The hadronic decays of hyperons are discussed in the context of broken chiral symmetry, the breaking being introduced according to the prescription of Gell-Mann, Oakes, and Renner. The corrections due to symmetry breaking lead to contributions to the $p$-wave amplitudes, giving better agreement with the experimental data, whereas the $s$-wave amplitudes remain almost unchanged.

We have calculated the radiative corrections to the Dalitz plot for ${K_{\mu 3}}^{\pm }$ and ${K_{\mu 3}}^0$ decays, assuming a phenomenological weak $K-\pi$ vertex and using perturbation theory. The answer depends logarithmically on a cutoff. We have evaluated all terms which contribute to order $\alpha$ analytically, without any approximations concerning the smallness of the muon mass or the "real inner bremsstrahlung." Thus, the dependence on the parameter $\xi$ (the ratio of the form factor $\frac{f_{-}}{f_{+}}$) is exact. The radiative corrections to the ${K_{\mu 3}}^0$ Dalitz plot, muon spectrum, and lifetime average around 2% over most of their respective ranges and are not especially sensitive to the cutoff. The radiative corrections to ${K_{\mu 3}}^{\pm }$ decays is a fraction of a percent over most of the Dalitz plot and is sensitive to the cutoff. The radiative correction to the $\Delta I=\frac{1}{2}$ rule prediction for the ratio of the charged and neutral decay rates is approximately 2%. The final-state Coulomb correction accounts for most of this numerical result, the rest being model-dependent noise.

The $\mathrm{CP}$-conserving decay mode ${\pi }^{+}{\pi }^{-}\gamma$ of the ${K_2}^0$ is calculated in the pion-pole model (with $\eta -{\pi }^0$ mixing) with the strong-interaction part of the decay amplitude described by the Veneziano model. Because of sign ambiguities introduced by a model of physical $\mathrm{PVV}$ couplings (which fits both ${\pi }^0\to 2\gamma$ and $\eta \to 2\gamma$ rates) and the unknown sign of $\eta -{\pi }^0$ mixing relative to the weak $K-\pi$ mixing, values of the branching ratio $r\left(\frac{({K_2}^0\to {\pi }^{+}{\pi }^{-}\gamma )}{({K_2}^0\to \mathrm{all}\mathrm{modes})}\right)$ are obtained ranging from 7.6×${10}^{-5\mathrm{}}$ to 3.1×${10}^{-4\mathrm{}}$, but all are consistent with the present experimental upper limit of 4×${10}^{-4\mathrm{}}$.

The $\pi -\pi$ amplitude in the low-energy region is parametrized in a crossing-symmetric way as the sum of the $\rho$ and $f^0$ resonance poles plus a polynomial background. The parametrization is flexible and capable of producing amplitudes having quite different features in the energy region below 1 GeV. The parameters are then varied so as to minimize the deviation from elastic unitarity on a set of closely spaced points. In addition, negative-moment finite-energy sum rules are used to connect the low-energy region with assumed Regge asymptotic behavior in the $I=1, 2$ amplitudes. With the mass and width of the $f^0$, the mass of the $\rho$, and the slope of the $\rho$ trajectory fixed, an approximate solution satisfying the constraints is found, yielding a $\rho$ width of 80± 30 MeV. The solution displays the usual characteristics of the low-energy $\pi -\pi$ amplitudes suggested by other analyses, namely, small scattering lengths and a large $I=0\mathrm{}$ $S$-wave phase shift near the mass of the $\rho$. This resonantlike behavior is found without introducing an $S$-wave pole in the parametrization, while the small scattering lengths are obtained as results of the numerical bootstrap, although no current-algebra constraints are included. Our proposed solution is also found to satisfy various inequalities proposed by Martin for the ${\pi }^0-{\pi }^0$ scattering amplitude.

Compton scattering of pions is investigated in the Veneziano model. It is shown that the removal of parity doubling causes undersirable features, such as inconsistency with the low-energy theorem or the appearance of an unwanted pole in the energy variable ($s=0\mathrm{}$) in one of the amplitudes. If we ignore the problem of parity doubling or overlook the pole at $s=0\mathrm{}$, we get a sum rule which closely resembles that obtained from superconvergence relations or the quark model, or current algebra.

The relation between the processes $\gamma +N\to \pi +N$ and $\pi +N\to \rho +N$, according to the vector-dominance model (VDM), is reexamined. The VDM is defined in terms of the behavior of the invariants in the matrix elements of the vector current. The consequences of the VDM, and assumptions about asymptotic properties, for measurable quantities are discussed. The inability of the VDM to account for the results of polarized-photoproduction experiments is confirmed. An appendix provides a detailed discussion of the relation between invariants and density matrix elements in various frames.

It is shown that the suppression of $\Delta S=1\mathrm{}$ leptonic decay modes of hadrons relative to the $\Delta S=0\mathrm{}$ modes can be successfully explained within the framework of the universal Fermi interaction by suitable assumptions regarding hadron states and weak hadron currents in the presence of symmetry-breaking effects.

We have measured the differential cross section for elastic scattering of $K^{-}$ mesons on ${\mathrm{He}}^4$ in the momentum intervals 100-150 MeV/c and 150-200 MeV/c, and the total inelastic cross section in the interval 150-200 MeV/c. We have calculated scattering lengths for the $K^{-}$-${\mathrm{He}}^4$ system using the zero-effective-range approximation. The results for the scattering lengths have been compared with other experiments, including a measurement of $K^{-}$-mesonic x rays in ${\mathrm{He}}^4$. Our results are in disagreement with the latter.

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.