Regge Pole Theory Research Articles

Theory of Pion-Pion Scattering

Strong-interaction dynamics is formulated on two main assumptions. The first is similar to the one used in the Regge-pole-resonance interference model, and the other is that the potentials arising from the exchange of a few dominant particles and resonances in crossed channels can be accepted physically in the low-energy regions and that the convergent high-energy behavior of the potentials should be guaranteed by the Regge-pole theory. A long-range potential which satisfies both the low-energy and the high-energy boundary conditions stated above is introduced. The dynamical model with only Regge-pole exchange potentials (as in the new form of the strip approximation) does not produce low-energy resonance behavior as a dynamical output. We show that a potential which does produce the main low-energy resonance behavior as output can be constructed by an appropriate superposition of single-particle exchange potentials and Regge-pole exchange potentials according to our second assumption. Also, two other potentials arising from the large-$t$ parts of the Mandelstam double spectral functions are defined under the first assumption.

Factorization and Constraints in Regge-Pole Theory

The behavior near zero momentum transfer of the Regge residues for a two-particle reaction is determined by means of analyticity and factorization. It is shown that, at least in all cases of present interest, the solution obtained satisfies the kinematical constraints provided that a classification and certain relations between the trajectories involved (identical to those obtained by group-theoretical methods) are imposed.

Regge-Pole Formalism for Pionic Disintegration of Deuteron

We investigate the reaction ${\ensuremath{\pi}}^{+}+d\ensuremath{\rightarrow}p+p$ within the framework of Regge-pole theory. Reggeization of the amplitudes for this process is carried out in detail, and the asymptotic behavior of the helicity amplitudes at zero momentum transfer is discussed. By assuming that the lowest anomalous threshold singularity in the $t$ channel dominates in the nearby region, we calculate the nucleon-deuteron Regge residue in terms of the pion-nucleon Regge residue. We also discuss the relations to the Regge-pole formalism of various low-energy models used to study this reaction and its inverse.

SU(3) Crossing Relation for Meson-Baryon Scattering and Regge Pole Theory

The meson-nucleon scattering data from 6-18 GeV/c have been analysed under the hypo­ theses of the SU(3) crossing relation and the Regge pole theory. The cross sections associated with the unitary singlet trajectory are well explained with the parameters of the Pomeranchuk trajectory in the current analysis. Those associated with the 88 trajectory show some structure and require the introduction of new octet tensor mesons in addition to known ones,. The factorization apparently does not apply to the 8A associated cross sections and, hence, to the p and (() trajectories. The 10 + 10* and 27 plets associated cross sections are zero within ex­ perimental error. A physical interpretation of this result is discussed. In a recent development of high energy physics the superconvergertce rela­ tion!) (abbreviated s.c.r.) and the Regge pole theory combined with higher sym­ metry seem to give a consistent description of various phenomena. The S.C.L for the imaginary part of the forward scattering amplitude has usually been derived by assuming that the Regge trajectory ai (t) belonging to the particular unitary spin in the crossed channel crosses the negative value at t = 0**) in the Chew-Frautschi plot. Sakita and Wali 2 ) have analysed the s.c.r. for the B ampli. tude of C.G.L.N. 3 ) by assuming that a 27 (0) <0 and that the SU(3) crossing matrix 4 ) applies correctly. If they saturate ,that relation by the nucleon Born term and the N*(1236) in a narrow width approximation, then the F/D ratio is close to the one suggested by SU (6) symmetry. Palmer 5 ) has extended this work' by assuming that a lO (0) < -1. He could then write art additional s.c.r. for the whole amplitude f(v) = A (v) + vB (v), viz. CD

Forward and near forward limits in Regge pole theory

The regularity of the limit s→ ∞, t → 0 is demonstrated for the case of the reaction πN → ϱN with the exchange of an M = 0 (A 1) conspiracy. Some general implications for Regge phenomenology are noted.

SU(3) symmetry and Regge poles at high energy

In the framework of the Regge-pole theory, various authors have given predictions concerning the differential cross section of the charge-exchange scattering K + + n → K o + p at high energy, making use of the measured differential cross sections for the processes π − + p → π o + n, π − + p → η o + n and K − + p → K o + n . Here it is shown that one cannot be sure whether Regge-pole theory is being tested, or simply SU(3) symmetry. Another relation is given between the same differential cross sections, which is more closely related to the Regge-pole behaviour.

