Relations between processes related by crossing are proposed as a test of (i) exchange degeneracy and (ii) dominance by trajectories of the same signature. Various possible experiments are discussed.Received 28 August 1969DOI:https://doi.org/10.1103/PhysRev.188.2281©1969 American Physical Society

The singularity structure of the Veneziano model in the angular momentum and Khuri planes is discussed. The continued partial-wave amplitude is shown to have an infinite number of Regge poles, spaced by integers, together with an infinite number of fixed poles at wrong-signature nonsense points in the $l$ plane. The residues of both the moving and fixed poles are calculated, and consequences of their structure are discussed. In the Khuri plane, the Veneziano model is shown to be characterized by an infinite number of moving poles, but there are no fixed poles. The residues of the moving poles are presented.

The three-particle discontinuity equations are expressed in forms convenient for the study of unitarity violations. As an application, the constraints on the two-particle transition operators imposed by requiring consistency with three-particle unitarity are deduced. This provides a framework for some recent proposals for generating approximate, finite-rank, two-particle transition operators which do not satisfy off-shell unitarity. Also, the general features of some quasi-unitary impulse approximations are discussed in a unified fashion in order to clarify the conditions for their validity as well as for higher-order quasi-unitary approximations.

For any spin, the Coulomb bound states can be described by an irreducible unitary representation of $O(4, 1)$. The relativistic Coulomb problems that have been solved (spins 0 and \textonehalf{}) are described in this way.

For multiparticle reactions involving massive particles of any spin, the amplitudes introduced by Bali, Chew, and Pignotti (BCP) are considered as functions of the scalar products between four-momenta. A method previously used by Trueman for 2-to-2 particle reactions and by this author for multiparticle helicity amplitudes is used to classify and explicitly extract the kinematic singularities of the BCP amplitudes. This method concentrates on the Lorentz-group parameters that define the state vectors in terms of which the amplitudes are constructed. The basic assumption is that the kinematic singularities of the amplitudes are due solely to the singular behavior of these group parameters on certain surfaces, given by the vanishing of particular Gram determinants, in the space of the invariant variables. The kinematic singularities take a form which seems suitable for analyzing kinematic constraints in a factorizable multiperipheral model.

In this paper we begin an investigation of the properties of vector currents consistent with the hadron bootstrap, assuming duality and zero resonance widths. First, on general grounds and independently of current algebra, we show that two-current amplitudes must have fixed singularities in the angular momentum plane. Then we discuss some general consequences for current amplitudes of duality and the zero-width approximation. Throughout we treat amplitudes for one or two vector currents and an arbitrary number $N$ of spinless hadrons.

We illustrate in detail the summation of multiphoton exchange diagrams for $\mathrm{ee}$, $\ensuremath{\gamma}e$, and $\ensuremath{\gamma}\ensuremath{\gamma}$ elastic scattering amplitudes at the high-energy limit using the infinite-momentum technique reported earlier. These diagrams are shown to give rise to amplitudes proportional to $s$, the center-of-mass energy squared, multiplied by simple combinations of the eikonal forms of high-energy scattering.

${K}^{\ensuremath{-}}d$ interactions were studied at an incident momentum of 5.5 GeV/c in a 5-eV/\ensuremath{\mu}b exposure of the 30-in. deuterium bubble chamber at the Argonne Zero-Gradient Synchrotron. The dominant feature of the reaction ${K}^{\ensuremath{-}}d\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}d$ is ${\overline{K}}^{*}(890)$ production, although the low-mass enhancement, usually referred to as ${d}^{*}$, is also prominent in the $d{\ensuremath{\pi}}^{\ensuremath{-}}$ mass spectrum. The low momentum transfer to the deuteron imposed by coherent production strongly favors a $K\ensuremath{\pi}\ensuremath{\pi}$ mass in the region of the $Q$ enhancement. As is usually observed, the production and decay characteristics of the $K\ensuremath{\pi}\ensuremath{\pi}$ system are generally compatible with a ${1}^{+}$ spin-parity assignment. A study of the ${K}^{\ensuremath{-}}{\ensuremath{\pi}}^{+}$ system reveals an $s$-wave-$p$-wave interference similar to that observed in $K\ensuremath{\pi}$ scattering. The data are compared with the predictions of a double-Regge-pole model.

Based on exchange degeneracy and $\mathrm{SU}(3)$ symmetry, a Regge-pole model fitting the differential cross sections for pion-nucleon and kaon-nucleon charge exchange and $\ensuremath{\eta}$ production as well as polarization in ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{\ensuremath{\pi}}^{0}n$ is given. Besides the $\ensuremath{\rho}\ensuremath{-}{A}_{2}$ trajectory, a conspiring and exchange-degenerate ${\ensuremath{\rho}}^{\ensuremath{'}}\ensuremath{-}{{A}_{2}}^{\ensuremath{'}}$ trajectory with the same slope as $\ensuremath{\rho}\ensuremath{-}{A}_{2}$ but with an intercept near zero is taken into account. The residues are assumed to have $\frac{1}{\ensuremath{\Gamma}(\ensuremath{\alpha})}$ behavior. A four-parameter fit gives good agreement with the experimental data.

Excitation functions are reported for the reactions of ${\mathrm{Cd}}^{114}$ and ${\mathrm{Cd}}^{116}$ with ${\mathrm{Ar}}^{40}$ to produce ${\mathrm{Tb}}^{149}$, ${\mathrm{Dy}}^{150}$, and ${\mathrm{Dy}}^{151}$. Range measurements in Al for the recoiling Dy products indicate that compound-nucleus formation is the first step in the reaction. From the cross sections, it is concluded that the angular momentum spectrum for the reactions $\mathrm{Cd}({\mathrm{Ar}}^{40},6n \mathrm{and} 7n)$ is very similar to that for ${\mathrm{Ne}}^{20},6n \mathrm{and} 7n$ reactions. The range measurements extend the span of experimental range-energy information for these nuclei from 4 to 60 MeV. These range data expressed in terms of fractional effective charge $\ensuremath{\gamma}=\frac{{Z}_{\mathrm{eff}}}{Z}$ are found to correlate well with data for ${\mathrm{Br}}^{79,80}$, ${\mathrm{I}}^{127}$, and fission fragments.