Pole Exchange Research Articles

Exchange structure of N, Δ backward peaks

The I u = 1 2 and I u = 3 2 cross sections and interference term in πN backward scattering are separated from data for p lab > 3 GeV/ c. The separated cross sections and recent 6 GeV/ c polarization data imply restrictions on the structure of N and Δ exchange amplitudes near the dip location in π +p backward scattering. The possibility of an amplitude analysis is discussed and the importance of polarization experiments in KN → Λπ stressed. The determinations of π N → Nπ I u = 1 2 and 3 2 contributions permit unambiguous studies of SU(3) for the exchanges in π N → Nπ and KN → Yπ reactions. Finally we show how isospin regularities observed in 180° scattering at low energies are implied by duality of N α, Δ δ Regge pole exchanges.

Application of continuous moment sum rules to ππ scattering

Continuous moment sum rules are applies to ππ scattering using phase shifts obtained from π-production data by OPE analysis. The calculation indicates that P, P′ and ϱ Regge pole exchanges offer an adequate and consistent descriotion of the available data. The fits suggest that P′-ϱ exchange degeneracy is violated, with P′ choosing no compensation and ϱ choosing nonsense.

Application of the double Regge pole exchange model to 8 GeV/ c π +p and 16 GeV/ c π -p interactions

The double Regge pole exchange model of Chan, Kajantie and Ranft is applied to reactions involving three uncorrelated final particles in 8 GeV/ c π +p and 16 GeV/ c π -p interactions. Restricting the analysis to the central region of the Dalitz plot we studied the exchange of various trajectory pairs. It is found that the exchange of meson trajectories is favoured against the exchange of the pomeron. The results are consistent with some well known characteristics of corresponding two body processes.

An Approach to Regge Behaviour and Duality Based on an Infinite Sum of One-Particle-Exchange Amplitudes

The implication of Regge asymptotic behaviour is studied on the basis of an infinite sum of one-particle-exchange (lOPE) amplitude, which provides a wide framework including vari­ ous versions of dual amplitudes. The imaginary part of Regge-behaved amplitude comes from the s-u crossing term of the convergent lOPE amplitude, accompanied with the diver­ gence of lOPE expression. Duality between t-poles and u- or s-singularities is necessarily contained in Regge behaviour. A general expression for the lOPE amplitude satisfying full Regge behaviour is persued and comments on related models are made in connection with our approach. Phenomenological aspects of various solutions are also discussed. The analysis of hadron scattering using finite energy sum rules has revealed the existence of an intimate connection between Regge pole exchanges and re­ sonant states in direct channel and has developed into Veneziano amplitude. This has created a problem of understanding of the physical implication of Regge pole exchanges. Regge pole exchange originally gave an exchange picture of composite par­ ticles at high energies. Its connection with the one-particle-exchange (OPE) mo­ del (which was proposed as an application to hadron reactions of the Sakata model) is quite interesting, especially when we consider its success in describ­ ing low energy scattering phenomena, such as nucleon-nucleon scattering. Among the interpretations of Regge behaviour so far proposed, that of an infinite sum of single exchanges of Regge recurrences is the most attractive one for a gener­ alization of OPE model. The purpose of the present paper is to give a general expression for the scattering amplitude based on the infinite sum of one-particle-exchange (lOPE) model/), 2 ) in which Regge behaviour is imposed at the asymptotic energy region. As an a posteriori result, the duality concept comes from the requirement of Regge behaviour in all the complex u plane except a positive real axis, where

Reggeized differential cross sections for fermion-exchange processes in the covariant formalism

A scheme developed by Scadron and Gault for calculating reggeized spin-averaged differential cross sections for boson exchange is extended, via s channel helicity vertices, to backward processes involving fermion Regge pole exchanges including those initiated by photons.

On two-particle correlations in high energy production experiments

One-particle and two-particle inclusive distributions are considered in the light of future production experiments at CERN Intersecting Storage Rings machine. We discuss the general properties of those models which are based on factorized approximations to the production amplitudes and are in agreement with some general hypotheses like the Feynman scaling law. First the role of phase space arguments is clarified and the importance of detecting correlations in high energy production experiments as an hint for understanding the underlying dynamics is emphasized. Then two peculiar (and, in a sense, complementary) kinds of correlation in two-particle inclusive distributions are examined: the one coming from multiperipheral dynamics with Lorentz pole exchanges, the other due to “direct channel” resonances. Some general properties of inclusive distributions are expressed in terms of quantities which are suitable for direct measurement.

