Pomeranchuk Exchange Research Articles

Analysis of vector-meson photoproduction in terms of a multichannel impact-parameter formalism

An analysis of high-energy data on ρ0, ω0 and ϕ0 photoproduction on protons is carried out in the context of the multichannel impact-parameter formalism which had been successfully applied previously to Compton scattering on protons and neutrons providing a unified theoretical description for all these photon-induced diffractive processes. Particular attention has been devoted to the determination of the helicity-flip structure for the asymptotically leading,i.e. Pomeranchuk, part of vector-meson photoproduction amplitudes. The proposedK-matrix description allows the existence of a helicity-flip contribution to Pomeranchuk exchange albeit with unknown coupling strength. ϕ0 photoproduction is especially suited to investigate in detail the nature of the Pomeranchuk coupling in diffractive photoproduction processes since no lower-lying trajectories can contribute here. The analysis lends support to the presence of a substantial helicity-flip contribution for the nucleons in high-energy vector-meson photoproduction which is to be associated with Pomeranchuk exchange.

Failure of a Self-Consistent Diffractive Multiperipheral Model in the Strong-Ordering Limit

A multiperipheral model incorporating both ordinary Regge and Pomeranchuk exchange is considered. The Pomeranchukon is limited to a single exchange, and the calculation assumes strong ordering of final particles. It is found that both trajectories can be treated in a self-consistent manner, but that the predictions of the model disagree strongly with experiment when the bootstrap condition is satisfied.

Isobar Production and Elastic Scattering inp−pInteractions from 6 to 30GeVc

Differential cross sections have been measured for nucleon-isobar production and elastic scattering in $p\ensuremath{-}p$ interactions from 6.2 to 29.7 $\frac{\mathrm{GeV}}{c}$ in the laboratory angle range $8l{\ensuremath{\theta}}_{\mathrm{sc}}l265$ mrad. ${N}^{*}$' s at 1236, 1410, 1500, 1690, and 2190 MeV were observed. Computer fits to the mass spectra under varying assumptions of resonance and background shapes show that conclusions on $t$ and $s$ dependence are only slightly affected despite typical variations in absolute normalization of \ifmmode\pm\else\textpm\fi{} 35%. Logarithmic $t$ slopes in the small- $|t|$ range are $\ensuremath{\sim}15 {(\frac{\mathrm{GeV}}{c})}^{\ensuremath{-}2}$ for the ${N}^{*}(1410)$, $\ensuremath{\sim}5 {(\frac{\mathrm{GeV}}{c})}^{\ensuremath{-}2}$ for the ${N}^{*}$'s at 1500, 1690, and 2190 MeV, and $\ensuremath{\sim}9 {(\frac{\mathrm{GeV}}{c})}^{\ensuremath{-}2}$ for elastic scattering. Also for the small- $|t|$ data, cross sections for ${N}^{*}$'s at 1410, 1500, 1690, and 2190 MeV and for elastic scattering vary only slightly with ${P}_{\mathrm{inc}}$ consistent with the dominance of Pomeranchuk exchange and with diffraction dissociation. A fit of ${N}^{*}(1690)$ total cross sections to the form ${\ensuremath{\sigma}}^{\ensuremath{\propto}}{P}^{\ensuremath{-}n}$ gives $n=0.34\ifmmode\pm\else\textpm\fi{}0.06$, while for elastic scattering $n=0.20\ifmmode\pm\else\textpm\fi{}0.05$. For the ${N}^{*}(1690)$ the effective Regge trajectory has the slope ${{\ensuremath{\alpha}}_{\mathrm{eff}}}^{\ensuremath{'}}(0)=0.38\ifmmode\pm\else\textpm\fi{}0.17$. When compared with ${N}^{*}$ production in ${\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{\ensuremath{-}}$, and $\overline{p}$ beams these data also agree with approximate factorization of the Pomeranchuk trajectory. ${N}^{*}(1236)$ cross sections are consistent with other measurements at similar momenta. For $\ensuremath{-}tg1 {(\frac{\mathrm{GeV}}{c})}^{\ensuremath{-}2}$, elastic scattering cross sections decrease approximately as ${{P}_{\mathrm{inc}}}^{\ensuremath{-}2}$, and they and ${N}^{*}(1500)\ensuremath{-}$ and ${N}^{*}(1690)\ensuremath{-}$ production cross sections have $t$ slopes consistent with 1.6 ${(\frac{\mathrm{GeV}}{c})}^{\ensuremath{-}2}$.

