A Conjecture about Hadrons

S.R. Beane and M.J. Savage

We thought for a long time about the chiral structure of baryons, as advocated by Weinberg. This is an area that Beane has devoted a significant fraction of his time to. We were able to arrive at a conjecture about the structure of the hadron spectrum and their interactions [35] that has testable consequences. We conjecture that in the chiral limit of QCD the spectrum of hadrons is comprised of decoupled, reducible chiral multiplets. A simple rule is developed which identifies the chiral representations filled out by the ground-state hadrons. Our arguments are based on the algebraic structure of superconvergence relations derived by Weinberg from the high-energy behavior of pion-hadron scattering amplitudes. The large-$N_C$ construction, ala Dashen and Manohar appears to be a subset of the framework we arrived at. It follows directly from Weinbergs observations that axial matrix elements between states in the $I=J$ tower of hadrons are those of a spin-flavor SU(4) algebra for ANY value of $N_C$ (they are required to be degenerate).