A nonet-symmetrical and PCAC-violating term is introduced into a Lagrangian with $S{U}_3\otimes S{U}_3$ chiral symmetry and PCAC (hypothesis of partially conserved axial-vector current). Breaking of the nonet symmetry of this term is achieved through the renormalization of the fields. This renormalization is necessary because of the requirement that the kinetic-energy terms of the Lagrangian be correctly normalized after the removal of the tadpole terms. Using as input the decay rate for ${\pi }^0\to 2\gamma$, we predict $\Gamma (\eta \to 2\gamma )=0.41\mathrm{}\pm 0.08$ keV and $\Gamma (X^0\to 2\gamma )=6\mathrm{}\pm 1$ keV. The result for $\Gamma (\eta \to 2\gamma )$ agrees with experiment within 2 standard deviations. It is argued that errors of about 20% should be expected in our calculations, mainly because of the neglect of the effects due to the finite width of the various particles.

The structure of ${\rho }^0-\omega$ interference is discussed. Applications are made to photoproduction of $3\pi$ states, ${\pi }^{+}{\pi }^{-}$ production in electron-positron colliding beams, as well as in other processes, and lepton-pair photoproduction. The various parameters that appear in all these experiments are discussed, and the correlations of the various results are pointed out.

A statistical model for the production of multibody hadronic states by $e^{+}{e}^{-}$ annihilation is discussed. We associate the secondary hadron momentum distributions for colliding-beam processes with the exponentially failling transverse-momentum distributions in hadron-hadron collisions. The consequence of this picture is that at high energies hadron multiplicity rises linearly with c.m. energy, unlike the $\ln s$ behavior for the multiplicity of secondaries in hadron-hadron collisions. If the total annihilation cross section is assumed to have a power falloff $\sim s^{-m}$, the $n$-pion cross sections follow a Poisson distribution with the most probable multiplicity $n_{\pi }=\frac{s^{\frac{1}{2}}}{〈E_{\pi }〉}+3-m$ and $〈E_{\pi }〉\sim 375$ MeV. An alternative statistical model based on jets is also briefly discussed. The storage rings now being constructed or envisaged should easily distinguish between the various possibilities.

A crossing-symmetric pion-nucleon scattering amplitude with Regge behavior is constructed using suitable combinations of beta-function terms. Observed spins, isospins, and widths of resonances in a limited low-energy region are enforced, and the Regge residue functions for high-energy scattering are obtained in terms of these resonance parameters. Forward charge exchange and backward elastic differential cross sections are compared with experiment, and a version of $\rho$ universality is checked.

The $\mathrm{np}\to \mathrm{pn}$ amplitudes are written in simple Veneziano form. Only an $M=0\mathrm{}$ pion pole and an $M=1\mathrm{}$ pion parity doublet with corresponding exchange-degenerate $B$ are considered in our case to give rise to a sharp peak in $\frac{d\sigma }{\mathrm{dt}}$ at $t=0\mathrm{}$, giving qualitative agreement with experimental data.

Combining conserved vector current, partially conserved axial-vector current, and the meson-dominance approximation, we develop a theory of current algebra ($S{U}_3\otimes S{U}_3$) "on the mass shell" by means of Ward-Takahashi-type identities for three-point functions. Models of mixing are presented which are compatible with the spectral-function sum rules derived from broken chiral $S{U}_3\otimes S{U}_3$ symmetry and with CVC to the first order of symmetry breaking. Further, requiring absence of divergences from radiative corrections to pion $\beta$ decays, we deduce an asymptotic sum rule which relates two different types of three-point functions and thus enables us to correlate two different meson processes: radiative and strong decays. In addition to these decay processes, applications are made to electromagnetic form factors of mesons, $K_{l3\mathrm{}}$ form factors, and $\pi \mathrm{}\left(K\right)\mathrm{}\to l\nu \gamma$ decays. Agreement with experiments is very reasonable.

Using the Fierz-Bargmann-Wigner basis, we construct independent covariants, free of kinematic singularities and zeros, for vertices in which two external particles carry arbitrary spins, with one off-mass-shell leg corresponding to a totally symmetric Lorentz tensor. Results for (pseudo) scalars, (pseudo) vectors, and symmetric tensors of second rank are tabulated explicitly.

A previously derived sum rule, based on $U\left(6\right)\mathrm{}\otimes U\left(6\right)\mathrm{}$ equal-time commutation relations for the space components of the electromagnetic current, implies mean polarization asymmetries of greater than 20% throughout most of the inelastic continuum.

An estimate of the strength of the magnetic radiation term in $K^{\pm }\to {\pi }^{\pm }{\pi }^0\gamma$ decays is made by relating it to the ${\tau }^{+}$ decay rate and using the Veneziano model to give the off-mass-shell dependence of the amplitudes. We find this strength to be small ($\left|x_m\right|\le 0.14$) and practically constant in the kinetic-energy range $55 \mathrm{MeV}\le T_{{\pi }^{+}}\le 80 \mathrm{MeV}$. The results are discussed in the light of $K^{\pm }\to {\pi }^{\pm }{\pi }^0\gamma$ data, particularly for possible $\mathrm{CP}$-violating effects.