A duality formulation of the parity-change rule for baryons

Diffraction dissociation reactions can be expected to gain particular importance at high energies because of the asymptotic constancy of their cross-sections. In Regge theory such reactions go by Pomeranchuk exchange, for they involve no change in the internal quantum numbers (B, S, 1, G, etc.) of the dissociating particle. Whether there exist selection rules governing changes of spin and pari ty has been a controversial question, various rules having been proposed (1), in particular the empirical rule AP = (-1) AJ proposed by GRIBOV and ~r (2). This rule can be derived from Regge theory (3) for a spinless particle dissociating at 0 ~ and it follows (at all angles) from simple angular-momentum considerations on making a j e = 0 + assignment for a pomeron. When applied to baryons the rule A P = (--1) A: requires that diffractively produced I = 89 nucleon resonances must belong to the (~ natural ~> pari ty sequence 1+ a~ , 2 , 5+ 7-2 , 2 . . . . , i.e. P = (-1) J-~. Experiments (4) show peaks at about 1400, 1520, 1690 and 2190 MeV suggestive of known resonances in the vicinity of these masses having this sequence of quantum numbers, but in the absence of proper spin-parity analyses the evidence must be taken as inconclusive. Furthermore, simple angular-momentum arguments fail to exclude resonances of opposite (~ unnatura l ~>) parity, and as yet the rule has no theroetical foundation. The aim of this paper is to consider the pomeron (~ : I e = 0 +, J P = 0 +) exchange dissociation of a nucleon into a r:J~ final state

Pomeranchuk Dominance of the Imaginary Part of theK+pElastic Amplitude

Author(s): Bander, M; Stone, TM | Abstract: Using a phase-shift solution for K+p scattering, it is found that ImA′(ν,t) is well described by a Pomeranchuk exchange in agreement with the Harari-Freund duality conjecture. © 1971 The American Physical Society.

Bootstrap Calculations ofππScattering Using the Mandelstam Iteration

The results of some strip-model calculations of $\ensuremath{\pi}\ensuremath{\pi}$ scattering are presented. In these calculations, unitarity is imposed by means of the Mandelstam iteration. This procedure has the advantage that the output trajectories and residues (including their imaginary parts) may be computed above as well as below threshold; this is at present not feasible in calculations using the $\frac{N}{D}$ technique. First, a bootstrap calculation of the $\ensuremath{\rho}$ trajectory is carried out, neglecting Pomeranchuk exchange. The extra requirement of self-consistency above threshold is very strict, but a solution with satisfactory consistency between -1 and +2 Ge${\mathrm{V}}^{2}$ is obtained. The scale of energy is established by giving the $\ensuremath{\rho}$ resonance the physical mass; the self-consistent $\ensuremath{\rho}$ width is then about 400 MeV. Various dynamical approximations are investigated, and it is shown explicitly that the pion mass is not a significant parameter of the dynamics. Finally, a bootstrap calculation of both the $\ensuremath{\rho}$ and Pomeranchuk trajectories is presented. Except for the Pomeranchuk residue, the results show satisfactory self-consistency throughout the range -1 to +2 Ge${\mathrm{V}}^{2}$. The self-consistent Pomeranchuk trajectory has an intercept ${\ensuremath{\alpha}}_{P}(0)\ensuremath{\approx}1$ and a slope $\ensuremath{\alpha}_{P}^{}{}_{}{}^{\ensuremath{'}}(0)\ensuremath{\approx}0.5$ Ge${\mathrm{V}}^{\ensuremath{-}2}$. The inclusion of Pomeranchuk exchange increases the slope of the $\ensuremath{\rho}$ trajectory, but the effect of this on the $\ensuremath{\rho}$ resonance width is offset by a more rapid increase in the imaginary part of the trajectory, and the self-consistent $\ensuremath{\rho}$ width is now about 600 MeV. In contrast to the more encouraging consequences of including Pomeranchuk exchange in recent $\frac{N}{D}$ calculations, these results suggest that the physical $\ensuremath{\rho}$ is in fact primarily a bound state of some channel other than $\ensuremath{\pi}\ensuremath{\pi}$.

