Supersymmetry in the Quark-Diquark and the Baryon-Meson Systems

Abstract

A superalgebra extracted from the Jordan algebra of the 27 and 27 dim. representations of the group E₆ is shown to be relevant to the description of the quark-antidiquark system. A bilocal baryon-meson field is constructed from two quark-antiquark fields. In the local approximation the hadron field is shown to exhibit supersymmetry which is then extended to hadronic mother trajectories and inclusion of multiquark states. Solving the spin-free Hamiltonian with light quark masses we develop a new kind of special function theory generalizing all existing mathematical theories of confluent hypergeometric type. The solution produces extra “hidden” quantum numbers relevant for description of supersymmetry and for generating new mass formulas.