A previous calculation of the radiative corrections to the rate for pure Fermi $\beta$ decay in the $V-A$ theory, computed to first order in $\alpha$ and to zero order in the lepton momenta, is extended here to include, in addition, the corrections linear in the product of a lepton momentum and a nuclear charge radius. These additional contributions are shown to modify the Coulomb correction to the positron wave function to account for the finite distribution of electric and isotopic charge within the nucleus. They are evaluated and taken together with the other electromagnetic corrections, the origin of which are reviewed in the text, to reassess the question of the universality of the weak vector coupling constant. The conclusions obtained, although basically in agreement with the results of others, differ in detail from previous surveys of universality, generally in a direction to strengthen the concept of universality in the sense of Cabibbo.

Starting from the equal-time commutator of the vector currents and the assumption that the contributions from "exotic channels" are small, we find bounds on the asymptotic behaviors of various form factors. For instance, the pion electromagnetic form factor and both of the $K_{l3\mathrm{}}$ form factors are found to be bounded by $\frac{1}{\surd \mathrm{}\left|t\right|\mathrm{}}$ as $\mathrm{}\left|t\right|\mathrm{}\to \infty$. Implications of this result for $K_{l3\mathrm{}}$ decay are analyzed.

The electroproduction of $\rho$, $\omega$, and $\phi$ 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 $0^{\pm }$, $1^{\pm }$) dominates the $t$ channel in some kinematic region. The extension to the production of a $2\pi$ continuum is straightforward. Vector-meson and $2\pi$ production by neutrinos is also treated.

A phenomenological amplitude for proton Compton scattering is obtained, and fits are made to the differential cross-section data. The amplitude is used to calculate the cross sections for the Compton scattering of polarized photons and the polarization of the recoil proton. It is found that the polarized-photon cross sections are sensitive to the amount of $P_{11}$ resonance in the scattering amplitude.

Cross sections for pion production were calculated using several different chiral-dynamics Lagrangians including those of Schwinger and Weinberg. In order to compare the results with cross sections above threshold all tree diagrams were retained and integrations over final state variables were performed by a Monte Carlo method. A model in which the symmetry-breaking term transforms as a rank-2 chiral tensor was found to give the best fit to the total cross-section data for incident pion energies of less than 330 MeV, but none of the models gave good fits to the differential cross-section data.

An analysis of the recently measured photon-proton total cross sections is performed. Smooth fits to the cross sections are obtained and used to calculate, by means of the forward dispersion relation, the real part of the spin-averaged forward amplitude. The resulting predictions for the real part are given. At high energies, the fits to the present total cross-section data, together with the calculated real part, suggest the presence in the high-energy behavoir of an extra real constant in addition to what one would have predicted from Regge theory and the high-energy behavior of the imaginary part. This extra real constant, which is consistent in sign and magnitude with the Thomson limit, $-\frac{\alpha }{M_N}$, could correspond to a fixed pole at $J=0\mathrm{}$ in Regge-pole language. Possible ways to test the forward dispersion relation are discussed.

A model is constructed as an alternative to, and for examination of, various extrapolation procedures used in determinations of $\pi \pi$ phase shifts from the reaction $\pi +N\to \pi +\pi +N$. This model is similar to that suggested by Ross and Kane in that it incorporates absorption effects approximately.

Interference effects in the leptonic decay modes of photoproduced $\rho$, $\omega$, and $\varphi$ mesons are considered. Two experimental methods for determining the relative phase angles of the final-state muons are discussed. The phase-angle difference between the $\rho$ and $\omega$ is estimated from existing data and appears to be in disagreement with the value of 0°.

The Dalitz plot density of $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ is examined. We find the asymmetry on the ${\pi }^{\pm }$ energies to be $A=\frac{(N^{+}-N^{-})}{(N^{+}+N^{-})}=-0.014\mathrm{}\pm 0.030$, where $N^{\pm }$ is the number of events for which $T_{\mp }>T_{\mp }$. The density is well fitted with a linear dependence on $T_0:{\mathrm{}\left|M\right|\mathrm{}}^2\propto 1+2\alpha \left[\right(\frac{3T_0}{Q})-1]$, with $\alpha =-0.47\mathrm{}\pm 0.04$.

Electrons have been scattered inelastically from a hydrocarbon target containing protons polarized normal to the scattering plane. Scattered electrons with energies corresponding to the production of the $\Delta \mathrm{}\left(1236\right)\mathrm{}$, $N\left(1512\right)\mathrm{}$, and $N\left(1688\right)\mathrm{}$ pion-nucleon resonances were observed. A search was made for changes in the cross section as the target polarization was reversed. Any changes would have been evidence of a violation of time-reversal invariance in the electromagnetic interactions of the hadrons. No such changes were observed. With the maximum time-reversal-violating effect possible, the asymmetry would be 10 times the upper limit of this experiment. Early attempts at a coincidence-polarization experiment are described in an appendix.

The energy spectrum of the decay pions in ${\tau }^{+}$ decay was obtained from a sample of 17 898 events. It is found that the spectrum is adequately fitted by a squared matrix element of linear form, ${\mathrm{}\left|M\right|\mathrm{}}^2\propto 1+{\alpha }_{\tau }\times \left(\frac{M_{K}Q}{{m_{\pi }}^2}\right)Y$, with ${\alpha }_{\tau }=0.131\mathrm{}\pm 0.008$. No evidence for $\mathrm{CP}$ noninvariance is found for ${\tau }^{\pm }$ decays. A significant violation of the $\Delta I=\frac{1}{2}$ rule is observed for $K^{+}\to 3\pi$ decays. Comparison with several theoretical models for $K\to 3\pi$ decays shows fair agreement between experiment and theory.