Sum-Rule Constraints on Baryon Regge Trajectories

Abstract

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 Yi* trajectory is consistent with this zero, although the approximations made would seem to make a definite conclusion impossible.

Parity Doubling in Particle Physics

“…Then one has according to classification (26): ǫ > 1 -superstrong form of parity doubling; ǫ = 1 -strong form; 1/2 < ǫ < 1 -moderate form; ǫ = 1/2 -weak form; 0 < ǫ < 1/2 -superweak form. In papers [144,169,170,173] the authors arrived at the superstrong form of parity doubling (interpreted as CSR at high energies).…”

“…This fact seemed to contradict the MacDowell symmetry and caused much discussions. Different ways out were proposed, for instance, vanishing residues for the corresponding parity partners [26], but such ad hoc solutions did not seem to be satisfactory [4]. Different authors tried to adjust the situation in the framework of representations of the Lorentz group or its extensions (see, e.g., [27][28][29][30][31][32]).…”