J.S. Bell

Shifman-Vainshtein-Zakharov moments and quark-antiquark potentials

Abstract From the SVZ moments, for heavy quark-antiquark systems, we extract an “equivalent” non-relativistic potential. It increases as the fourth power of the distance and linearly with the quark mass. Numerical integration of the “equivalent” Schrodinger equation leads to much higher estimates of the gluon condensate parameter o 1 than the original inverse power moment method or even the Borel transformed exponential version.

Dirac equations with an exact higher symmetry

Abstract A family of external potentials for the Dirac equation is exhibited for which there is an exact SU(2) symmetry leading to exact spin-orbit doublet degeneracy. The family in question, includes an equal superposition of Coulomb-like and Lorentz-scalar potentials.

Current algebra and η → 3π

Abstract A critical review is given of developments in the theory subsequent to the demonstration that in first approximation η → 3 π is forbidden. It remains difficult to understand the process with conventional ideas without reducing to an accident the success of current algebra, and a simple linear matrix element, in K → 3 π .

On solitons with half integral charge

Can certain soliton states, with half integral expectation value of charge, be also eigenstates of charge X with half integral eigenvalue? It can be so only with a somewhat sophisticated definition of charge.

High energy behaviour of tree diagrams in gauge theories

Abstract Tree diagram scattering amplitudes may behave extra badly at high energy when vector mesons are involved. The cancellation, among bad terms, implied by gauge invariance is discussed. It is shown that in the renormalizable spontaneously broken gauge theories such cancellation is complete.

Quasielastic neutrino nucleus interactions

Abstract Calculations of the Pauli exclusion effect are made in a simple shell model. Shell structure effects, associated with spin-orbit splitting, appear, but are not large and decrease rapidly with increasing momentum transfer. The shell model remains less exclusive on the whole than the standard Fermi gas, but not sufficiently so to explain the apparent experimental absence of the exclusion effect.

Hydrogen atom on null-plane and Melosh transformation

Abstract The null-plane dynamics of hydrogen-like atoms is studied in approximations depending on c , the velocity of light, being large. Neglecting terms in the Hamiltonian of order c −3 (relative to electron rest energy) a symmetry SU (2) W appears which is analogous to the SU (6) W of hadron classification. This symmetry, if accurate, would dictate zero ground state magnetic moment. The symmetry is broken by terms of third order, which can, however, be transformed a way by the appropriate approximation to the Melosh transformation. There then emerges a better symmetry, SU (2) M , broken only at fourth order. The ground state magnetic moment acquires its usual non-relativistic value. The symmetry SU (2) M corresponds to a subgroup of a symmetry [U (2) × U (2)] FW which appears in the old Foldy-Wouthuysen approach when spin-orbit coupling is neglected. As well as “current” and “constituent” pictures, “classification” pictures are distinguished; it is to one of the latter that the Melosh transformation transforms.

NEAR-FORWARD NEUTRINO REACTIONS ON NUCLEAR TARGETS

A simple model is considered for near-forward neutrino reactions on nuclear targets in the conditions of the CERN experiment. The model accounts for the failure to observe the shadow effect, which is compensated by the elastic interaction and masked by unshadowed terms which grow rapidly away from the forward direction.

Hadronic vacuum polarization and gμ−2

Abstract The possibility of bounding the hadronic vacuum polarization contribution to the muon magnetic moment anomaly is considered. A proposed theoretical bound, based on the hypothesis of field current identity, is found not to add usefully to the vector meson dominance estimate. However, it is observed that improved electron-electron scattering experiments will yield a useful empirical bound.

On duality between resonances and free quark-antiquark pairs

Abstract The semi-classical formula due to Krammer and Leal-Ferreira, and Quigg and Rosner, for the S wave bound state wave function at the origin, is generalized to all partial waves, and the relation to duality is traced to a common dependence on short time behaviour.