We show that the Serpukhov data on $\pi N$ total cross sections between 30 and 65 GeV/c are in excellent quantitative agreement with the fits obtained earlier using a Reggeized quark model with multiple scattering. The predictions of the model for pion-nucleon differential cross sections and polarizations in this energy range are given.

A recently developed description of Reggeon couplings to baryons in terms of $s$-channel baryonic resonances is extended to more general $\frac{f}{d}$ ratios for meson-baryon-resonance couplings, including those values of $\frac{f}{d}$ appearing in $\mathrm{SU}\left(6\right)\mathrm{}$.

The selection rule derived from vector-meson decay is further investigated. It is found that the selection rule can be formulated consistently in the framework of field theory, if we work with a quark model with three degrees of freedom. Applying this theory to evaluate the real part of the high-energy forward scattering amplitudes, it is found that the fit with experiment is quite satisfactory.

Suzuka and Sugawara's theory of $S$-wave nonleptonic hyperon decay is reviewed to see to what extent their theory tests current algebra and the current×current form of interaction. The only argument for the current×current form in nonleptonic decays that it is all compelling is the vanishing of the $S$-wave amplitude $A\left({{\Sigma }_{+}}^{+}\right)$ for the decay ${\Sigma }^{+}\to n+{\pi }^{+}$. For the $P$-wave decay, to which the soft-pion formalism is inapplicable, an octet pole model is used. To fit the empirical $P$-wave amplitudes, strong-coupling shifts are required in both the $S$ and the $P$ waves. Including $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry breaking leads to parity-violating Born terms in the $S$ waves; to estimate the parity-violating spurion coupling, the kaon tadpole model and $K_2\pi$ decay rate are used. If pionic and kaonic strong-coupling constants are suppressed by $\frac{2}{3}$ and $\frac{1}{3}$, all the $S$- and $P$-wave amplitudes are given within 20%, but $A\left({{\Sigma }_{+}}^{+}\right)$ now does not precisely vanish. If $A\left({{\Sigma }_{+}}^{+}\right)=0\mathrm{}$ exactly is insisted on, then the suppression of pionic strong-coupling constants by $\frac{2}{3}$ and $\frac{1}{3}$ is necessary.

The scattering amplitude for scattering through several resonances is derived and shown to be always a sum of simple Breit-Wigner terms even for nontrival "particle mixtures." The formalism affords a particularly simple interpretation of the nonexponential decay or "dipole" phenomenon.

We present an eikonal model for the small-angle high-energy scattering of nucleons and antinucleons on nucleon targets. The model uses a flat Pomeranchon with a residue function given by a squared dipole. We also use exchange-degenerate trajectories and residue functions for the three pairs of Regge poles (the $\omega$ and $P^{\prime }$, the $\rho$ and $A_2$, and the $\pi$ and $B$). Using previous work by Arnold and Blackmon and other work by the present authors to fix trajectories and relative sizes of residue functions, we find that the model satisfactorily describes elastic scattering. We give an interpretation of the secondary maximum in the differential cross section of $\overline{p}p$ scattering which occurs around $-t\simeq 0.9$ Ge${\mathrm{V}}^2$. We find a crossover in the differential cross sections of $\mathrm{pp}$ and $\overline{p}p$ elastic scattering, and we show our results for various polarizations. We also discuss $\mathrm{np}\to \mathrm{pn}$ and $\overline{p}p\to \overline{n}n$, which are not described satisfactorily by the model.

Broken chiral $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ symmetry is considered by extending the Glashow-Weinberg-Berdeen-Lee scheme to include spin-1 mesons. Vector-meson decays and $K_{l3\mathrm{}}$ decays are treated on the basis of the resultant Lagrangian. Numerical estimates are made on the assumption of nonet symmetry, at the $\mathrm{SU}\left(3\right)\mathrm{}$ level, for the spin-$1^{-}$ mesons. It is found that $\frac{F_K}{F_{\pi }}\simeq 1.10$, $f_{+}\mathrm{}\left(0\right)\mathrm{}\simeq 0.96$, $\xi =\frac{f_{-}\mathrm{}\left(0\right)\mathrm{}}{f_{+}\mathrm{}\left(0\right)\mathrm{}}\simeq -0.048\mathrm{}$, ${\lambda }_{+}\simeq 0.022$, and $\xi {\lambda }_{-}\simeq -0.002\mathrm{}$.

Relations among total muon-capture rates in nuclei and the equal-time commutators of the space and time components of the strangeness-conserving weak hadron current are derived. Using the quark field algebra and the closure approximation, this relation yields a total muon-capture rate in ${\mathrm{He}}^3$ of $\Gamma \left({\mathrm{He}}^3\right)\approx 2.36\times {10}^3$ ${\sec }^{-1\mathrm{}}$, in very good agreement with experiment. We demonstrate that application of the gauge field algebra to our relations does not yield a result that can be compared with experiment, since we cannot justify the use of the closure approximation in the context of this algebra. Using the quark field algebra and the closure approximation, similar relations are also derived for the total "elastic" differential cross section for forward scattering of neutrinos off nuclei.

