D. J. Ernst

(j, 0) ⊕ (0, j) COVARIANT SPINORS AND CAUSAL PROPAGATORS BASED ON WEINBERG FORMALISM

A pragmatic approach to constructing a covariant phenomenology of the interactions of composite high-spin hadrons is proposed. Because there are no known wave equations without significant problems, we propose to construct the phenomenology without explicit reference to a wave equation. This is done by constructing the individual pieces of a perturbation theory and then utilizing the perturbation theory as the definition of the phenomenology. The covariant spinors for a particle of spin j are constructed directly from Lorentz invariance and the basic precepts of quantum mechanics following the logic put forth originally by Wigner and developed by Weinberg. Explicit expressions for the spinors are derived for j=1, 3/2 and 2. Field operators are constructed from the spinors and the free-particle propagator is derived from the vacuum expectation value of the time-order product of the field operators. A few simple examples of model interactions are given. This provides all the necessary ingredients to treat at a phenomenological level and in a covariant manner particles of arbitrary spin.

PARADOXICAL KINEMATIC ACAUSALITY IN WEINBERG’S EQUATIONS FOR MASSLESS PARTICLES OF ARBITRARY SPIN

Weinberg’s equations for massless free particles of arbitrary spin are found to have acausal solutions. On the other hand, the m→0 limit of Joos-Weinberg’s finite-mass wave equations satisfied by (j, 0)⊕(0, j) j) covariant spinors are free from all kinematic acausality. This paradoxical situation is resolved and corrected by carefully studying the transition from the classical group theoretical arguments to quantum mechanically interpreted equations.

New arbitrary spin wave equations for (j,0)+(0,j) matter fields without kinematic acausality and constraints

Abstract Following Weinberg, we note that for arbitrary spin the covariant spinors and the field operators can be constructed directly from Lorentz covariance. The propagator may then be defined as the vacuum expectation value of the time-ordered product of the field operators. We produce a new arbitrary-spin wave equation by inverting this propagator. The equation so produced, even at the free-particle level, is nonlocal. Explicit results for j = 1 are given and we have checked the procedure for j = 3 2 and 2 The equation does not support kinematically anomalous solutions, as do Weinbergs equations. In addition, unlike Weinbergs equations for integral spins, it has the particle and antiparticle spinors as its solutions for both fermions and bosons. No constraint equations, as required in the Rarita-Schwinger/Bargmann-Wigner formalism, are needed.

Crossing symmetric solution of the Chew-Low equation

Abstract An N / D dispersion theory is developed which solves crossing symmetric Low equations. The method is used to generate crossing symmetric solutions to the Chew-Low model. We show why the technique originally proposed by Chew and Low was incapable of producing solutions.

Anomalous electron-pair production in π−p collisions

Abstract Anomalous e + e − pairs with invariant mass 0.2 ⩽ M ⩽ 0.7 GeV / c 2 have been observed in the collision of pions with protons at a momentum p π ⋍16 GeV /c . Conventional hadronic mechanisms have been unable to reproduce the qualitative features of the observed spectra. The two-photon mechanism for pair production is evaluated in a semi-classical limit. The resulting differential cross sections as a function of the invariant mass, Feynman x , and transverse momentum of the pair are in reasonable quantitative agreement with the data. The dominant contribution to the pair amplitude arises from the magnetic spin-flip term of the proton current. These anomalous lepton pairs are thus consistent with an ab initio calculation of the two-photon mechanism.

Dispersive effects in low energy pion-nucleus scattering

Abstract Dispersive effects on intermediate nucleons and deltas in the pion-nucleon scattering amplitude are shown to be very important for low energy ( T π ⩽80 MeV) pion-nucleus reactions. The inclusion of this interaction in comparison with familiar three-body approaches is shown to alter the predicted differential cross sections of a first-order optical potential by more than an order of magnitude and total cross sections by more than a factor of four. In the presence of a second-order potential which incorporates the effect of pion true absorption, differential cross sections differ by a factor of more than three and total cross sections by a factor of two. The large effect is caused by the rapid energy dependence of the imaginary part of the two-body amplitude near the elastic threshold.

Meson-nucleus dynamics

Abstract A diagrammatic perturbation theory for the interaction of a pion with a finite nucleus is developed. The theory allows us to identify the various pieces of the physics which are believed to be important and to put into a unifying language the understanding which is emerging from apparently diverse studies. The theory proposed here is arranged so that it maintains the use of the nearly free pion-nucleon T-matrix and contemporary nuclear structure work which utilizes a nucleon-nucleon Bethe-Goldstone g-matrix. Within this framework, we calculate in momentum space and without approximation the first-order optical potential. This potential includes: (1) an exact performance of the Fermi-averaging integral (delta propagation), (2) covariant kinematics including the recoil of the nuclear target, (3) the use of invariant amplitudes and invariant normalizations and phase space factors, (4) the inclusion of the delta-nucleus interaction through a mean-spectral approximation, and (5) a realistic off-shell extrapolation of the pion-nucleon amplitude. The elastic scattering cross sections predicted by this potential are remarkably close to the data. The higher-order effects are classified and their inter-relationships discussed. Three of the higher-order corrections, Pauli effects, pion true-absorption, and short range correlation effects, are calculated and the success of the first-order potential is found to be validated by a large cancellation between the Pauli and true-absorption corrections. A detailed discussion of and comparison to alternate approaches to investigating pion-nucleus dynamics is provided.

A time-dependent external-field model for particle emission in heavy-ion reactions☆

Abstract We study a time-dependent external-field model for fast particle emission in nuclear heavy-ion reactions. The relative motion of the ions is treated classically and the internal excitations are treated quantum mechanically. The model is applied to study fast nucleon emission in the reaction 16 O + 93 Nb.

Microscopic approach to pion-nucleus dynamics.

Elastic scattering of pions from finite nuclei is investigated utilizing a contemporary, momentum-space first-order optical potential combined with microscopic estimates of second-order corrections. The calculation of the first-order potential includes (1) full Fermi-averaging integration including the [Delta] propagation and the intrinsic nonlocalities in the [pi]-[ital N] amplitude, (2) covariant kinematics, (3) invariant amplitudes, and (4) a finite-range off-shell pion-nucleon model which contains the nucleon-pole term. The [Delta] nucleus interaction is included via the mean spectral-energy approximation. This approach produces a convergent perturbation theory in which the Pauli corrections (treated as a second-order term) cancel remarkably against the pion true-absorption terms. Parameter-free results, including the [Delta]-nucleus shell-model potential, Pauli corrections, pion true absorption, and short-range correlations, are presented.

Conceptual framework for high‐spin hadronic physics

A formal structure for a calculable and covariant phenomenology of particles with arbitrary spin is presented. As wave equations for particles with high spin have difficulties, the construction proceeds without reference to any specific wave equation. The 2(2j+1) covariant particle/antiparticle spinors for any spin are explicitly constructed. These covariant spinors are then used to construct configuration, as well as momentum space, Feynman‐Dyson propagators for arbitrary spin.