Study of some three-body reactions in π+d interactions at 5.1 and 9.0 GeV/c

Some three-body reactions obtained in π+ interactions on deuterium at 5.1 and 9.0 GeV/c of incident momentum are studied. The analysis is made in the longitudinal phase space. The results show the presence of a Pomeranchuk exchange in the region ω < 120°.

Fixed Poles in High-Energy Compton Scattering, Electroproduction, and the Vector-Dominance Models

It is shown that the vector dominance of $s$-channel helicity amplitudes requires the existence of a nonsense wrong-signature fixed pole at $J=1$ in virtual photon-hadron scattering. Furthermore, in the amplitudes for electroproduction, where the virtual photon masses are spacelike, it is argued that such fixed poles must exist simply from such general requirements as analyticity, gauge invariance, and positivity of cross sections. This fixed pole occurs multiplicatively with the Pomeranchuk pole if the photon-hadron cross sections ${\ensuremath{\sigma}}_{L}$ or ${\ensuremath{\sigma}}_{S}$ are constant asymptotically with energy. A minimal amount of analyticity then allows one to extend this result to general values of the virtual photon masses. If the asymptotic cross section for photoproduction of $\ensuremath{\rho}$ mesons is dominated by Pomeranchuk exchange and if it conserves helicity, then the multiplicative fixed pole is present there, too. Further, the presence of this fixed pole tests for the compositeness of the $\ensuremath{\rho}$ meson or third-double-spectral-function effects.

Inert Hadron Reaction for the Determination of the Pomeranchuk Trajectory Slope

A reaction with no expected secondary Regge poles ($\ensuremath{\gamma}p\ensuremath{\rightarrow}\ensuremath{\phi}p$) is suggested as a means for direct experimental study of the Pomeranchuk exchange amplitude. From existing data on this reaction, we find a Pomeranchuk trajectory slope of ${{\ensuremath{\alpha}}_{P}}^{\ensuremath{'}}(0)\ensuremath{\simeq}\frac{1}{2}$.

Vector-Meson and Dipion Production in Lepton-Nucleon Collisions

The electroproduction of $\ensuremath{\rho}$, $\ensuremath{\omega}$, and $\ensuremath{\varphi}$ mesons is discussed. The spin-density matrix elements are shown to satisfy a number of conditions if and where the production is dominated by Pomeranchuk exchange. Constraints are also given for the case that a single spin-parity (of type ${0}^{\ifmmode\pm\else\textpm\fi{}}$, ${1}^{\ifmmode\pm\else\textpm\fi{}}$) dominates the $t$ channel in some kinematic region. The extension to the production of a $2\ensuremath{\pi}$ continuum is straightforward. Vector-meson and $2\ensuremath{\pi}$ production by neutrinos is also treated.

Dependence upon the toller azimuthal angle as a consequence of pomeranchuk exchange in the multipheral model at very high energies

It is shown that when a Pomeranchuk is exchanged from a proton-proton vertex to an internal vertex the distribution in the Toller azimuthal angle ω is given by the distribution as computed from the standard Reggeized matrix element times a polynomial in cos ω, A o + A 1cos 2 ω. It is noted that there is a possibility of a kinematic depression of the effective coupling at an internal vertex for a Pomerachuk, an external spin-zero boson, and a Reggeized boson with a large spin-zero component, for example at an internal vertex coupling a Pomeranchuk to two pions.

