Pion System Research Articles

Padé approximants in strong interactions two-body pion and kaon systems

We construct the Pade approximants to theS-matrix starting from a formal perturbation series. Starting with a first-order «germ» we calculate the higher-order terms by repeatedly applying unitarity and crossing in the Mandelstam representation. The germ is chosen to be compatible with crossing and analyticity requirements, and to lead to a nonincreasing number of subtraction constants. We consider meson-meson scattering in which case the germs are simply constants. We have studied systems involving pions and kaons. In that case, there are only three parameters. Resonances and Regge trajectories have been computed. The seven lowest-lying two-body resonances (ρ, K*(890), ϕ, K*(1420), f0, f0′, A2) are obtained within a few percent of their actual masses. Also, the intercepts of the ρ and f0 trajectories agree very well with present estimates. Some degeneracies between channels with different quantum numbers appear and are discussed. The comparison with a pure π-π calculation shows promising improvement. We explain the further extensions of the model to compute meson states, and also baryon-meson and baryon-baryon amplitudes. In the course of this work, we have studied many mathematical and practical aspects of Pade approximants and their application to various fields.

Quantum number assignment for the A o2 meson

An enhancement is observed at 1310 MeV in the neutral 3 pion system in the reaction π + p → N ∗++π +π −π o . Evidence is presented for the assignment of spin-parity J P = 2 + and isospin = 1 for this resonance.

Properties of the neutral A-mesons

The neutral three pion system (π +π −π 0) from the reaction π ++n→p+ π ++ π −+ π 0 at 3.29 GeV/ c, is examined in the mass region of the A-mesons. It is shown that the enhancement at 1310 MeV can be identified with the neutral component of the A 2 meson. However, no compulsive evidence is found for the neutral component of the A 1 meson even though the unrestricted three-pion mass spectrum demonstrates an enhancement in the region from 900–1200 MeV. There is also an indication that the H-meson is present in this reaction.

Amplitude parity and radiative effects in pion systems

We assume that the electromagnetic couplings of strongly interacting systems can in principle be accounted for by a renormalizable theory. From this we prove, by an invariance argument, that real or virtual processes in which an odd number of pions are created or destroyed must proceed through virtual nucleon-antinucleon intermediate states. Examples are \gp{su0} \ar 2\gg,\gw \ar \gg,, ω→,γ, and η→3π. Some implications are discussed.

Possible relationships between the K-nucleon interactions and the hyperonic resonant states

We investigate the K−-proton scattering amplitudes representing by phenomenological parameters the longest-range forces due to the exchange of resonating pion systems between the\(\bar K\)-meson and the nucleon and between the pion and the hyperon. We discuss the possible relationships between the\(\bar K\)-nucleon interactions and the Y* resonant states.

Theory of strong interactions

Theory of strong interactions

Fit to dispersion relations of pion-nucleon scattering

Pion-nucleon scattering is described as the flipping and non-flipping of the spin and isotopic spin of the nucleon. These are expressed in terms of scattering amplitudes in pure isotopic spin states, and in turn are expressed in terms of phase shift. The basic assumptions needed for the dispersion theory to become more nearly a dynamical theory of the pion system are: causality, unitary condition, crossing theorem, high energy behavior of sigma ( omega ), and behavior of S( omega ), in the unphysical region, O < omega < mu . This dynamical theory must allow exact calculations of the four amplitudes of the pion system. Dispersion relations are utilized in the investigation of sign ambiguity of phase shifts, Fermi-Yang ambiguity of phase shifts, and the determination of the coupling constant f/sup 2/. The work of Puppi and Stanghellini in dispersion relations is briefly discussed. (B.O.G.)