On a model for saturation of a superconvergent sum rule

A superconvergent sum rule, regarded as an identity valid for all values of the momentum transfert in the neighbourhood oft=0, implies such conditions which are quite unlikely to be satisfied by saturating the sum rule by a finite number of resonances. Even though this may imply that there is an infinite number of resonances saturating the sum rule, the contributions from higher resonances to an amplitude are known to decrease rapidly so that they make up only a sort of background over a finite number of low-lying resonances. A model of achieving this using Regge pole theory without introducing a large number of higher resonances is presented.

Superconvergence sum rules for baryon-antibaryon scattering

Superconvergence sum rules for baryon-antibaryon scattering amplitudes are derived assuming that the Regge pole theory describes their high-energy behaviour. We obtain superconvergence sum rules in both the forward and backward direction. Explicit expressions for the sum rules for equal-mass baryon-antibaryon scattering are given assuming that they can be saturated by meson poles of zero width.

The homogeneous Lorentz group and πN charge-exchange scattering

The partial wave expansion of the scattering amplitudes in terms of the homogeneous Lorentz group extended to t ≠ 0 is studied with particular reference to the high-energy behaviour of πN charge-exchange scattering. In order that the analysis accomodate all the nice features of Regge pole theory, we find that it is necessary either that the ϱ-meson trajectory should contain both j o = 0 and j o = 1 contributions (a j o -mixing) or that there exist another trajectory ϱ′ with the same quantum numbers as ϱ.

Regge-Pole Theory and Spin Independence of the Total Cross Sections

The general conditions under which the total cross sections are independent of spin are discussed. It is shown that the forward elastic scattering matrix is proportional to the unit matrix in the helicity space if and only if the crossed channels either do not flip helicities, or do not flip helicities more than 1 and have the quantum number $P={(\ensuremath{-}1)}^{J}$. This theorem follows directly from the Trueman-Wick crossing relations. In particular, the theorem implies that the total cross sections are spin-independent at the high-energy limit if the forward elastic-scattering amplitudes are dominated by the Pomeranchuk trajectory.

Relation among theπNandKNCharge-Exchange Differential Cross Sections from theSU(3)Regge-Pole Theory

The $\mathrm{SU}(3)$ Regge-pole theory, applied to $\ensuremath{\pi}N$ and $\mathrm{KN}$ interactions, is reinvestigated. With the simple constraints provided by the $\mathrm{SU}(3)$ relations on the scattering amplitudes, the relation among the $\ensuremath{\pi}N$ and $\mathrm{KN}$ charge-exchange differential cross sections is found to be $\frac{d\ensuremath{\sigma}}{\mathrm{dt}}({K}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\overline{K}}^{0}n)+\frac{d\ensuremath{\sigma}}{\mathrm{dt}}({K}^{+}n\ensuremath{\rightarrow}{K}^{0}p){|}_{\mathrm{same} E, t}=\frac{d\ensuremath{\sigma}}{\mathrm{dt}}({\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n)+\frac{3}{{{F}_{0}}^{2}}\frac{d\ensuremath{\sigma}}{\mathrm{dt}}({\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\eta}}^{0}n){|}_{\mathrm{same} E, t},$ where ${F}_{0}=1$ for the exact $\mathrm{SU}(3)$. However, ${F}_{0}$ can be allowed to deviate from 1, and on the basis of the fit to the experimental data, we find that ${F}_{0}$ is not far away from 1. From the above relation, a prediction for ${K}^{+}n\ensuremath{\rightarrow}{K}^{0}p$ is possible in a straightforward way.

Kinematic Singularities of Partial-Wave Scattering Amplitudes

Those singularities (and zeros) introduced by partial-wave projection of unequal-mass scattering amplitudes are investigated. The particular points discussed are: (1) Threshold zeros, especially at the crossed threshold. We find that unitarity corrections vanish like ${k}^{L+{L}^{\ensuremath{'}}}$ at the crossed as well as the direct threshold, and thus it is appropriate to associate ${k}^{L+{L}^{\ensuremath{'}}}$ behavior of the amplitude with both thresholds. (2) The limit as $s\ensuremath{\rightarrow}0$ is related to the backward asymptotic behavior in the crossed $u$ and $t$ channels. The partial-wave amplitude goes like ${s}^{\ensuremath{-}\ensuremath{\alpha}}$ for all $L$ as $s\ensuremath{\rightarrow}0$, where $\ensuremath{\alpha}$ is the asymptotic power of the crossed-channel backward amplitudes. In Regge-pole theory, this would be leading direct-channel Regge trajectory. (3) Spin effects are shown to lead to $\ensuremath{\surd}s$ singularities for bosons as well as fermions. Generalized MacDowell relations are derived, relating negative-energy amplitudes to positive-energy amplitudes for any spin and determining the conditions under which there will be singularities.

