Sum rules of the preceding paper together with appropriate $\mathrm{SW}\left(2\right)\mathrm{}$ and broken $\mathrm{SU}\left(3\right)\mathrm{}$ relations have been solved numerically in the pole-dominance approximation. In this way, we compute all relevant parameters entering in the theory, including $\eta -X$ mixing effects. As applications, we calculate $\eta \to 2\gamma$, $X\to \eta 2\pi$, $X\to 2\gamma$, and $X\to 2\pi \gamma$ decay rates.

We investigate the general properties of the Gell-Mann model for chiral $U\left(3\right)\mathrm{}\otimes U\left(3\right)\mathrm{}$ symmetry breaking. From a study of the two-point functions, we find that the symmetry-breaking parameters cannot assume arbitrary values, but must be confined in specified domains. The boundaries of these domains are related to several interesting subgroup symmetries. We present arguments to show that one must have essential singularities at those values of the symmetry-breaking parameter which correspond to subgroup symmetries realized via the emergence of zero-mass bosons. In a suitable singularity-free range of physical interest, we next discuss the possibility of continuous transitions between different symmetry subgroups, and show how, with the use of a variational principle, one can obtain some mass formulas and relations between other physically relevant quantities in a nonperturbative manner. In particular, the relation obtained by Gell-Mann, Oakes, and Renner for the symmetry-breaking parameter is obtained naturally in this manner. Also, it is shown that this formalism requires the existence of scalar mesons.

By correlating recent experimental results on ${\pi }^0$ and ${\pi }^{+}$ photoproduction at backward angles with results on ${\pi }^{-}p\to p{\rho }^{-}$ at the same angles, it is found that any explanation of the three processes in terms of Regge poles must involve at least two isospin-½ trajectories. Furthermore, the two trajectories must be almost degenerate. Such a solution makes definite predictions about other processes which can be checked by experiments.

The explicit expressions for spin-$\frac{3}{2}$ density-matrix elements are obtained, and a straightforward way to get the decay distribution of a spin-$\frac{3}{2}$ particle is given. The photoproduction $\gamma +p\to N^{*++}+{\pi }^{-}$ and the decay $N^{*++}\to p+{\pi }^{+}$ are considered on the assumption of one axial-vector-meson exchange. The density-matrix elements of $N^{*++}$ contain one parameter which is the ratio of two form factors, and they are compared with the recent experimental data from DESY. A special case of the linearly polarized photon is also considered, and the decay distribution of $N^{*}$ turns out to be close to the Sakurai-Stodolsky distribution near the threshold. Several other models are also considered and compared with the axial-vector-meson-exchange model.

We present the final results of a measurement of the decay parameters for ${\Sigma }^{\pm }\to n+{\pi }^{\pm }$. We find ${\alpha }_{-}=-0.134\mathrm{}\pm 0.034$ and ${\alpha }_{+}=0.037\mathrm{}\pm 0.049$ Defining $\phi$ by $\beta ={(1-{\alpha }^2)}^{\frac{1}{2}}sin\phi$, $\gamma ={(1-{\alpha }^2)}^{\frac{1}{2}}cos\phi$, we find ${\phi }_{-}=(-5\mathrm{}\pm 23)°$ and ${\phi }_{+}=(176\mathrm{}\pm 24)°$.

${\overline{K}}^{0}n$, $\Lambda {\pi }^0$, and ${\Sigma }^0{\pi }^0$ final-state cross sections and $\Lambda {\pi }^0$ and ${\Sigma }^0{\pi }^0$ polarizations are obtained in $K^{-}p$ interactions, for $P_{K^{-}}$ in the range 350-430 MeV/c, near the $\Lambda \mathrm{}\left(1520\right)\mathrm{}$ resonance. Two fits to the partial-wave amplitudes have been found, both assuming a standard Breit-Wigner amplitude for the $\Lambda \mathrm{}\left(1520\right)\mathrm{}$ resonance and a constant-scattering-length $D_{\frac{3}{2}}$ isospin-1 amplitude, but differing in their treatment of the $S$- and $P$-wave backgrounds. One method used a constant $K$ matrix, the other a momentum-dependent effective-range expansion for the inverse of the $K$ matrix. From the fitted partial waves, an upper limit of 10% is set for an isospin mixing between the $\Lambda {\pi }^0$ and ${\Sigma }^0{\pi }^0$ amplitudes.

The differential and total cross sections for the reaction $n+p\to d+{\pi }^0$ were measured for neutron kinetic energies between threshold (275 MeV) and 700 MeV. Results are presented based on 90 000 events. A comparison is made with existing data for $p+p\to d+{\pi }^{+}$ to test the prediction of charge independence, $d\sigma (np\to d{\pi }^0)=\frac{1}{2}d\sigma (pp\to d{\pi }^{+})$, at the same c.m. energy and angle. No evidence for a violation is seen. Limits of a few percent are placed on the real part of certain amplitudes for isospin-nonconserving transitions from a study of the symmetry of the angular distributions about ${\theta }^{*}=90\mathrm{}°$.

