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The Koide formula is an unexplained empirical equation discovered by Yoshio Koide in 1981. It relates the masses of the three charged leptons so well that it predicted the mass of the tau. ==Formula== The Koide formula is: : It is clear that . The superior bound follows if we assume that the square roots can not be negative. By Cauchy-Schwarz can be interpreted as the squared cosine of the angle between the vector : and the vector : The mystery is in the physical value. The masses of the electron, muon, and tau are measured respectively as ''m''e = , ''m''μ = , and ''m''τ = , where the digits in parentheses are the uncertainties in the last figures. This gives ''Q'' = .〔Since the uncertainties in ''m''e and ''m''μ are much smaller than that in ''m''τ, the uncertainty in ''Q'' was calculated as .〕 Not only is this result odd in that three apparently random numbers should give a simple fraction, but also that ''Q'' is exactly halfway between the two extremes of (should the three masses be equal) and 1 (should one mass dominate). While the original formula appeared in the context of preon models, other ways have been found to produce it (both by Sumino and by Koide, see references below). As a whole, however, understanding remains incomplete. Similar matches have been found for quarks depending on running masses, and for triplets of quarks not of the same flavour.〔 〕〔 〕〔 〕 With alternating quarks, chaining Koide equations for consecutive triplets, it is possible to reach a result of 173.263947(6) GeV for the mass of the top quark.〔 〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Koide formula」の詳細全文を読む スポンサード リンク
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