Present Phenomenological Status of the Regge Pole Theory

Few theories have generated so much emotion amongst physicists as the Regge Pole theory has \ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{}\ifmmode\cdot\else\textperiodcentered\fi{} and still does. With the gradual accumulation of a vast amount of precise experimental data, it has become possible to attempt to give an objective survey of the present status of the theory in relation to experiment. The analysis herein is restricted to elastic and charge-exchange scattering processes in the region of high energies and small momentum transfers. A strong distinction is made between strictly forward ($t=0$) and nonforward ($t\ensuremath{\lesssim}0$) processes. In discussing the latter, an attempt is made to examine the phenomenological validity of the so called "factorisation theorem," the proof of which depends critically upon the assumption of the Regge poles being simple poles.

R-matrix theory of regge poles: Ralph Roskies, Department of Physics, Yale University, New Haven, Connecticut

R-matrix theory of regge poles: Ralph Roskies, Department of Physics, Yale University, New Haven, Connecticut

Phenomenological Approach to Explain the Behavior of the Diffraction Peak in High-Energy Scattering

It is pointed out that (i) the observed shrinkage of the diffraction peaks in both $p\ensuremath{-}p$ scattering and ${K}^{+}\ensuremath{-}p$ scattering does not necessarily correspond to the shrinkage predicted by Regge-pole theory, (ii) an upper limit to the width of the diffraction peak can be predicted from a theoretical point of view, and (iii) the observed widths of the diffraction peaks can be explained in terms of total cross sections and a parameter having the same value for various kinds of meson-nucleon scattering (similarly for nucleon-nucleon and nucleon-antinucleon scattering).

Regge-pole theory of the photoproduction of pions

In an attempt to apply a Regge-pole treatment to photoproduction it was found that in order to obtain the desired results massive photons have to be introduced into the theory thus allowing effects arising from longitudinal polarization of the photon. A new set of invariant amplitudes for the electroproduction of pions naturally suggest themselves from these considerations.

STRONG INTERACTIONS AT VERY HIGH ENERGY

During recent years, studies of strong interactions at high-energy levels underwent several changes. Experiments were carried out at 1 to 3 x 10/ sup 10/ ev with accelerators and even beyond 10/sup 11/ ev with cosmic rays. Among the theories developed, the theory of complex orbital moments or the Regge pole theory and the more rigorous one-meson approximation are considered; the latter represents a more sophisticated version of the Weizsacker-Williams theory. Some of the main conclusions of the Regge pole theory were confirmed by proton- proton (p-p) scattering experiments carried out in the 10- to 20-Bev range. Although at one time the theory was viewed as having general validity in view of these experiments, more-recent studies indicated that this is not the case; results of pi /sup -/-p interaction experiment carried out after the p-p scattering tests, did not bear out the predictions of the theory. The one-meson approximation method is not applicable to all phenomena but was developed gradually to cover a limited set of experimental facts. Current work is directed toward establishing a connection between elastic and inelastic processes in the field of high-energy interactions. Considerable attention is devoted to the experiments with cosmic rays. Data are availablemore » in the 10/sup 11/ to 10/sup 13/ ev range and experiments are being carried up to the 10/sup 16/ ev level. It was concluded that data on the interaction of high-energy particles cannot be explained on the basis of a single theory. (Review article, 127 refs.) (TTT)« less

Dynamical model of the deuteron based on the theory of Regge poles

An approximation scheme, based on the unitarity condition and dispersion relations, is applied to the calculation of the deuteron Regge trajectory.

Exact form for scattering amplitude in Regge pole theory

The exact form for the contribution of a single Regge pole is given both for positive and negative angular momentum without making the usual approximations. This exact form involves Legendre functions of the first and second kind with nonintegral index and argument greater than one. These functions are plotted. A one-parameter fit is made to the high-energy p-p elastic scattering data that give good agreement with experiment. (auth)

Elasticπ++pScattering from 7 to 17 BeV/c

Differential cross sections obtained for the momentum range 7 to 17 Bev/ c and the 4-momentum-transfer squared range of 0.2 to 0.1 (Bev/c)/sup 2/ failed to show the shrinkage with increasing center-of-mass energy squared that was predicted by Regge-pole theory. Similar results were previously obtained for pi /sup -/-p scattering, while shrinkage was observed in p-p cross sections. These results contradict the dominance of the vacuum pole or three-pole models. (D.C.W.)