Absorption Regge Cut in πNBackward Scattering

nN backward scattering data above 5 GeV /c are analyzed in terms of the baryon Regge pole exchange and accompanying Regge cut due to the strong absorption. The fit of the cross sections is reasonable. The role of the cut turns out to be very important: (1) The extrapolated magnitude of the L10 residue at a 4 =! is significantly larger than that without the cut. Ll0 residue with or without the wrong signature sense zero at a 4=t is equally probable. (2) Prediction of polarization in n+p-7prc+ is quite different from that without the cut. Moreover, large polarization in rc-p-7prc- is ecpected.

Veneziano Duality inSU(3)-Symmetric Meson-Baryon Scattering

An SU(3) symmetric Veneziano model for pseudoscalar meson-baryon scattering is con­ structed. The model incorporates the full content of the exchange degeneracy pattern of baryon spectrum. A hypothesis is made that the leading trajectories bootstrap themselves as long as it is consistent with the crossing relation, no ghosts on the leading trajectories and certain physical requirements. If we further adopt a subsidiary hypothesis on the SU (3) structures of the daughter states, the A amplitude (we use CGLN's notation) is completely determined to within a scale factor. Possible SU (3) splitting of the trajectories is considered. Theoretical prediction for threshold values of A amplitudes agrees quantitatively with ex­ perimental values (which are given in terms of the s-wave and p-wave scattering lengths) for rrN and KN scattering. It is shown that in the limit of quantized intercepts, the present model satisfies Adler's condition approximately. When applied to high-energy forward scat­ tering, the model predicts the t-dependence of the F/ D ratios of vector and tensor meson couplings. The theoretical value of the A amplitude associated with the nonstrange vector and tensor Regge pole exchange agrees with the empirical value within a factor of two. § I. Introduction In vanous dynamical schemes ever proposed to describe hadron scattering processes, exchanges play a primary role. In the early days, particle exchanges in the s-, t- and u-channels were treated separately and added up to give the whole amplitude. The results, however, are sensitive to the choice of types of couplings and the way of extrapolating resonance formula to the off-mass shell region. Even if the particle exchange is Reggeized, the t-dependence of residue functions remains undetermined. Furthermore, it has become evident from the study of finite energy sum rules applied to pion-nucleon scattering that the extrapolation of Regge pole terms down to the intermediate energy region gives the average of the contributions of the direct channel resonances. 1 ),Z) The problem of double counting would occur m general if one simply sums resonance terms in all three channels. Veneziano has proposed a new model as a solution to this problem. 3 ) The

Elastic scattering of a spin zero and a spin [formula omitted] particle at u = 0

We examine the elastic scattering of a scalar particle (a pion) off a spin 1 2 particle (a nucleon) at u = 0 in a model of continuous-spin (E 2 representation) pole exchange and compare the results with the usual Regge-pole models. An interesting result is that continuous-spin pole exchange at u = 0 gives an asymptotic polarization which, depending on the magnitude of the exchanged spin, is different than zero in contrast to the vanishing polarization expected in any single Regge-pole exchange model or when we exchange a u-channel twin-Fermion Regge-pole pair that satisfies Mac-Dowel's reflection symmetry. Indeed measurement of this polarization tells us about the value of the second Casimir operator κ 0 characteristic of the mass-zero representation under exchange. The asymptotic unpolarized cross section then gives us the residue function.

Analyticity constraints and residue functions of E 2 pole exchange

We consider the analyticity constraints of the spectral functions of the E 2 representation of unequal mass scattering amplitudes at light-like momentum transfers. Using these constraints we reduce the number of independent couplings, or residue functions, of the E 2 representation poles.

