Regge Exchange Research Articles

Measurement of the Coherent Dissociation Reactionp+A→pπ+π−+A

The coherent reaction $p+A\ensuremath{\rightarrow}p{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}+A$ was measured at 22.5 and 15.3 GeV in order to study diffraction dissociation free from normal Regge exchange background. Glauber-model analysis yields a $\mathrm{pN}\ensuremath{\rightarrow}{N}^{*}N$ signal in good agreement with $\mathrm{pp}$ scattering. Through the model it is found that ${\ensuremath{\sigma}}_{T}({N}^{*}N)$ decreases rapidly from 36\ifmmode\pm\else\textpm\fi{}3 mb for $M({N}^{*})=1.4$ GeV to 18\ifmmode\pm\else\textpm\fi{}4 mb for $M>~1.7$ GeV and that $\ensuremath{\alpha}({N}^{*}N)\ensuremath{\sim}\ensuremath{-}0.5$ for $M<1.7$ GeV.

SU(4) × SU(4) analysis of high energy cross-sections and photoproduction

Formulas for high energy total cross-sections are obtained using the method of Cabibbo, Horwitz and Ne'eman to compute the vector and tensor Regge exchange couplings in the framework of SU(4) × Su(4). Inequalities and identities between cross-sections found for SU(3) × SU(3) remain valid and some new relations are obtained which involve charmed particles. A fit to high energy total cross-sections is constructed and, with the assumption of vector dominance, this fit is consistent with photoproduction data above threshold.

Transition Feature between Large and Small Momentum Transfer Regions

Hadron reactions with small momentum transfers are well described by the Regge exchange model or the Regge-resonance dual model. The Regge exchange amplitude, however, is too small in the large momentum transfer region to repro­ duce the cross sections. It leads to an exponentially decreasing amplitude of s at fixed 8(c.m.s. scattering angle), while the cross sections behave as a power form of s.n The power seems to be related to the total number of constituents 21 composing the hadrons which participate in the reaction in the large momentum transfer region. The amplitude which shows the fixed angle scaling has quite different structure compared with the dual one. It will be very important to make it clear where and how the change of the s-dependence from the Regge-resonance dual form to the fixed angle scaling form occurs. In this paper, we will investigate the problem and suggest the following: i) There is a critical value of four-momentum square t, (u,) when the amplitude contains the t-(u-)channel exchange of the Regge trajectory a(t) (a(u)). ii) The value oft, (u,) is determined from the condition that a(t) (a(u)) is equal to a value given by the numbers of the constituent participating in the reaction. iii) In order to study the critical value t, (u,), it is convenient to see the s-depend­ ence of the cross section along fixed 6. The change of the s-dependence from the Regge-resonance dual form to the fixed angle scaling form is expected to occur nearly at the energy s (6) determined by t, or u,. Especially, a rather small value of s is predicted from t, and u, at e~ 180° and e~oo respectively. Actually we

A unitary calculation of particle exchange in KN scattering and ‘composite’ resonances

The Blankenbecler-Sugar equation is solved for kaon-nucleon elastic scattering; the driving term is taken as a sum of Regge exchange amplitudes. The coupling constants of the exchanges, as previously determined from high partial-wave analyses, give an essentially zero-parameter investigation. Of the ten predicted partial-wave amplitudes nine are in agreement with experiment, in sign and magnitude, over the whole elastic region. From our calculation it is not clear whether or not the P 01 wave is resonant; such a resonance (Z 0 ∗) is a distinct possibility. However, its size and sharpness are sensitive to small charges in our parameters. With exact SU(3) symmetry the Z 0 ∗ must belong to a 10 multiplet. It is tentatively suggested that the N(1470) may be a partner to the Z 0 ∗, having large components of this multiplet.

Inclusive electroproduction of hadrons

The inclusive processes ep → e′p′X and ep → e′π±X are studied on the basis of Regge exchange mechanisms. Some implications for pion structure functions are discussed.

ω Production in the reaction π−p → π+π−π0n at 8 and 12 GeV/c

The reaction π −p → ωn has been studied at 8 and 12 GeV/ c incident momenta with the CERN Omega spectrometer using a neutron time of flight trigger. The differential cross sections and the ω-decay density matrix elements are presented as functions of the momentum transfer squared − t in the range of 0.02 to 0.80 GeV 2. The data are used to evaluate the intercept and slope of both the natural and unnatural parity exchange trajectories. Regge exchange amplitude factorisation tests involving the reaction πN → ωN are investigated.

