Sum-Rule Constraints on Baryon Regge Trajectories

The well-known MacDowell symmetry imposes conditions on the trajectory and residue functions of parity doublets of baryon Regge trajectories. A much stronger condition, degeneracy of these doublets, seems to be suggested by experiment. In order to build a consistent theory incorporating this parity degeneracy, trajectory residues must vanish at values of invariant (mass)² corresponding to unobserved states. A sum rule is derived assuming parity doubling which directly involves these zeros and which may therefore be used to check the consistency of the parity-doubling concept. A simple calculation for the Y₁* trajectory is consistent with this zero, although the approximations made would seem to make a definite conclusion impossible.