Analyticity Constraints on Unequal-Mass Regge Formulas

A Regge-pole formula is derived for the elastic scattering of two unequal-mass particles that combines desirable l-plane analytic properties (i.e., a simple pole at l=α in the right-half l plane) and Mandelstam analyticity. It is verified that such a formula possesses the standard asymptotic Regge behavior u^(α(s)) even in regions where the cosine of the scattering angle of the relevant crossed reaction may be bounded. The simultaneous requirements of I-plane and Mandelstam analyticity enforce important constraints, and the consistency of these constraints is studied. These considerations lead to the appearance of a "background" term proportional asymptotically to u^(α(0)-1) which has no analog in the equal-mass problem. We also conclude that a necessary condition for consistency is α(∞)<0

Accuracy of Measurement for Counting and Intensity-Correlation Experiments

A quantum-mechanical analysis is made of the experimental accuracy to be expected for particle-counting and intensity-correlation experiments. The mean-square fluctuation for an ensemble, consisting of a large number of experiments each conducted over a time interval T, is calculated

Light-cone behavior of the pion Bethe-Salpeter wave function in the ladder model

The Bethe-Salpeter wave function χ(q^ν+P^ν, q^ν) for two spin-½ quarks bound by the exchange of a scalar meson is examined in the ladder model. We seek the behavior of χ as the squared momentum, (q+P)^2, on one leg becomes infinite while the squared momentum, q^2, on the other leg remains fixed. This behavior is investigated by making a Wick rotation, expanding χ in partial-wave amplitudes χ^i_J(q^2) of the group O(4), and then looking for the rightmost poles of χ^i_J(q^2) in the complex J plane. Our results verify (in the ladder model) the useful hypothesis that the locations of these poles are independent of q^2 and can thus be computed in the q^2→∞ limit by using conformal invariance

Large-Q^2 behavior of the pion electromagnetic form factor

We study the large-Q^2 behavior of the electromagnetic form factor of the pion, which is viewed as a quark-antiquark bound state in a (nongauge) quantum field theory. When the pion's Bethe-Salpeter wave function is expanded in O(4) partial waves, it is found that the information needed about the partial-wave amplitudes is their scaling behavior at large momentum and the locations of their poles in the complex J plane. This information is determined by using the operator-product expansion, conformal invariance at short distances, and a regularity property that holds at least in the ladder model. The resulting behavior of the form factor is roughly F(Q^2)~(Q^2)^(-1), with corrections due to anomalous dimensions

On the analysis of nucleon-nucleon scattering experiments

A method of perturbation calculation, especially adapted to nucleon-nucleon scattering problems, is described. Any contribution to the energy of the system which is relatively small where the nuclear potential is large may be treated as the perturbation. Two principal examples are discussed. (1) Energy as the perturbation: An expansion of the phase shifts in powers of the energy is written down which extends earlier results of Schwinger, Blatt, and Jackson. (2) The Coulomb field as the perturbation in the proton-proton problem: Expansions are given which relate the nuclear phase shifts in a combined nuclear and Coulomb field to the corresponding phase shifts for a purely nuclear problem. Attention is confined to central forces throughout

Galilean and Dynamical Invariance of Entanglement in Particle Scattering

Particle systems admit a variety of tensor product structures (TPSs) depending on the algebra of observables chosen for analysis. Global symmetry transformations and dynamical transformations may be resolved into local unitary operators with respect to certain TPSs and not with respect to others. Symmetry-invariant and dynamical-invariant TPSs are defined and various notions of entanglement are considered for scattering states.Comment: 4 pages, no figures; v.3 has typos corrected, a new reference, and a revised conclusio

Causality conditions and dispersion relations. I. Boson fields

The dispersion relations of Kramers and Kronig as generalized for charged and neutral Bose particles with finite rest mass are derived in a new way using the formalism of quantum field theory. The alternative forms of dispersion relations obtained by making various assumptions on the high-frequency limit of total cross sections are used to obtain information about the high-frequency behavior of the total cross section for the scattering of γ rays by electrons

Note on zero-zero transitions

Zero-zero nuclear transitions have been suggested by Sachs(1) as an explanation of long lived isomers. He computed the energy spectra and transition probabilities for two-electron and two-quantum emissions. Stimulated by preliminary results of experiments by Goldhaber, Muehlhause, and Turkel(2) on the isomeric transition in Ir192 (mean life 2.16 min., energy 58 kev), which shows a continuous γ-ray spectrum in addition to conversion electrons, we have computed the γ-ray energy spectrum and lifetimes for zero-zero transitions in which one electron and one quantum are emitted. For comparison, the lifetime for the transition og→og (or ou→ou) is computed by direct emission of an electron. The analogous transition in the case og→ou is strictly forbidden

The saga of the SI Jelly Donut (continued)

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