Longitudinal phase space analysis of three-body final states in meson-nucleon collisions

The longitudinal phase-space analysis is applied to various three-body final states of meson-nucleon collisions at 5–16 GeV/ c primary momentum. The distributions of the angle ω along the hexagonal phase space plot and the dependence of average transverse momenta on ω are investigated in some detail. From the very rich structure of the ω distributions it is possible to conclude that, whenever allowed, the diffraction mechanism (single Pomeranchuk exchange) dominates the three-body reactions at high energy. The study of the transverse momentum distributions reveals the existence of strong correlations between longitudinal and transverse momenta which cannot be explained by phase-space effects. Some consequences of our analysis for the Regge-exchange models are briefly mentioned.

Regge pole exchange analysis of [formula omitted] at 7.3 GeV/ c

A Regge pole exchange model is applied to the reaction K + p → K ∗ O (890)π + p at 7.3 GeV/c . The reaction is well described by exchanges of pion and Pomeranchuk trajectories with the Pomeranchuk exchange approximated by either a diffraction mechanism or on-mass shell π +p scattering. The model fits the production of the Q enhancement and also gives an adequate description of the virtual π +p scattering.

Pomeranchuk Exchange and Low-Energy Theorems in Compton Scattering

The method, introduced in a previous work, of deriving the kinematical properties of zero-mass bosons from the limit of a theory with massive particles is here applied to the problem of Compton scattering. It is shown that the same mechanism that eliminates the factor of ${\ensuremath{\alpha}}_{\ensuremath{\pi}}(t)$ from the nonsense amplitude in pion photoproduction processes and allows the pion pole to occur in such amplitudes also removes the nonsense factor of ${\ensuremath{\alpha}}_{P}\ensuremath{-}1$ from the residue of the Pomeranchuk trajectory in Compton scattering. This allows the Pomeranchuk exchange to contribute to the photoabsorption total cross section. The connection of this result with the vector-dominance model is discussed. A short derivation of the low-energy theorems for Compton scattering using this limiting procedure is also given.

Pomeranchuk exchange and multi-pion production

A simple test for Pomeranchuk exchange dominance in multi-pion production is obtained from isospin relations and used to show that present production data are not compatible with this assumption.

The multi-Reggeon model and Pomeranchuk exchange

It is shown that when the multi-Reggeon model takes account of mixed inelastic events (that is. events in which groups of particles are emitted travelling together with low relative momenta) a consistent picture. free from paradox. can be made based on Pomeranchuk exchange. The effect of unitarity on Mandelstam cuts is also evaluated and it is suggested that it leads to a softening of the asymptotic behaviour associated with the cut by a factor (log log s) −2.

Multiple Pomeranchuk exchange violates unitarity

Multiple Pomeranchuk exchange violates unitarity

Pomeranchuk-Exchange Contribution to Forward Photon Processes

Assuming pure Regge-pole behavior and the crossing relations for helicity amplitudes, we show that (1) the Pomeranchuk trajectory does not contribute to Compton scattering from spin-0 or spin-\textonehalf{} particles in the forward direction; (2) Pomeranchuk exchange does contribute to forward vector-meson photoproduction, and at high energies the production of vector mesons with helicity\ifmmode\pm\else\textpm\fi{}1 dominates over the production of those with zero helicity. Some interesting properties of the crossing relations are derived and used to obtain these results. We briefly discuss the difficulties associated with conclusion (1).

Equivalent-Potential Calculation ofππandπKScattering

A method suggested by Bal\'azs is used to calculate the $\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}K$ amplitudes in the resonance region. An input force corresponding to vector-meson exchange reproduces the vector mesons, and also produces ${2}^{+}$ mesons at roughly the masses of the ${f}^{0}(1250)$, ${f}^{0\ensuremath{'}}(1500)$, and ${K}^{**}(1405)$. Inclusion of an estimate of Pomeranchuk exchange in the input improves the output slightly. Regge trajectories and residues are computed, and their intercepts agree approximately with estimates based on high-energy experiments.