Exchange degeneracy, flat total cross sections and the absence of exotic resonances

Abstract

Conditions imposed on Regge trajectories by requiring flat total cross sections for all reactions in ‘exotic’ channels are systematically investigated under very general conditions. For meson-meson scattering, a degenerate quartet of trajectories coupled to kaons and pions with quantum numbers of the ω, ϱ, f 0 and A 2 is required, plus an additional trajectory coupled only to kaons. Additional optional trajectories include ( ϱ′, f o′) pairs coupled only to pions, ( ω′, f o′) and ( ϱ′, A 2′) pairs coupled only to kaons and quartets coupled to both kaons and pions. A quark model with universal U(3) symmetry is shown to be the unique solution consistent with broken SU(3) symmetry and having flat exotic total cross-sections for meson-meson scattering. Other solutions also exist for meson-baryon and baryon-baryon scattering. For Δ Δ scattering, there is no solution; isospin considerations show that non-trivial saturation of finite-energy or superconvergent sum rules is impossible without exotic ( I ⩾ 2) contributions. The nature of the required exotic contributions in baryon-antibaryon scattering are discussed.