We derive upper and lower bounds on the imaginary part of the elastic scattering amplitude of two spinless particles in the physical region, in terms of the elastic cross section ${\sigma }_{\mathrm{el}}$ and the total cross section ${\sigma }_{\mathrm{tot}}$, using unitarity alone. The bounds derived are the best possible ones, given only the stated unitarity constraints. The upper bound for high energies and small values of the momentum transfer squared $t$ has a particularly simple and "universal" form, $\frac{\mathrm{Im}F(s, t)}{\mathrm{Im}F(s, 0)}<~1-\frac{1}{9}\rho +\frac{3}{8}{\left(\frac{\rho }{9}\right)}^2-\left(\frac{21}{320}\right){\left(\frac{\rho }{9}\right)}^3+\cdots$ if $2.5>~\rho \equiv (-\frac{t}{4\pi })\frac{{{\sigma }_{\mathrm{tot}}}^2\mathrm{}\left(s\right)\mathrm{}}{{\sigma }_{\mathrm{el}}\mathrm{}\left(s\right)\mathrm{}}$, which depends on the particular scattering process and on the energy and momentum transfer only through the dimensionless parameter $\rho$. We give explicit formulas and numerical values for the upper bound up to $\rho =8.42\mathrm{}$. We compare the experimental curve of $\frac{\left(\frac{d\sigma }{\mathrm{dt}}\right)}{{\left(\frac{d\sigma }{\mathrm{dt}}\right)}_{t=0\mathrm{}}}$ versus $4(-t)\mathrm{}\frac{{\left(\frac{d\sigma }{\mathrm{dt}}\right)}_{t=0\mathrm{}}}{{\sigma }_{\mathrm{el}}}$ with the theoretical upper bound on ${\left[\frac{\mathrm{Im}F(s, t)}{\mathrm{Im}F(s, t=0)]}\right]}^2$ versus $\rho$. The quantities plotted in the experimental and theoretical curves are the same if the unpolarized cross sections are spin-independent and purely absorptive in the diffraction-peak region. We find that the experimental points for $\mathrm{pp}$, $\overline{p}p$, ${\pi }^{+}p$, and ${\pi }^{-}p$ scattering in the lab momentum range 6-13 GeV/c fall on a curve lying only slightly below the theoretical upper-bound curve, the difference being less than 10% for $\rho$ in the range (0,3) and less than 25% for $\rho$ in the range (3,5). We further notice that this experimental curve is universal. We also derive unitarity lower bounds on the $n\mathrm{th}$ derivatives of the absorptive part at $t=0\mathrm{}$, and on the absorptive part for positive values of $t$ within the Lehmann-Martin ellipse, in terms of ${\sigma }_{\mathrm{el}}$ and ${\sigma }_{\mathrm{tot}}$. The corresponding bounds if ${\sigma }_{\mathrm{tot}}$ alone is known are also derived.

Using a double-Regge-pole model, we investigate the $\pi \rho$ mass enhancement in the backward reaction ${\pi }^{-}p\to p{\left(\pi \rho \right)}^{-}$. Broad peaks occur in this model near the $A_1$ mass. They are found to persist under a wide range of Regge-parameter values. Similar features also hold for the forward reaction cases. We conclude that the mass enhancement comes from the interplay of the phase-space kinematics and the peripheral nature of the Regge amplitude; the specific intercept and slope values of the trajectories are not very crucial. On the basis of our findings, we discuss the implications of the duality principle, isospin complications, and the practical problem of how to describe the $A_1$.

The $K_{l4\mathrm{}}$, $K_{l3\mathrm{}}$, and $K_{l2\mathrm{}}$ form factors, as well as the pion electromagnetic form factor, are derived from the matrix element $〈\pi \left|A_{\mu }\right|\pi K〉$ by using partial conservation of axial-vector current, current algebra, and the field-current identity, in addition to the Veneziano representation for the scattering amplitudes. This model contains essentially only one free parameter, by which all the quantities are expressed. The results agree with the present experimental data excellently.

Preliminary results on the application of the Reggeized $U\left(6\right)\mathrm{}\otimes U\left(6\right)\mathrm{}\otimes O\left(3\right)\mathrm{}$ absorptive peripheral model to photoproduction reactions are presented, with a detailed treatment for $\gamma p\to {\pi }^{+}n$. The agreement of the theory with experiment is most encouraging.

Coherent inelastic contributions to the absorptive corrections in high-energy exchange scattering are studied in a model in which hadrons are taken to be composite systems. General expressions for a momentum-transfer-independent "$\lambda$ factor" (i.e., the ratio of the complete absorptive correction to its elastic-only approximation) are obtained, and evaluated for a particular case meant to approximate neutron-proton charge-exchange scattering. In the forward direction, the $\lambda$ factor is about 1.36 and 1.17 for two- and three-constituent nucleons, respectively. In both cases, however, it decreases rather rapidly with increasing momentum transfer, falling somewhat below 1.0 for momentum transfer squared greater than about 0.5 ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$ before beginning to increase again.

