Regge-pole Exchange Research Articles

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.

Study of the reaction [formula omitted

Results are presented on effective-mass distributions, differentisl cross sections and longitudinal c.m. momentum distributions for the channels K − p→ K − pπ o, K o pπ − and K −π + n , obtained from a sample of approximately 28 000 inelastic two-pronged interactions at 4.2 GeV/ c incident momentum. The results are in satisfactory agreement with the prediction of a generalized Veneziano-model corrected for (non-dual) π-and pomeron exchange. For the channel K −pπ o pomeron exchange contributes about 20% of the cross section. In the channel K −π +n the dual, pion and pomeron contributions are responsible for resp. 15%, 65% and 20% of the total cross section. We also present results on total and differential cross sections and spin-density matrix elements for the quasi two-body reactions K − p→ K ∗−(890) p and K ∗o(890) n . These results are compared with single Regge-pole exchange model predictions. The reaction mechanism of K ∗−(890) production is dominated by the ω(θ) trajectory exchange with some admixture of π-exchange. The mechanism for K ∗o(890) production is dominated by π-exchange with some admixture of (A 2) trajectory exchange.

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.

Secondary Regge contributions in charge exchange reactions at t = 0

Second order contributions to Regge-pole exchange are analyzed in πN and KN charge-exchange reactions at zero angle, using recent experimental data. Models involving secondary trajectory exchange, contributions from cuts and complex Regge dipoles are compared. The breaking of the ϱ − A 2 exchange degeneracy is found to be rather important for the residues; the second order corrections to pure ϱ and A 2 Regge-pole exchange are small, too small to account for the high-energy behaviour of the total cross section Δσ π = σ tot( π −p) − σ tot( π +p) measured at the Serpukhov accelerator. It seems impossible to distinguish between second-order corrections from secondary trajectory exchange and cuts, at t = 0. The cut contribution to ϱ exchange predicted by a simple absorption model is very small in the forward direction; this is confirmed by the fit.

Multiple-quark-scattering analysis of hadron charge-exchange scattering

We investigate the hadron charge-exchange (CEX) scattering processes in terms of the multiple-quark-scattering formalism. We extend the Glauber formalism to include the spin and isospin effects of the constituent particles, and the nucleons and mesons are assumed to belong to 56- and 35-dimensional representations of the nonrelativisticSU6 group. The fundamental quark-scattering amplitudes are expressed as Regge-pole exchange amplitudes. We explain the energy and momentum transfer dependences of the π−p, np and\(\bar p\)p CEX scattering differential cross-sections and polarization data of π−p CEX scattering. The multiple-scattering picture provides natural explanations of the π−p CEX scattering polarization effect and the forward peak in np CEX scattering differential cross-section without invoking the extra ϱ′ and pion-conspirator trajectories. New understandings of the connections of the multiple-scattering model, the absorptive-correction model and the Regge-pole model are discussed.

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

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.

High-energy single-particle production on the Van Hove plot

Several single-particle production processes are analysed on the Van Hove longitudinal phase-space plot in terms of a model which includes both Regge-pole exchanges and their related phases at high subenergies and possible resonance formation at low energies. With this model it is found possible to simultaneously fit the data for reactions corresponding to different charge states over a range of incident pion momentum. The analysis stresses the importance of pion exchange in these reactions at the energies considered.

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.

Duality in Backwardπ+pElastic Scattering

A duality-inspired model for the scattering amplitude is used to explain backward ${\ensuremath{\pi}}^{+}p$ elastic-scattering data from $2.18 \frac{\mathrm{GeV}}{c}$ (incident pion laboratory momentum) on up. The quantitative success of this model gives support to the assumption that the dip at $u\ensuremath{\sim}\ensuremath{-}0.15$ Ge${\mathrm{V}}^{2}$ is due to a wrong-signature nonsense zero in the ${N}_{\ensuremath{\alpha}}$ Regge-pole exchange amplitude. A particularly interesting polarization prediction (which can soon be compared with experimental data) is also presented.

Direct- and Cross-Duality Amplitudes

General considerations based on analyticity and asymptotic behavior lead us to construct two crossing-symmetric model amplitudes for equal-mass spinless scattering, interpolating imposed asymptotic forms at low and high energy. One, the direct-duality amplitude, is a generalized Veneziano model. In the other, Regge-cut exchange is dual to the direct-channel resonances while Regge-pole exchange is dual to the direct-channel cut.

