Duality

Abstract

I n elementary particle physics, low energy interactions are characterized by resonance formation and high energy interactions by Regge pole exchanges : two quite different and apparently unrelated mechanisms. Duality is the hypothesis that they are in fact simply and quantitatively related. T h e present review describes the background and motivation for this hypothesis, and the different degrees of severity with which it can be formulated, together with some of its most notable predictions. Applications to the scattering amplitude are discussed in 0 3 ; the most significant results being exchange degeneracy for high energy scattering and the Regge interpolation of resonances at low energy. Section 4 describes applications to particle classification. Duality constraints tie together several SU(3) multiplets, like a higher symmetry scheme ; the exoticity prediction for the baryon-antibaryon channel is discussed in detail. Section 5 describes duality diagrams that provide a simple prescription for deriving most of the duality results. Section 6 is about the Veneziano model, a simple form of amplitude that satisfies duality explicitly; extensions to multiparticle scattering are also sketched. T h e final section discusses applications of duality to the inclusive reaction, which is a field of immense activity at present. The most significant results are again exchange degeneracy and the Regge interpolation of resonances-this time for the regions of high and low missing mass.

Nucleon-antinucleon interaction

“…The name "baryonium" denotes mesons that are preferentially coupled to baryon-antibaryon channels. The baryonium was predicted by Rosner [54], on the basis of duality arguments (for a review, see, e.g., [55]): schematically, a reaction a + b → c + d can be described either as a sum of s-channel resonances or t-channel exchanges; then, a coherent dynamics in the t-channel implies the existence of s-channel resonances; for NN, the meson-exchanges in the t-channel are dual of s-channel NN resonances. Some indications were found in the 70s, as reviewed by Montanet in [56], and these discoveries have motivated the construction of the low-energy facility LEAR at CERN.…”

Analysis Tools for Next-Generation Hadron Spectroscopy Experiments

“…The observation that the low-energy contribution to FESR when saturated by resonances reproduces the contribution from leading Reggeons at high energy led to the concept of duality [166,167]. According to this hypothesis directly produced resonances in low partial waves are dual to Reggeons, and residual, non-resonant backgrounds are dual to the Pomeron.…”

History of exotic meson (four-quark) and baryon (five-quark) states

“…Moreover when extrapolated to lower energies, they provide a good average description of the s-channel resonance contributions, which shows a duality between the Regge pole and resonance contributions. Thus the Regge pole and duality formalism provides a consistent and economical parametrisation of a host of soft two-body scattering processes [4]. Subsequently this has been extended to inclusive scattering cross-section,…”

“…which is related via optical theorem to a three-body forward elastic scattering amplitude A abc [5]. The Regge pole and duality formalism for this amplitude provides an effective description of inclusive scattering as well as resonance production in the channel X [4,6].…”