 respectively.) Using current values of the masses as of the latest Review of Particle Physics by the Particle Data Group (, the left-hand side is 0.666 660 5 ± 0.000 006 7 (so, 0.9 standard deviations away from the Koide formula prediction).

Immediately resolves as NO if any future edition of the Review of Particle Physics before the market closing date lists a tau lepton mass more than 5 standard deviations away from the Koide formula prediction (namely 1776.969 MeV using current m_e and m_mu values, and unlikely to change enough to matter). Resolves as YES if the 2050 edition still lists a value within 2 standard deviations of the prediction. The closing date will be postponed if the 2050 RPP lists a value between 2 and 5 standard deviations of the prediction.

P.S.: I may resolve this YES early if some theory which predicts the Koide formula to be correct becomes such consensus among particle physicists that the RPP starts listing its prediction (or a weighted average including it, which would be pretty much the same) as the main value for the mass of the tau lepton.

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It has always baffled me that particle physicists don’t talk about this more often. It would be an outrageous coincidence.

I think it is but waiting to 2050 is a long time.

@ConnorDolan No theoretical reason, just believe in the power of numerology.