TheK-matrix, absorption corrections and Regge poles

By suitably defining theK-matrix with only the two-particle cuts removed, we investigate its cut structure at high energy and show that it is not unreasonable to approximate this amplitude by single Reggepole exchange. It is also shown that the integral equation relating thisK-matrix to the fullT-matrix can be solved approximately at high energies giving a modified form of the absorption model. Thus we find a theoretical framework in which it is reasonable to apply absorptionlike corrections to a Regge-pole exchange amplitude.

π−pCharge Exchange at Backward Angles

Results of a measurement of the ${\ensuremath{\pi}}^{\ensuremath{-}}p$ charge-exchange process at backward angles are presented. Differential cross sections were measured in the angular region $\ensuremath{-}0.5<cos{\ensuremath{\theta}}^{*}<\ensuremath{-}1.0$ at incident momenta of 2, 3, 4, 5, and 6 GeV/c. An additional background subtraction to a version of the data published previously has a significant effect at 6 GeV/c and brings the data into agreement with more recent measurements. The 6-GeV/c data were combined with existing measurements of the differential cross sections for backward ${\ensuremath{\pi}}^{+}p$ and ${\ensuremath{\pi}}^{\ensuremath{-}}p$ elastic scattering to yield values for the isotopic-spin-\textonehalf{} and $\ensuremath{-}\frac{3}{2}$ $u$-channel and $s$-channel amplitudes for backward pion-nucleon scattering and for the magnitude of the phases between them. It is found that the $u$-channel amplitudes can be explained by pure Regge-pole (${\ensuremath{\Delta}}_{\ensuremath{\delta}}, {N}_{\ensuremath{\alpha}}$) exchange only near the extreme backward direction, but that a Reggeized absorption model agrees at least qualitatively with the data. The phase difference between the $I=\frac{1}{2} \mathrm{and} \frac{3}{2}$ $s$-channel amplitudes is approximately 90\ifmmode^\circ\else\textdegree\fi{} over the region $\ensuremath{-}0.8<u<0$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^{2}$.

Rise and Fall of Relativistic Trajectories

The general problem of rising and falling Regge trajectories is investigated in a fully relativistic model in which an arbitrary two-particle interaction is unitarized by summing generalized ladder diagrams. The trajectories are extracted from the infinite sum by an extension of the technique previously applied to ladder diagrams in an ordinary scalar field theory. Any basic interaction which vanishes faster than any power of the momentum transfer t generates infinitely falling trajectories. A physical explanation of falling trajectories is given in terms of the scattering of infinitely composite particles where the standard single-particle-exchange interaction is modified by exponentially damped form factors. A variety of models for rising trajectories is constructed, all of which violate either the Jaffe bound on form factors or the Froissart bound on forward scattering amplitudes. If the interaction is single-particle exchange with form factors e −γ(−t) β , the trajectory has Reα→+∞ as s→∞ if β≥1 , but it is not of narrow width. Energy-dependent interactions based on Regge-pole exchange, energy-dependent coupling constants, or direct form factors yield rising trajectories, but not narrow widths. Moreover, the energy dependence must be such that the Froissart bound appears to be grossly violated.

Bootstrap Conditions from Unitarity at High Energy

The unitarity relation for the high-energy scattering of two particles is investigated under the assumption that the production amplitudes which enter the unitarity sum are given by a single Regge-pole exchange; the further assumption of multi-Regge exchange is not made. It is seen that the unitarity sum can be expressed as an integral involving the particle-Reggeon scattering amplitude (which may be defined in terms of the six-point function), and by representing this amplitude by Regge exchange, one obtains an equation which leads to self-consistency conditions on the Regge parameters. Solutions to this equation have, in addition to Regge poles, Regge cuts which interfere destructively with the poles. Comparisons are made with related models, in particular, the multi-Regge model. It is suggested that, while the Regge cuts calculated by the multi-Regge method are model dependent, the bootstrap condition on the Regge pole is more general.

Partial wave amplitudes for π−p elastic scattering and charge exchange in the 2–5 GeV/ c region

The experimental data, for the elastic scattering of π − mesons by protons and for charge exchange in the momentum interval 2 to 5 GeV/ c, has been fitted by a model in which the amplitudes are represented as the sum of Regge-pole exchange terms and parametric terms based on polynomial expansions in cos θ. Phase-shift parameters are subsequently obtained by partial wave projection, and the resonant structure of the region is tentatively identified.

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.