The polarised beam asymmetry in photoproduction of eta mesons from protons at 2.5 GeV and 3.0 GeV

Measurements of the polarised beam asymmetry parameter Σ for eta photoproduction from protons, have been carried out at incident energies of 2.5 GeV and 3.0 GeV, and for various t-values between −0.2 (GeV/c) 2 and −1.2 (GeV/c) 2. The values of Σ are close to +1 for values of | t| less than 0.7 (GeV/c) 2, showing that there can be little contribution from unnatural parity exchange in any Regge exchange model of the process, in disagreement with present theories. Differential cross sections for the process werre also measured, and are consistent with those from other experiments.

Regge exchange and absorption in the inclusive reactionπ−p→π0X

We predict the cross section for the inclusive process ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}+\mathrm{anything}$ in the region ${x}_{{\ensuremath{\pi}}^{0}}\ensuremath{\gtrsim}0.7$, using a triple-Regge model with absorption corrections. Absorption is calculated by a generalization of Regge-cut theory in two-body reactions, and is consistent with data on ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$. We conclude that measurements of ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}X$ at laboratory energies > 100 GeV will yield important new information on the strength of absorptive effects in strong interactions. In particular, we predict that the effective $\ensuremath{\rho}$ trajectory in ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}X$ will lie higher than in ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ by \ensuremath{\sim}0.3, for $\ensuremath{-}t\ensuremath{\gtrsim}0.8$ Ge${\mathrm{V}}^{2}$ and $x\ensuremath{\sim}1$. The cross section will show no dip structure at $\ensuremath{-}t\ensuremath{\simeq}0.6$ Ge${\mathrm{V}}^{2}$ or elsewhere, contrary to the predictions of models with nonsense-wrong signature zeros.

An optical interpretation of polarization parameters

We stress the simplicity of the language of optics in discussing experiments with polarized beams and/or polarized targets, and present a semi-classical model which permits simple calculations of polarization and spin-correlation parameters for general spins. The assumptions that nucleons interact primarily diffractively, and that the only spin dependence of the interaction arises from a weak spin-orbit force, leads us to a simple model for all the nucleon polarization and spin-correlation parameters which is consistent with the available data. A number of predictions are given for future experiments, and possible test of the model are noted. The relation between the s-channel optical language and the t-channel exchange language is also discussed. It is shown that several features of the Regge exchange picture (suppression of unnatural parity exchanges, approximate factorization of the amplitude, and the presence of weak cuts) are natural consequences of the model.

Study of the p π− system produced in the reaction K +n→K +π−p at 8.25 GeV/ c and comparison with data at 4.6 and 12 GeV/ c

The fragmentation of the neutron into p π − induced by incident K + of 8.25 GeV/ c is studied using data from the CERN 2 m deuterium bubble chamber and compared with data at 4.6 and 12 GeV/ c. The p π − low-mass enhancement below 1.85 GeV is analyzed and the major part exhibits the properties expected for diffraction dissociation. The presence of resonances is discussed. The data are fairly well represented by a double Regge exchange model involving pion and pomeron exchanges. The violation of the s-channel and t-channel helicity conservation is observed and compared to the s-channel description of Humble.

Spin structure of compton scattering at high energies

In preceding papers (L2) a model for the diffractive photon-induced processes a t high energies was developed and an analysis of the most important reactions was carried out. The description was based on a multiehannel impact-parameter formalism which provided a unified picture of the elastic, i.e. Compton process, as well as the inelastic diffraction dissociation channel (like vector-meson photoproduction) at high energies. The analysis of Compton scattering was carried throughout neglecting spin because of lack of appropriate experimental information concerning the helieity structure of the reaction (3). However, since in the case of vector-meson photoproduction there is an important amount of knowledge on the density matrix elements of the decaying vector meson (especially for the p0) and, furthermore, one possesses a lot of information from experiments with polarized photon beams, the model was enlarged in order to incorporate these facts into the actual analysis of data. A specific feature of the model is the inherent possibility of existence in the asymptotic amplitude of a helicity-fiip component which is absent in the usual descriptions of diffraction. Moreover, this Pomeranchuk flip amplitude was supposed to completely dominate the flip components coming from secondary Regge exchanges and, indeed, this assumption was subsequently tested in the analysis of ~0 photoproduction, where, as is well known, the Pomeranchuk contr ibution is the only exchange present in the production mechanism (4). In fact, a better fit to the data required a substantial amount of helicityflip present at the nucleonic vertex. Also in po photoproduction the best agreement with the differential-cross-section data was achieved imposing a flipping pomeron at the nucleon vertex, whose coupling strength turned out to be of the same order as in ~o photoproduetion. The lack of experiments with polarized targets does not allow us to directly check the actual existence of such a term since this amplitude cannot be separated with present experiments from the nonflip one. Owing to the fact that great progress has been recently made in obtaining highly polarized ((70--80)%) targets,

