Self-consistent low-energy meson mass spectrum

In a typical hadron mass calculation the long-range (confining) part of the interaction between quarks (q) is assumed to be spin-independent. Any spin dependence is then attributed to short-range one-gluon exchange. This procedure tends to give an excessively small mass difference between pseudoscalar (P) and vector (V) mesons, at least if the quark-gluon coupling is fixed by other properties of the hadron spectrum. In the present paper we introduce an approach in which a large P-V mass difference arises naturally. A confining interaction does not have to be assumed a priori. The spectrum is generated by imposing duality on an infinite sum of ladder graphs without crossed quark lines; this ''planar bootstrap'' corresponds to the limit N/sub flavor/ → infinity (in quantum chromodynamics we would have to take N/sub color/ → infinity at the same time). By making a certain simple dynamical approximation we then derive an explicit infinitely rising exchange-degenerate leading Regge trajectory α (t) = S1 + S2 + L (ν/sub a/) for any given equal-mass-channel hadron + hadron → hadron + hadron process; S1 and S2 are external spins, L (ν/sub a/) approx. = -0.5 + 2α'ν/sub a/, and ν/sub a/ = s/sub a/ + (t - Σm/sub i/ 2)/2, where the m/sub i/ are the external masses and √s/sub a/ is the mass of an exchanged cluster a. By requiring the s/sub a/ to be as low as possible and imposing simultaneous consistency for complete sets of meson + meson → meson + meson processes, we are able to calculate the entire natural- and unnatural-parity low-energy leading-trajectory qq-bar mass spectrum in terms of m/sub rho/ and m/sub K/* alone