Algebras for flavor quantum numbers

It is shown that the flavor quantum numbers of the basic elementary particles, leptons and quarks, as well as hadrons (with quarks as constituents), can be described withSU(2)×U(1) type of algebras. To treat simultaneously leptons and quarks (hadrons), we introduce the grace quantum number,G, in place ofL (the total lepton quantum number) andB (the baryon quantum number). The formalism developed here requires the basic elementary particles to come in even numbers. For the case of four basic particles we have quantum numbers denoted asQ, X, andY and their duals denoted asQ, X, andY. For the four leptonsQ is the ordinary charge, while —Y andY areL (the muon lepton number) andL_e (the electron lepton number), respectively. For the four quarksQ is the ordinary charge,Y the ordinary hypercharge, whileX, a new quantum number, is simply theX charge, which, however, can be related to charmC.