Particle Exchange, Regge-Pole Exchange and the Veneziano Amplitude forKNScattering

Based on the observation that the (t, u) -Veneziano terms can be expressed as an infinite sum of one-particle exchange contributions in the physical region, contrary to the (s, t) and (s, u) terms where the particle exchange picture is divergent, the validity of the particle exchange picture and the transcendental mechanism to the Regge pole exchange picture is examined in a KN Veneziano amplitude consisting of (t, u) terms only. At threshold, the contribution of meson exchanges with the lowest mass almost saturates the KN Veneziano amplitude. The hyperon exchange contributions should be discarded there, because of the duality between meson exchange contributions and hyperon exchange contributions. As energy increases, the meson towers with various spin states and degenerate mass begin to contribute one by one. Regge behaviour is obtained as a result of a detailed cancellation among the contributions of meson exchanges with various masses and spins. Here, Regge behaviour in a limited energy region is given by a finite sum of one-meson exchange terms. On the other hand, the hyperon exchange picture with finite terms does not approximate well the amplitude in the low energy region, even at threshold. These situations are understood through the study of the condition for an approximate truncation of infinite series of poles in the (t, u) -terms. The low energy interpolations of Regge asymptotic forms are studied, and the meson Regge pole exchange is also confirmed to give the gross features of the amplitude down to the threshold. The problem of double counting between the t- and u-Regge poles in low energy is noted.

Double Particle Exchange in Hadronic Reactions

We show that, contrary to present practice and belief, double-particle-exchange contributions to hadronic scattering amplitudes are not negligible. We introduce a hierarchy of exchange mechanisms: (i) Pomeranchon; (ii) single pole exchange (including pole-Pomeranchon cuts), (iii) double particle exchange, etc. The relative strength of any pair of consecutive terms in this hierarchy of amplitudes is of order $\ensuremath{\eta}={\ensuremath{\eta}}_{0}{\ensuremath{\nu}}^{\frac{\ensuremath{-}1}{2}}$, where ${\ensuremath{\eta}}_{0}\ensuremath{\sim}0.6$ Be${\mathrm{V}}^{1/2}$. At $\ensuremath{\nu}=5$ BeV, double-particle-exchange amplitudes may contribute to 25-50% of the cross section for inelastic processes and should not be ignored.

Observation of a Four-Pion Resonance at 1630 MeV inK+pInteractions at 10 GeV/c

We report the observation of a new four-pion resonance $\ensuremath{\rho}(1630)$ with mass 1632\ifmmode\pm\else\textpm\fi{}23 MeV and width ${110}_{\ensuremath{-}30}^{+40}$ MeV produced in the channel ${K}^{+}p\ensuremath{\rightarrow}{K}^{0}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}p$ and decaying predominantly to ${\ensuremath{\rho}}^{0,\ensuremath{-}}{\ensuremath{\pi}}^{0,+}{\ensuremath{\pi}}^{+}$ and $\ensuremath{\omega}{\ensuremath{\pi}}^{+}$. No decay is observed into ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{0}$, ${K}^{+}{\overline{K}}^{0}$, ${\ensuremath{\rho}}^{+}{\ensuremath{\rho}}^{0}$, or ${A}_{2}\ensuremath{\pi}$, so that association with the $g$ is precluded and the spin and parity probably lie in the unnatural series. The $\ensuremath{\rho}(1630)$ is associated with a $K\ensuremath{\rho}(1630)$ enhancement near threshold. This and other production characteristics are consistent with a double Regge pole exchange mechanism.

Particle Exchange, Regge Pole Exchange and the Generalized Potential in πNScattering

The generalized potentials for the πN system are formulated as functions of the (s, t, u) variables, in a form free from kinematical singularities, and their values in the resonance region are obtained from experimental phase shifts. The contributions from the N, Δ, ρ and ε(700) exchange as elementary particles reproduce qualitatively the generalized potentials near the threshold and in the forward direction, but they differ from the generalized potentials in the region of large momentum transfer and/or higher energy. The generalized potential can be well reproduced by multiplying the Regge-like damping factors to all the particle exchange terms and omitting the t-dependence of the residues of the Δ-exchange terms.

