General S-Matrix Methods for Calculation of Perturbations on the Strong Interactions

Recently, the authors proposed an on-the-mass-shell, S-matrix method for computing the effects of small perturbations on the masses and coupling constants of strongly interacting particles. In the present paper, the method is generalized to the multichannel case. The use of group-theoretical techniques in reducing the complexity of the method is described in detail

Dynamical Theory for Strong Interactions at Low Momentum Transfers but Arbitrary Energies

Starting from the Mandelstam representation, it is argued on physical grounds that "strips" along the boundaries of the double spectral regions are likely to control the physical elastic scattering amplitude for arbitrarily high energies at small momentum transfers. Pion-pion scattering is used as an illustration to show how the double spectral functions in the nearest strip regions may be calculated, and an attempt is made to formulate an approximate but "complete" set of dynamical equations. The asymptotic behavior of the solutions of these equations is discussed, and it is shown that if the total cross section is to approach a constant at large energies then at low energy the S-dominant ππ solution is inadmissible. A principle of "maximum strength" for strong interactions is proposed, and it is argued that such a principle will allow large low-energy phase shifts only for l<~lmax, where lmax~1

Some general features of the bootstrap theory of octet enhancement

Some general features of the boostrap theory of octet enhancement, which can be understood without detailed calculations, are discussed. These features include: (i) the connection of this theory to the vector-mixing theory of symmetry breaking advocated by Sakurai, and to the tadpole theory of Coleman and Glashow; (ii) an understanding of why it is representations of low multiplicity that are dynamically emphasized in symmetry breaking; (iii) a demonstration that the theory remains valid when a number of assumptions made in previous applications are dropped

S-matrix method for calculation of electromagnetic corrections to strong interactions

We develop an S-matrix method for calculating the effect of small perturbations on a partial-wave amplitude, and in particular, on the positions and residues of bound states. The method is applicable to both nonrelativistic and relativistic problems. It has, as a particular virtue, rapid convergence of the dispersion integrals. Electromagnetic corrections to strong interactions are the main application we have in mind, and modifications useful for handling the infrared divergence that occurs in this case are described in detail

Potential scattering as opposed to scattering associated with independent particles in the S-matrix theory of strong interactions

A definition of a relativistic generalized potential is given, suitable at arbitrary energies for a pair of particles whose elastic scattering amplitude satisfies the Mandelstam representation. It is shown that the generalized potential plays a role in the dynamics analogous to that of the ordinary nonrelativistic potential in a Schrodinger equation and determines the scattering to the same extent. Below the threshold for inelastic processes the generalized potential is real and its energy dependence in the elastic region is expected for certain particle combinations (such as the nucleon-nucleon) to be weak. In such cases one may uniquely define, for use in the Schrodinger equation, an energy-independent ordinary potential that coincides with the potential of Charap and Fubini (Abstr. 1960A01252). In general, when the potential is complex and energy-dependent the dynamical problem involves iteration of an integral equation deduced by Mandelstam (Abstr. 1959A04941). The generalized potential may be decomposed according to range and it is shown that keeping only the long-and medium-range parts, corresponding to transfer of one or two particles, is almost equivalent to the "strip approximation." Finally, a general definition is given of "pure potential scattering" as opposed to scattering associated with "independent" particles, either stable or unstable, and a variety of experimental situations are discussed with respect to this distinction, which is shown to be susceptible to experimental test

Neutrino Opacity. II. Neutrino-Nucleon Interactions

The contribution of neutrino-nucleon interactions to the neutrino opacity of matter is studied, special attention being paid to possible astrophysical applications such as supernova explosions. The results of recent accelerator experiments with high-energy neutrinos are used to show that nonresonant neutrino-nucleon scattering does not make a significant contribution to the neutrino opacity for astrophysically important conditions. The results of deep-mine cosmic-ray studies are then used to show that, (a) there are no resonances in the ν_μ-nucleon and ν̅ _μ-nucleon systems with masses less than 60 BeV (laboratory neutrino energies <2×10^(+3) BeV), and (b) there are no resonances in the ν_(e)-neucleon and ν̅_(e)-nucleon systems with masses less than 7 BeV (laboratory neutrino energies <30 BeV). Neutrino absorption by bound nucleons is also discussed and a sum rule is proved for neutrino capture that is sufficiently accurate for most astrophysical applications. The effect of the exclusion principle on the capture cross sections is described and some applications to specific nuclei are presented. The accelerator experiments with high-energy neutrinos are then used to show that neutrino radioactivity, i.e., nuclear de-excitation by emission of a neutrino-antineutrino pair, is a substantially less important mechanism for stellar energy loss than was suggested by some previous estimates