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

Interview with Steven C. Frautschi

An interview in two sessions with Steven C. Frautschi, professor of theoretical physics in the Division of Physics, Mathematics, and Astronomy. Dr. Frautschi discusses his family background and his early years in Madison, Wisconsin. He recalls matriculating, age 16, at Harvard, where his advisor was J. H. van Vleck; graduating in 1954 with an AB in physics, entering Stanford after a year spent bicycling around Europe on a Harvard traveling fellowship. At Stanford, under Sidney Drell, he and James Bjorken worked out the theory for an experiment being conducted by Nobel laureate Burton Richter. After receiving his PhD in 1958 he spent a postdoctoral year at Hideki Yukawa's Institute for Theoretical Physics in Kyoto, followed by a two-year postdoctoral stint at UC Berkeley, where he worked with Geoffrey Chew on Chew's "bootstrap" theory of strongly interacting particles and with Stanley Mandelstam on Regge poles. To Cornell in 1961. Invited to Caltech by Murray Gell-Mann; 1962 paper with Gell-Mann and Fred Zachariasen on Regge poles. Joins Caltech faculty as an assistant professor in the fall of 1962. Comments on the teaching of physics at Caltech in the early sixties; Gell-Mann and Richard P. Feynman; Gell-Mann's interest in linguistics. Discusses his "statistical bootstrap" theory of the early 1970s for newly discovered strongly interacting particles. Discusses his 1982 paper in Science on the entropy of the observable universe. Discusses his work for The Mechanical Universe television project. Nine years as executive officer for physics, beginning in 1988; comments on the physics core curriculum and "take-home" labs. Comments on his work as master of student houses beginning in 1997, on the gradual "professionalization" of student affairs, and on his encouragement of the performing arts at Caltech

Regge poles in π-π scattering

The connection between Regge poles, bound states and resonances, and asymptotic behavior in momentum transfer is reviewed within the framework of the analytically continued S matrix, and a convergent iteration procedure is given for calculating the position and residue of a Regge pole in terms of a given (generalized) potential. By examining the long-range potential in the ππ system, it is inferred that Regge poles should appear in the I=0 and I=1 states, and that the latter pole may be responsible for the ρ meson while the former may well dominate high-energy behavior at low-momentum transfer in the crossed channels. The connection of this possibility with forward coherent (diffraction) scattering in general is explored, and a number of experimental predictions are emphasized. Finally it is shown that the short-range forces due to exchange of 4, 6, ... pions are likely to be repulsive and must be included in some form if a consistent solution is to be achieved

Octet enhancement in the B and Δ supermultiplets

The bootstrap theory of octet enhancement is described in general, and applied in particular to strong and electromagnetic mass splittings within the JP=1/2+ baryon octet and J=3/2+ decuplet. The results are in good agreement with experiment

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