The results of a previous paper are specialized to photoproduction, electroproduction, and neutrino-induced production of a single pion. A detailed analysis is given of possible $T$-violation effects. In particular, the problem of eliminating spurious effects arising from final-state interactions is studied, and suitable prescriptions are given for eliminating these spurious effects. Detailed estimations are given of $T$-violation effects in the various cases and under different kinematical situations. In particular, the interplay of the various multipole transitions is discussed and numerically estimated. The electroproduction of a single pion near threshold and the neutrino-induced production of a single pion appear particularly interesting.

The scattering of $\pi \text{'}\mathrm{s}$ and $K\text{'}\mathrm{s}$ from a ${\mathrm{He}}^3$ nucleus has been calculated using the Regge-eikonal model proposed by Arnold, Blackmon, and Goldstein. A phenomenological form factor is used to relate the Regge amplitude for scattering from a weakly bound composite system to the scattering from the components of the system. In this way qualitative features of the elastic and charge-exchange differential cross sections and polarizations for ${\pi }^{\pm }$-${\mathrm{He}}^3$ and $K^{\pm }$-${\mathrm{He}}^3$ processes are predicted.

The general form of the coincidence cross section for electroproduction of nucleon resonances is reviewed and discussed using the helicity formalism. The predictions of a coupled-channel relativistic $\frac{N}{D}$ model are discussed for nucleon levels in the first four resonance regions. These predictions serve to indicate important questions concerning the structure of the nucleon, and consideration is given as to how these questions may be answered by means of coincidence experiments.

A model in which the backward ${\pi }^{+}p$ angular distribution is assumed to arise from a sum of direct-channel resonances is compared with the data at intermediate energies. Many as yet undiscovered resonances are assumed to exist as Regge recurrences of experimentally known resonances. The agreement between the results of the model and experiment is qualitatively quite good at angles near the backward direction for incident pion momenta between 2.2 and 5.0 GeV/c. In particular, the position and the shape of the minimum around $u\simeq -0.2\mathrm{}$ ${(\mathrm{G}\mathrm{e}\mathrm{V}/\mathit{c})}^2$ in the differential cross section is correctly obtained. Since a similar minimum has previously been obtained in a model with Regge-pole exchange in the crossed channel, the result of the calculation gives support to the concept of duality at intermediate energies.

We obtain many sum rules for meson-baryon scattering amplitudes considering the quark-quark and the quark-antiquark amplitudes, for the appropriate meson and baryon states. The main differences from earlier work are that mesons are consistently treated as quark-antiquark pairs and not as elementary fields, and that the usual symmetry representation of the states has been taken into account. Further, the assumption that the real part of the amplitude is dominated by quark-quark forces and the imaginary part by quark-antiquark forces yields sum rules connecting these real and imaginary parts for different processes, in consonance with duality requirements.

The contribution of Ne'eman's fifth $\chi$ interaction to the muon-proton cross section is shown to be in disagreement with recent experimental results. This conclusion is based upon the value of $g_{\chi }$ suggested by Ne'eman, the value of $\frac{g_{\chi }}{m_{\chi }}$ consistent with high-energy $p-p$ scattering, and the assumption that the $\chi$ form factors are not appreciably different from the one-photon-exchange form factors. The conclusion is not changed by a reasonable variation of the values of $g_{\chi }$ and $m_{\chi }$.

We make a systematic test of soft-meson-theorem predictions for both elastic and inelastic pseudoscalar-meson-baryon threshold scattering amplitudes. The predictions are obtained by using an extrapolation procedure developed by Fubini and Furlan and by ourselves. Our results give considerable support to a theory of $\mathrm{SU}\left(3\right)\mathrm{}\times \mathrm{SU}\left(3\right)\mathrm{}$ symmetry breaking proposed recently by Gell-Mann, Oakes, and Renner, and imply that, in the absence of symmetry breaking, the mass of the $J^p={\frac{1}{2}}^{+}$ baryon octet would be approximately that of the physical nucleon.