On polarization effects in high-energy vector-meson photoproduction

In a recent paper (1) an analysis of vcetor-meson photoproduetion at high energies was presented in terms of a multiehannel impact-parameter formalism which provided a unified description of all diffractive photon-induced reactions. I t was argued there that a helieity-flip component of the asymptotic part of the amplitude, i.e. the pomeron, may well be present in the proposed unitarized multiple-scattering picture of diffraction and it was indeed subsequently found in the analysis of 7 ~ and p~ data. As is well known, ~0 photoproduction is an ideal testing ground for the properties of the Pomeranchuk contribution since no other Regge exchanges are supposed to contr ibute there (2). I t was shown that for the c~~ amplitude (and for the i~ ~ amplitude) there is a substantial amount of helicity flip at the proton vertex (*). Of course, this model-dependent result has to be confirmed by direct measurement of the relevant density matrix elements. Unfortunately, the present data cannot provide information about this point because of lack of appropriate data on polarization experiments. One is therefore forced to use the available differential cross-section data in order to get information on this particular helicity amplitude with flip at the nucleon-~nucleon transition. I t seems therefore worth-while to discuss the possible experiments with polarized beams and/or polarized target which could directly test our rather indirect finding of a violation of SCIIC (s-channel helicity conservation) (a) for the recoiling proton in ~o (po) photoproduction. In view of the recent progress in preparing polarized targets possessing polarizations up to (70--80)~o it is feasible to carry out such experiments in the near future. Let us represent the state of polarization of the incoming nucleon and of the photon by the spin density matrices (4.5)

ππ crossing sum rules and high-energy amplitudes

Physical region ππ crossing sum rules are systematically derived, several new rules being obtained. In conjunction with finite energy sum rules they are applied to the results of recent ππ phase-shift analyses. It is found not possible to resolve the ambiguities in the phase-shift solutions. We examine the imaginary part of the rho Regge exchange amplitude and find this to have a zero near t = −0.4 GeV 2. We determine separately the structure of the imaginary part of the pomeron and of the f exchange amplitude; whilst there is insufficient information to carry out this separation uniquely, rho-f-exchange degeneracy is found to be broken. The greatest uncertainties come from the poorly known low-energy isospin-two amplitudes.

Exchange-component analysis of neutral pseudoscalar meson photoproduction

π 0 and η photoproduction data in the region of 4 GeV are decomposed into t-channel exchange components of definite isospin and parity. The latter are discussed in terms of Regge exchange models and compared to vector-meson dominance related processes. The isospin-one natural parity-exchange component is smooth and structureless. The dominant unatural parity exchange in π 0 photoproduction has isospin zero. As in π ± photoproduction the ratio of natural to unnatural parity exchange is found to be larger than the vector-dominance expectation. Complementary information from a recent spin decomposition of γp → π 0p gives further insight into the SU (3) properties of the exchanges. We predict unmeasured quantities and stress, in particular, the importance of studying γn → π 0n with polarised photons.

Spin-parity analysis of ππ systems produced in pp → pp π+π− and the question of double pomeron exchange

Data on the reaction pp π + π − in the momentum range 2–25 GeV/ c are analysed for features indicating double pomeron exchange (DPE). The moments of the ππ angular distributions are examined in the quasi three-body frame of reference which is analogous to the s-channel helicity frame for quasi two-body processes. Inequality constraints on the moments are shown to suggest the presence of both S and P waves of the ππ system in the relevant pp(ππ) kinematic region, arguing against the dominance of DPE. The energy dependence of cross sections for selected events in different ranges of ππ mass is shown to be in accord with the predictions of a double Regge exchange model incorporating pomeron-reggeon exchange and not DPE. Both the cross sections and the ππ angular distributions are also examined in the light of a reggeized one-pion exchange model.

