Observed Supersymmetry and Parity Doubling of Excited Hadrons from a Simple Spectrum-Generating Algebra

We find remarkable agreement with the observed excitations of hadrons with a simple three parameter mass relation of the SU(3) subgroup of the underlying U(15/30) graded Lie group. The baryons are the appropriate supersymmetric partners of the mesons. An interesting feature, which is a focus of current interest, is that the baryons and isobars show parity doubling. Significantly, the ground state baryons and mesons have no place in the fit, so that the parity doubling is indicated only when excitation energy is available. This has correspondence with the parity doubling seen in recent lattice calculations, when thermal excitation is present. The agreement with experiment is comparable to the semi-relativistic quark model which fits with many force parameters and where the observed parity doubling is accidental. The gross splitting of the levels is the same for the strange and the non-strange sectors, suggesting flavour independence.