Mass relations among family members of quarks and leptons

The various mass relations among members of quark and lepton families are given. Three mass relations for the charm, beauty, and top quark family members are given and three mass relations for the electron, muon, and tau lepton family members are presented. Quantum Choromodynamics (QCD), the theory of strong interactions, is unique among physical theories in its combination of logical closure and empirical success. In the asymptotic Bjorken limit, the study of the properties of strong interactions has proved to be one of the most creative ideas [1]. In Regge asymptotics, the number of partons increases rapidly due to QCD bremsstrahlung, relatively little work has been done. This limit of strong interactions, which we shall call the Regge limit, was studied intensively in the 60’s and indeed led eventually to string theory [2]. The rapid growth in the number of partons due to QCD bremsstrahlung in the leading logrithmic approximation is described by the BFKL equation [3]. There is a sense in which QCD is better than it has to be. It is not a complete theory of the world. Even within the standard model quarks have additional interactions, beyound QCD, that become significant – indeed, problematic – at short distances [4]. In the words of Professor Frank Wilczek, “I find QCD disturbing that it takes vast computer resources, careful limiting procedures, to simulate the mass and properties of a proton with decent accuracy. And for real time