The major purpose of this paper is a description of coherent $\rho$ photoproduction which takes the rather substantial width of the $\rho$ into proper account. The optical-model analysis due to Drell and Trefil is extended to include $\rho$ decay inside the nucleus, as well as the subsequent absorption of the decay pions. The eikonal method is used throughout, and is found to yield compact analytic expressions for the production amplitude. The decay effects produce an appreciable shift of the $\rho$ peak towards lower mass for production in heavy nuclei and at the lower photon energies of current interest (2.7-4.5 GeV). On the whole, the differential cross sections are not significantly affected in either shape or magnitude by the effects arising from $\rho$ decay. In particular, the decay corrections do not appreciably influence the determination via vector dominance of the $\rho$-photon coupling constant.

Finite-energy sum rules with generalized weight functions are discussed with emphasis on methods for obtaining precise determination of high-energy parameters from low-energy data. Regge parameters for $t=0\mathrm{}$ $\pi N$ charge-exchange amplitudes are deduced as an example from a new sum rule.

A determination is made of the constraints which are imposed upon the low-energy ${}_{}{}^3{}_{}{}^{}S_1^{}{}_{}{}^{}-{}_{}{}^3{}_{}{}^{}D_1^{}{}_{}{}^{}$ scattering parameters in order that the $S$ matrix may satisfy the known static deuteron properties. A multichannel effective-range representation is used to derive a relationship between the phase parameters ${\delta }_S$, ${\delta }_D$, and ${\epsilon }_1$ at "low" energies. The relationship is violated by all of the present low-energy phenomenological determinations. This indicates a discrepancy between the existing low-energy $\mathrm{np}$ scattering data and the static deuteron properties, and suggests that low-energy energy-dependent phenomenology should manifestly contain the deuteron constraints.

Total cross sections for the production of single $W$ mesons in electron-positron colliding beams and in the electron scattering experiments have been calculated. If the first type of cross sections are estimated by calculating the simplest lowest-order dominant Feynman graph, one finds that they are remarkably large (∼${10}^{-30\mathrm{}}$ ${\mathrm{cm}}^2$). Indeed, a calculation in the literature which includes all lowest-order contributions apparently confirms this result. These estimates are in striking disagreement with calculations for the related process of neutrino-induced production of single $W$ mesons. These suggest a cross section of ∼${10}^{-37\mathrm{}}$ ${\mathrm{cm}}^2$, a result which is to be expected from a naive power-counting argument. We have calculated the cross sections and have found that they are in fact quite small and of the same order of magnitude as the neutrino-induced cross sections. We present a general gauge-invariance argument which illustrates how almost any trivial error in the calculation can easily lead to errors in the result of at least ${\mathrm{}\left[\right(\mathrm{m}\mathrm{a}\mathrm{s}\mathrm{s}\mathrm{o}\mathrm{f}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{p}\mathrm{r}\mathrm{o}\mathrm{t}\mathrm{o}\mathrm{n})/(\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{positron}\left)\right]}^2$∼${10}^6$. Basically, gauge invariance demands a critical cancellation in the differential cross section when the mass of the exchanged photon ($K^2$) becomes very small. If such a cancellation does not take place (because of some small error), the region around $K^2=0\mathrm{}$ is enormously enhanced by the smallness of the mass of the positron, and large errors are induced in the final result. An examination of the calculations that lead to a large total cross section does indeed show that each violates the constraint of gauge invariance.

A framework is suggested for interpreting processes of the type $a+b\to a+b+\left(n \mathrm{poins}\right)$ at energies from tens to hundreds of GeV. The model predicts, without any adjustable parameters, the observed average transverse momenta of the pions in the entire range, as well as the existence and observed masses of "fire-balls." The advantages of this model over the multi-Regge models is discussed.