We present a study of the $3\pi$ system in $\mathrm{pp}\to \mathrm{pp}{\pi }^{+}{\pi }^{-}{\pi }^0$ at 6.6 GeV/c. Both $\eta \mathrm{}\left(549\right)\mathrm{}$ and $\omega \mathrm{}\left(783\right)\mathrm{}$ production are observed. The Dalitz plot is displayed for the $\mathrm{pp}\omega$ events, in addition to several other experimental distributions. There is no evidence for $p\omega$ resonances. The $\mathrm{pp}\omega$ events have been assigned separately to the six possible multiperipheral diagrams on the basis of criteria in the four-momentum transfers and c.m. longitudinal momenta, respectively. In addition, we discuss the means of achieving an effective diagram separation.

It has been suggested that vector-meson-dominance comparisons of charged-pion photoproduction by polarized photons and vector production by pions be made in the frame where the vector production by pions be made in the frame where the vector-meson density matrix is diagonal (the Donohue-Högaasen frame). This suggestion is investigated in detail, and it is found that despite the empirical success, the basic idea of vector-meson dominance, that is, a smooth extrapolation in mass, is violated. The suggestion implies that two eigenvalues of the vector-meson density matrix possess a smooth extrapolation in mass to the photon cross sections. But the well-known tendency of eigenvalues to repel each other, plus the experimental fact that $\rho$-meson production is mainly longitudinal, forces the extrapolation to be violent rather than smooth. The behavior of the eigenvalues is illustrated using the Born model of Cho and Sakurai and a variation thereof. It is concluded, although not proved rigorously, that the apparent success of the comparison using the diagonal frame cannot be used as evidence for the vector-meson-dominance hypothesis.

We have studied the time distribution of the neutral $K$ decays in 53 hydrogen bubble-chamber events of the type $K^{-}p\to {\overline{K}}^{0}n$, neutral $K\to {\pi }^{+}{\pi }^{-}{\pi }^0$. In 20 of these events, the neutral $K$ decay occurs less than four $K_S$ mean lives after production. We find no evidence for a $\mathrm{CP}$-violating amplitude. We point out that a combination of experiments of our type, using an initial ${\overline{K}}^0$ state, with experiments using an initial $K^0$ will provide much more information than either type of experiment alone. This is demonstrated when we combine our results with those of an earlier experiment based on 18 $K^0$ events.

Final states with a ${\Xi }^{-}$ hyperon have been studied in 5.5-GeV/c $K^{-}p$ interactions. Center-of-mass production angular distributions for the ${\Xi }^{-}$ have a peak in the beam direction, while those for the $K^{+}$ or $K^0$ meson peak in the opposite direction. Approximately half of the observed events involve the ${\Xi }^{*}\mathrm{}\left(1530\right)\mathrm{}$ or $K^{*}\mathrm{}\left(890\right)\mathrm{}$ resonances. The four- and five-body final states show production of the ${\Xi }^{*}\mathrm{}\left(1930\right)\mathrm{}$ in the ${\Xi }^{-}{\pi }^{+,0\mathrm{}}$ mass spectrum and a narrow peak at 2295 MeV in the ${\Xi }^{-}{\pi }^{+}{\pi }^{-}$ mass spectrum. The mass of the ${\Xi }^{-}$ hyperon is 1321.9±0.5 MeV as determined from 195 ${\Xi }^{-}$ decays with a visible $\Lambda$ decay, assuming a $\Lambda$-hyperon mass of 1115.58 MeV.

The cross section for photoproduction of single ${\pi }^{+}$ from hydrogen has been measured at laboratory angles of 110°, 127.5° and 152°, between 0.9- and 3.2-GeV incident photon energy. Measurements have been made with approximately 15% statistical accuracy at about 40 photon energies at each angle. The results agree well with the previous Caltech data of Thiessen. The cross section shows a rapid drop with increasing energy with superimposed bumps or shoulders corresponding to the $N\left(1688\right)\mathrm{}$, $\Delta \mathrm{}\left(1920\right)\mathrm{}$, and $\Delta \mathrm{}\left(2420\right)\mathrm{}$. A shallow minimum is observed at the $N\left(2190\right)\mathrm{}$ resonance.

The branching ratios of the decay of the ${\eta }^0$ meson into neutral products have been measured. The ${\eta }^0$ is produced in the reaction ${\pi }^{-}p\to {\eta }^0+n$, and the decay products are observed as $\gamma$ rays by a system of optical spark chambers and counters in nearly $4\pi$ geometry. Emphasis was placed on examining evidence for the decay mode ${\eta }^0\to {\pi }^0\gamma \gamma (\to 4\gamma )$. Measurement of the neutron time of flight in the production process, together with detailed measurement and kinematical analysis of the pictures showing four $\gamma$ rays, enables us to test each event for consistency with such a decay mode, and also for the "background" process ${\pi }^{-}+p\to 2{\pi }^0+n$. From what is essentially a comparison of the observed rates for these processes, we obtain the upper limit for $\frac{({\eta }^0\to {\pi }^0\gamma \gamma )}{({\eta }^0\to \mathrm{all}\mathrm{neutrals})}\le 7\%$ (90% confidence level), a result which is relatively insensitive to estimates of the efficiency of the detecting system. We also obtain $\frac{({\eta }^0\to 3{\pi }^0)}{({\eta }^0\to 2\gamma )}=0.75\mathrm{}\pm 0.09$.