A dispersion-relation calculation of the real parts of forward ${\pi }^{\pm }p$ and $K^{\pm }p$ scattering amplitudes is carried out under the assumption of constant total cross sections in the Serpukhov energy range. Comparison with existing experimental results as well as predictions for future high-energy experiments are presented and discussed. Electromagnetic effects are found to be too small to account for the expected difference between the ${\pi }^{-}p$ and ${\pi }^{+}p$ total cross sections at higher energies.

A model is developed to provide a framework for analyzing large-momentum-transfer hadron production in high-energy, inelastic hadron-hadron scattering. Two different production mechanisms, a peripheral and a central process, are found to play an important role in the high-energy wide-angle region. Each of these leads to a characteristic differential cross section for the process hadron+hadron→hadron+anything when the momentum transfer to the measured final-state hadron is large and varied. The production differential cross section dominated by a peripheral process is given by a product of an elastic amplitude and an inelastic structure function, while the one dominated by a central process is given by the product of two inelastic structure functions integrated over a restricted portion of phase space. The measured pion-production differential cross section in inelastic proton-proton scattering is found to be dominated by a peripheral process, while the proton production amplitude in inelastic $\mathrm{pp}$ scattering and the pion production amplitude in an as yet unexplored kinematical region are dominated by a central process. In addition, qualitative predictions for pion production in high-energy $p\overline{p}$ annihilation and pion, kaon, and proton production in inelastic $\pi p$ and $\mathrm{Kp}$ scattering are made.

We discuss the interaction between a pseudoscalar and two vector mesons within the context of chiral $\mathrm{SU}\left(3\right)\mathrm{}\otimes \mathrm{SU}\left(3\right)\mathrm{}$ symmetry. Assuming that the interaction transforms like a combination of zeroth and eighth components of a (3, 3*) ⊕ (3*, 3) representation, we are able, in a phenomenological Lagranigan treatment, to reproduce a previous $\mathrm{SU}\left(3\right)\mathrm{}$ parametrization of the related meson decay rates. In addition we obtain interaction terms for the decays of the $X^0$ meson. We study also the mass spectrum of the vector, axial-vector, and pseudoscalar mesons when these last belong to a nonlinear representation and when they are part of a linear representation which includes scalar mesons. In the latter case we find that the $\kappa -K^{*}$ mixing is negligible.

The $s$-channel approach to forward charged-pion photoproduction above the resonance region by means of fixed-$t$ dispersion relations is known to be quite successful. In this paper we investigate the kind of behavior that can be expected for charged-pion electroproduction on the basis of such a model.

The quasiparticle concept introduced by Weinberg for two-particle scattering has recently been applied to the three-body problem. It leads to an exact representation of the scattering matrix in terms of a modified Born series, the lowest order of which yields just the widely used separable-potential approximation. To test this method, the binding energies of three identical spinless particles interacting via Yukawa potentials, and the elastic scattering of one particle off a bound state of the other two, are calculated in zeroth- and first-order quasi-Born approximation. Our calculation shows that the inclusion of the first quasi-Born correction greatly improves the zeroth-order, i.e., the separable-potential, results. Comparison is also made with other calculations recently performed in this model.

We numerically estimate the expectation value between baryons of the equal-time commutator [${{\dot{J}}_i}^a, {J_j}^b$] of $U\left(3\right)\mathrm{}\otimes U\left(3\right)\mathrm{}$ currents on the gluon model by using a symmetry-breaking theory based on Regge-pole dominance. The result is in excellent agreement with the electroproduction data.

Schmid's problem on the interpretation of the anticlockwise Argand diagram obtained from Regge-pole exchanges as the direct-channel resonance is studied. It is shown in the idealized models that the anticlockwise Argand diagram alone cannot guarantee the existence of a resonance, and that it is absolutely necessary to compute the cross section in order to establish the existence of a resonance. The partial-wave projection of the Regge-pole exchanges in pion-nucleon scattering is performed. The Argand diagram, real part of phase shift, absorption factor, partial-wave total cross section ${\sigma }^{\mathrm{tot}}$, elastic cross section ${\sigma }^{\mathrm{el}}$, $k^2{\sigma }^{\mathrm{tot}}$, and $k^2{\sigma }^{\mathrm{el}}$ are computed. It is found that all ${\sigma }^{\mathrm{tot}}$ and ${\sigma }^{\mathrm{el}}$ have no cross-section peak at all, despite the existence of the anticlockwise Argand loops in certain partial waves. They show only the monotonically decreasing behavior characteristic of the Regge-pole model as energy increases, except in the unitarity-violating low-energy region. The above facts indicate that the variation of the anticlockwise Argand loop with respect to energy is too weak to produce a cross-section peak by overcoming the variation of the barrier factor $\frac{1}{k^2}$ in ${\sigma }^{\mathrm{tot}}$ and ${\sigma }^{\mathrm{el}}$. It is concluded that Schmid's interpretation is incorrect. Several physical implications of this result are discussed.