A tractable, relativistic theory for the two-nucleon system is constructed. As a starting point, the Bethe-Salpeter (BS) equation is utilized. In order to reduce the BS equation to three dimensions, the Blankenbecler-Sugar method is generalized to include spin-½ particles. An instantaneous-interaction approximation to the BS equation is also investigated, and results similar to those obtained with the Blankenbecler-Sugar method are derived. Finally, as an application, the generalized potential or interaction kernel is approximated to order $g^2$ and compared to the one-pion-exchange potential (OPEP) used in conjunction with the Schrödinger equation. The singlet states are treated numerically, and results are presented which show that for a lab kinetic energy of 400 MeV, the phase shifts calculated from the relativistic theory differ from those calculated by solving the Lippmann-Schwinger or Schrödinger equation with OPEP by about 20%.

A formula relating the level shifts and widths to the meson-nucleus scattering lengths is examined for a momentum-dependent potential of general form, using a simple argument similar to that of Bethe and deHoffmann and Coulomb effective-range theory.

Expressions are given for the electromagnetic final-state interaction contribution to $D$, the triple-product correlation coefficient, in the nuclear $\beta$-decay transitions ½ → ½, $\frac{3}{2}\to \frac{3}{2}$, ${\frac{3}{2}}^{\pm }\to {\frac{1}{2}}^{\pm }$, ${\frac{5}{2}}^{\pm }\to {\frac{3}{2}}^{\pm }$, and $1^{+}$→$0^{+}$ to all orders of $\frac{Z\alpha }{v_e}$ in the Coulomb interaction.

The reaction ${\pi }^{-}p\to \eta n$ has been observed through the decay mode $\eta \to 2\gamma$ at $T_{{\pi }^{-}}=592, 655, 704, 875, 975, 1117, \mathrm{and} 1300$ MeV. The detection apparatus was a cubic array of six steel-plate optical spark chambers that completely surrounded a liquid-hydrogen target. We identified events attributed to the decay of an $\eta$ by the large c.m. opening angle between the two showers generated in the steel plates by the decay photons. We have calculated the total cross section for $\eta$ production, which is proportional to the number of events under the large-angle peak in the opening-angle distribution. The total cross section rises steeply from threshold to a maximum of about 2.4 mb at 650 MeV, and then falls gradually to about 0.66 mb at 1300 MeV. The differential cross section was obtained by taking the coefficients of a Legendre-polynomial fit to the angular distribution of bisectors of selected two-shower events, and converting them to the coefficients of the $\eta$ c.m. angular distribution. The differential cross section is found to be isotropic at 592 MeV, to require terms through $P_2\left({cos\theta }_{\eta }\right)$ between 655 and 975 MeV, and to have a forward peak fitted by terms through $P_3\left({cos\theta }_{\eta }\right)$ at 1117 MeV and through $P_4\left({cos\theta }_{\eta }\right)$ at 1300 MeV. It is suggested that production at threshold is predominantly through an $S$ state, with some $P_1$ and $D_3$ waves entering by 655 MeV. We suggest that all the absorption in the $S_{11}$ $\pi N$ state can be explained by the $\eta$ production.

A general phenomenological method for studying a two-pion mass spectrum is developed; it is shown that, without assumptions about the production mechanism of the two-pion system, no significant upper limit on the $\omega \to {\pi }^{+}{\pi }^{-}$ branching ratio can be set with present-day experiments. In general, a lower limit may be set if a significant effect is seen. This method is applied to data containing more than $8000\omega \to {\pi }^{+}{\pi }^{-}{\pi }^0$ events. The lower-momentum half of the sample, which shows a significant $\omega \to {\pi }^{+}{\pi }^{-}$ signal, was published previously but is here reanalyzed to set a lower limit on the $\omega \to {\pi }^{+}{\pi }^{-}$ branching ratio. The new data at higher momenta show no significant $\omega \to {\pi }^{+}{\pi }^{-}$ signal. The results from the various momenta are shown to be consistent.