Self-consistent low-energy meson mass spectrum

Abstract

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 ..cap alpha.. (t) = S/sub 1/ + S/sub 2/ + L (..nu../sub a/) for any given equal-mass-channel hadron + hadron ..-->.. hadron + hadron process; S/sub 1/ and S/sub 2/ are external spins, L (..nu../sub a/) approx. = -0.5 + 2..cap alpha..'..nu../sub a/, and ..nu../sub a/more » = s/sub a/ + (t - ..sigma..m/sub i/ /sup 2/)/2, where the m/sub i/ are the external masses and ..sqrt..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.« less