Fireball Model with Double Regge Pole Exchange for Multiple Meson Production in the Accelerator Energy Region

Fireball Model with Double Regge Pole Exchange for Multiple Meson Production in the Accelerator Energy Region

Complex Angular Momentum Theory in Particle Physics

AbstractA critical review of the techniques of complex angular momenta used at present in the Regge theory of strong interactions is presented. After discussing the kinematical singularities of helicity amplitudes, their crossing properties as well as the constraints they satisfy, the reggeization procedure for two‐body helicity amplitudes is reviewed in detail. The properties of the generalized Froissart‐Gribov continuation are investigated. The factorization properties of Regge pole contributions to a general two‐body scattering amplitude are studied and the various mechanisms producing the dip structure of differential cross‐sections are discussed. The complications of the reggeization for amplitudes describing unequal‐mass reactions at high energies in the forward direction are discussed and a survey of the status of “conspiracies” of singularities in the complex angular momentum plane is given. Both, the group theoretical and the analytical methods are discussed in treating the conspiracy problem. Finally, a review of the present situation is given regarding the influence of branch cuts in the complex angular momentum plane and their phenomenological consideration in various multiple scattering models. It is shown that the multiple scattering correction in the Glauber‐eikonal type of approach correspond to cuts in the angular momentum plane which represent absorptive corrections to the single Regge exchanges. It is clear from this discussion that cuts in the complex j‐plane, describing multi‐Regge pole exchanges, cannot be neglected.

On the Interpretation of Partial Wave Projection of Regge Pole Exchanges

On the Interpretation of Partial Wave Projection of Regge Pole Exchanges

Review of the Present Evidence for Multi-Regge Pole Processes

The present understanding of particle production processes in terms of the multi-Regge pole exchange model is reviewed from the theoretical and phenomenological point of view. It is concluded that the model discussed up to the present represents many different features of the data. Further tests of the model are discussed.

Models for High-Energy Processes

Recent developments in the concepts and models used to describe high-energy collisions of fundamental particles are reviewed. The areas of appreciable activity in research in high-energy physics are surveyed briefly and the general framework for the description of processes at high energies is outlined. There follows a sampling of recent experimental data designed to show the extent and detail of present-day experimental results. Recent applications of Regge pole models are reviewed with emphasis on the difficulties as well as the successes of models employing only Regge poles. The various multiple-scattering models are then discussed and correlated by means of the methods of Glauber. The connection of these models with amplitudes having branch cuts in the angular-momentum plane (Regge cuts) is described, as well as some comparisons with experiment. Finite energy sum rules as a means of relating the low-energy and high-energy domains are discussed in some detail. Next, the far-reaching concept of duality whereby the direct-channel resonances are (in some sense) the crossed-channel Regge exchanges is described, along with the related ideas of exchange degeneracy, the special role of the Pomeranchon Regge pole, and duality diagrams. An explicit realization of duality is achieved in the Veneziano model. This model is discussed in some detail for the relatively simple and interesting example of pion-pion scattering. Brief mention is also made of the extensions of the Veneziano model to the $n$-particle amplitude, attempts at unitarization, and various applications. The topic of multiparticle final states is covered relatively briefly with emphasis on the applications of double Regge pole exchange to three-body final states, the calculation of proton and pion energy and angular distributions in proton-proton collisions by means of the multi-Regge exchange model, and the generation of self-consistent Regge singularities with the multi-Regge exchange model and unitarity. The final section of the review concerns recent results on pion-pion scattering phase shifts and also $K\ensuremath{-}\ensuremath{\pi}$ phase shifts, and some remarks on theorems connecting decay correlations of resonances with the mechanism of production. The literature survey ended, with a few exceptions, in May 1969.

Polarization measurements at high energies

The problem of translating symmetry properties of the helicity amplitudes for two-body scattering into concise predictions for polarization experiments is discussed extensively. Particular attention is given to the asymptotic symmetries at high energies, which are characteristic for a Regge pole exchange model and which are associated with J-parity and G-parity exchange in a crossed channel. The idea is developed that the symmetry operator, as a matrix in the helicity space, “maps” one polarization measurement onto a superposition of other polarization measurements. Using this fact a systematic procedure is presented for separating different parts of the amplitudes which are even or odd under a symmetry. The procedure applies for any spins of the particles. To make the paper more complete and self-consistent a discussion of the density matrix formalism with particular emphasis on the choice of coordinate systems and phase conventions is included.