Total cross sections of $K^{\pm }$ and $\overline{p}$ on hydrogen and deuterium were measured in a standard transmission experiment with statistical precisions of the order of 0.05-0.25%. Data were obtained in the momentum range 2.45-3.30 GeV/c for $K^{-}N$, 1.55-3.30 GeV/c for $K^{+}N$, and 1.00-3.30 GeV/c for $\overline{p}N$. Cross sections for the pure isotopic spin states are obtained using a procedure for the deuterium data which takes into account Fermi motion and the shadow effect. Evidence for the following new structures was found: ${Y_1}^{*}\mathrm{}\left(2455\right)\mathrm{}$, ${Y_1}^{*}\mathrm{}\left(2620\right)\mathrm{}$, ${Y_0}^{*}\mathrm{}\left(2585\right)\mathrm{}$, ${Z_1}^{*}\mathrm{}\left(2150\right)\mathrm{}$, ${Z_1}^{*}\mathrm{}\left(2500\right)\mathrm{}$, ${{\pi }_1}^{*}\mathrm{}\left(2290\right)\mathrm{}$, ${{\pi }_1}^{*}\mathrm{}\left(2350\right)\mathrm{}$, and ${{\pi }_0}^{*}\mathrm{}\left(2375\right)\mathrm{}$.

Total cross sections of ${\pi }^{\pm }$ and $K^{\pm }$ on hydrogen and deuterium were measured in a standard transmission experiment in the momentum range 0.9-2.4 GeV/c at 50-MeV/c intervals with statistical precisions in the range of 0.2-1.0%. Cross sections for pure isotopic spin states were obtained using a procedure for the deuterium data which takes into account Fermi motion and the shadow effect. This procedure was tested on the pion data before applying it to kaons. Evidence for the following new structures was found: ${Y_0}^{*}\mathrm{}\left(2107\right)\mathrm{}$, ${Y_0}^{*}\mathrm{}\left(2344\right)\mathrm{}$, ${Y_1}^{*}\mathrm{}\left(1912\right)\mathrm{}$, ${Y_1}^{*}\mathrm{}\left(2025\right)\mathrm{}$, ${Y_1}^{*}\mathrm{}\left(2255\right)\mathrm{}$, ${Z_0}^{*}\mathrm{}\left(1780\right)\mathrm{}$, and ${Z_1}^{*}\mathrm{}\left(1900\right)\mathrm{}$.

Direct measurements of all two-nucleon interactions of stopping $K^{-}$ mesons in deuterium have been made in a bubble-chamber experiment. The production rates relative to the single-nucleon interactions of $K^{-}$ are $R(K^{-}d\to {\Sigma }^{-}p)=(0.505\mathrm{}\pm 0.036)\%$, $R(K^{-}d\to {\Sigma }^{0}n)=(0.337\mathrm{}\pm 0.070)\%$, and $R(K^{-}d\to \Lambda n)=(0.387\mathrm{}\pm 0.041)\%$. The ratio of the rates $R(K^{-}d\to {\Sigma }^{-}p)$ and $R(K^{-}d\to {\Sigma }^{0}n)$ is consistent with the prediction of isotopic-spin invariance for the strong interactions. The total two-nucleon production rate is (1.22±0.09)% and is compared with current theoretical predictions.

Direct measurements were made of neutron-proton elastic scattering differential cross sections at high energies. A neutron beam with a continuous momentum spectrum between 1.2 and 6.7 GeV/c was scattered off a liquid hydrogen target, and spark chambers were used to determine the neutron scattering angle and, in a proton spectrometer, to measure the momentum and scattering angle of the recoil proton. Differential cross sections are presented over the incident neutron momentum range in intervals of the order of 0.5-GeV/c wide. The cross sections have an exponential peak in the forward direction and then flatten and become isotropic about the 90° c.m. scattering angle. At larger angles, the cross sections again rise towards the expected charge-exchange peak, which was not within the range of this experiment. There is little evidence of any other structure in the cross section. Values are presented for the slope of the diffraction peak, and comparisons are made between these slopes, and the 90° c.m. cross sections, for $\mathrm{pp}$ and $\mathrm{np}$ elastic scattering. The results presented here differ from those previously reported because of an error in a Monte Carlo calculation and in the availability of improved data on the real part of the $\mathrm{np}$ elastic scattering amplitude. At 5 GeV/c, a direct comparison of $\mathrm{pp}$ and $\mathrm{np}$ data allows the $I=0\mathrm{}$ differential cross section to be extracted. The $\mathrm{np}$ data have been fitted in powers of ${cos\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}$ for $\left|{cos\theta }_{\mathrm{c}.\mathrm{m}.\mathrm{}}\right|<\mathrm{}0.8\mathrm{}$ for each energy range.