Partial-wave Unitarity Research Articles

πN S11partial-wave amplitude near theηnproduction threshold

From an analysis of the ${\ensuremath{\pi}}^{\ensuremath{-}}$ backward differential cross-section data, which clearly shows a cusplike structure near the $\ensuremath{\eta}n$ threshold, we deduce, using partial-wave unitarity relations, the size and the orientation of the cusp. The cusp appears because of the strong coupling of the $\ensuremath{\eta}n$ channel to an ${N}^{\ensuremath{'}}$ resonance just above its threshold. Using the above information on the cusp, the $\ensuremath{\pi}N {S}_{11}$ partial-wave amplitude is fitted through the $\ensuremath{\eta}n$ threshold and the resonance. The effect of the size of the cusp, acting as a constraint, on the resonance parameters determined in the fit is emphasized. The fit also determines the phase of the $\ensuremath{\eta}n$ production amplitude at the $\ensuremath{\eta}n$ threshold, which then using the knowledge of the orientation of the cusp gives information on the phase of the elastic no-spin-flip amplitude at the $\ensuremath{\eta}n$ threshold. This information could be a useful constraint in $\ensuremath{\pi}N$ partial-wave analysis.

Unitarity and partial width forφ→3π

It is shown that absorptive contributions to g φ ρ π coming from φ → KK¯ → 3π may account for the observed magnitude of Γ (φ → 3π ). Two complementary calculations, one based on the Gell-Mann-Sharp-Wagner model and the other based on partial-wave unitarity, are presented. It is argued that ψ (3105) and ψ (3695) are especially narrow since similar absorptive corrections are absent.

Multiparticle partial-wave amplitudes and inelastic unitarity. IV. A scattering model with production and its characteristic operator function

Multiparticle partial-wave amplitudes and inelastic unitarity. IV. A scattering model with production and its characteristic operator function

Fixed poles, unitarity and duality. Application to proton-neutron charge exchange phenomenology

It is shown that in some cases the partial-wave unitarity relation, is not only compatible with the presence of particular fixed poles in the J plane, but also causes these fixed poles to propagate from one reaction to another. It is also shown that, in amplitudes with an exotic s- or u-channel and no pomeron in the t-channel, duality leads to the quality (up to a sign) of the right- and wrong-signature fixed pole residues. These two results together provide a good argument in favor of the presence of some right-signature fixed poles in hadronic reactions. In particular the J = 0 wrong-signature fixed pole found by Dolen, Horn and Schmid in π −p → π 0n induces through the above reasoning a right-signature fixed pole at the same value of J in pn → np. This fixed pole is a good candidate for the slow varying background currently considered to explain the forward spike in np → np, through a destructive interference with the t-channel pion. In this type of explanation, a definite distribution of the background (whatever its origin may be) among the various amplitudes is required in order to describe the present experimental data, and then a well defined shape is predicted for the forward spike, which should be carefully checked by future experiments.

Two-Body Unitarity and the Asymptotic Duality Series

The discontinuity of the Regge trajectory obtained recently from a duality series by Kikkawa, Sakita, and Virasoro is investigated. The trajectory is shown to possess all the thresholds corresponding to two-particle intermediate states, i.e., Regge recurrences or daughters. A correction to a linear trajectory is also shown to arise by requiring the Born term (the Veneziano amplitude) to be modified to satisfy two-body partial-wave unitarity near the leading pole in the $J$ plane. This discontinuity is evaluated up to the third two-particle threshold and found to be identical to that obtained from the duality series. Above higher thresholds, such agreement is dependent on the function used to ensure factorization at internal vertices in each term of the duality series.

One-particle-exchange model for low-energy scattering I. The one-channel problem

A crossing symmetrical, one-particle exchange type simple spectral representation is proposed for the low-energy scattering of spinless mesons. This representation together with the partial-wave unitarity allows for methods of computing the low-energy scattering amplitude. The iterational methods, which use the reaction matrix formalism, permit one to obtain for low energy either crossing symmetrical, analytical amplitudes, satisfying approximately the unitarity or unitary, analytic amplitudes which verify approximately the crossing symmetry. A special attention is given to the case of narrow resonances, when several usefull approximations are proposed. selfconsistency, bootstrap-type conditions are derived for the determination of the masses and coupling constants of stable and unstable particles and antibound states, by imposing unitarity to our crossing symmetrical amplitude near the corresponding singularity.