Cluster Mass Distribution in Multiperipheral Cluster Emission Model

It is shown that dynamics of the multiperipheral cluster em1ss1on model uniquely determines the cluster mass (M) distribution. In particular, the mass distribution is dynamically suppressed by the output factor (M')-Po(fi,>g'(p.), p.: final hadron mass) in addition to a possible decreasing effect due to the input factors of the cluster emission (g'(M)) and decay (JJ(M)) vertices. A dynamical equation for solving fio is derived. Some quantitative estimates are also presented. Since proposed in 1962 by ABFST,l> a multiperipheral model has been a continuing laboratory of physical interest when the multiple production of hadrons is studied. Incorporation of Regge exchanges 2>·8> along the multiperipheral chain makes the model more suitable for analyzing a high-energy multiparticle production. Quite recently, an idea that hadrons are produced in clusters 4> has provided a popular interpretation of several features of multiparticle production data. In particular, the postulates of (A) independent emission of clusters along th.e multiperipheral chain and (B) their isotropic decay via a Gaussian distribution in rapidity give a facile imitation of data on two-particle inclusive rapidity cor­ relations in the central regioit. 6> It is not clear whether clusters have any intrinsic dynamical significance (e.g., generalized resonances) or whether they are primarily of phenomenological convenience. Experimentally we still have to wajt for eve~t-by-event data on an exclusive rapidity distribution in order to observe directly the cluster formation and its detailed properties. On the other hand, the observed high multiplicity in rapidity space suggests that final hadrons should be produced more preferably through cluster (or resonance) formation along the multiperipheral chain to through factorized Regge exchanges between the final hadrons. It is a reasonable guess that due to a small average spacing of .dy~0.3 to 0.5 between the final hadrons, there will be a strong correlation among the produced particles, which is better represented by the above postulates (A) and (B). The purpose of this paper is to show that the postulates (A) and (B) just mentioned uniquely determine the mass distribution of produced clusters which is usually assumed to take a certain form as a third input. What is important, the predicted mass distribution can be checked experimentally when the exclusive

Shrinkage, complex poles and the Chou-Yang model

The shrinkage of the diffraction peaks is reproduced by the interference of a geometric pomeron and of complex poles representing S-channel threshold effects (like heavy pair production). Asymptotically, one recovers the Chou and Yang model. The shrinkage is expected to stop at P lab ⋍ 10 5 GeV/c . The total cross section σ T is conjectured to have a maximum of 45–48 mb (for pp) at about the same energy where the shrinkage stops. The asymptotic value of σ T would only differ from the maximum value by about 1 mb. The break structure at |t| ⋍ 1.2 GeV 2/c 2 seen at low energies for pp elastic scattering is explained in term of secondary Regge exchanges only. At high energies, the dip at | t| ∼ 1.3–1.4 GeV 2/ c 2 is given by the geometric pomeron. Because of the eikonalization procedure one obtains an intermediate | t| shrinkage and a dip displacement in good agreement with experiment.

High-energy production and decay of vector and tensor mesons

The available charge-exchange data for πN → ϱN, πN → ωN and ϱ − ω interference effects in the momentum range 6–17 GeV /c are analyzed. Duality considerations are used to constrain as much as possible the exchanged Regge poles and also to relate their contributions to those made by the same Regge exchanges in πN → f 0N and πN → A 2N. Combined with an empirical investigation of the Regge cut contributions, this allows a simultaneous description of vector and tensor meson production. The resulting amplitudes are used to predict interference effects in the common KK̄ decay channel of f 0 and A 2. Other predictions include K ∗(1420) and K̄ ∗(1420) production, and many polarization effects.

Amplitudes for ϱ and A 2 Regge exchanges in δ production processes

In δ production processes like π + p → π 0δ ++, K + p → K 0δ ++, K − n → K 0δ − , exchange degeneracy breaking between ϱ and A 2 Regge poles is shown to be present in all s-channel helicity amplitudes including the double-flip one. Once. the dominance of two among four amplitudes and SU(3) invariance are assumed, the amplitudes are obtained in a rather model-indenpendent way. The peculiar feature of these amplitudes are analyzed and in particular some evidence for universality in the impact parameter representation is pointed out. Possible explanations are proposed.

Study of the reactions π+p → Δ++π0 and π+p → Δ++η AT 5.45 GeV/ c

Results are presented on the quasi-two body reactions π +p → Δ ++ π 0 and π +p → Δ s++ η and 5.45 GeV/ c. Differential cross sections and Δ ++ spin density matrix elements in the t-channel and s-channel helicity systems are presented and compared with a Regge exchange model and the dual absorptive model.