Bertrand Desplanques

Explicitly Covariant Light-Front Dynamics and Relativistic Few-Body Systems

Abstract The wave function of a composite system is defined in relativity on a space–time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane ω · x =0, where ω is an arbitrary four-vector with ω 2 =0. The standard non-covariant approach is recovered as a particular case for ω=(1, 0, 0,−1) . Using the light-front plane is of crucial importance, while the explicit covariance gives strong advantages emphasized through all the review. The properties of the relativistic few-body wave functions are discussed in detail and are illustrated by examples in a solvable model. The three-dimensional graph technique for the calculation of amplitudes in the covariant light-front perturbation theory is presented. The structure of the electromagnetic amplitudes is studied. We investigate the ambiguities which arise in any approximate light-front calculations, and which lead to a non-physical dependence of the electromagnetic amplitude on the orientation of the light-front plane. The elastic and transition form factors free from these ambiguities are found for spin 0, 1 2 and 1 systems. The formalism is applied to the calculation of the relativistic wave functions of two-nucleon systems (deuteron and scattering state), with particular attention to the role of their new components in the deuteron elastic and electrodisintegration form factors and to their connection with meson exchange currents. Straightforward applications to the pion and nucleon form factors and the ρ −π transition are also made.

Parity-non-conserving nuclear forces

Abstract Theoretical and phenomenological approaches to parity-non-conserving nuclear forces are reviewed. Recent developments in the calculation of weak meson-nucleon coupling constants, whose knowledge is necessary to determine theoretically the parity-non-conserving nucleon-nucleon potential, are described. The consistency of different measurements of parity-non-conserving effects is discussed and the information they provide is compared to theoretical predictions.

PARITY-NON-CONSERVATION IN NUCLEAR FORCES AT LOW ENERGY : PHENOMENOLOGY AND QUESTIONS

Abstract The information available from the analysis of parity-non-conserving (pnc) effects in nuclear systems at low energy is considered. While five pieces of information corresponding to the five transitions between S and P nucleon–nucleon states should be at least determined, only three are presently more or less known. They are the strength of the pnc proton–nucleus and neutron–nucleus forces and that of the proton–proton force. Although it is not complete, this knowledge already provides a valuable discussion when it is compared to theoretical expectations. The discussion concerns the strength of the pnc πNN coupling constant, which determines the long-range part of pnc isovector forces, and the contribution of the pnc proton–proton force to the pnc proton–nucleus force. Both are too low in comparison with current expectations. Several issues to overcome these difficulties, that appeared with the advent of more accurate measurements of pnc effects in 18F and proton–proton scattering, are examined. They include an update of earlier estimates of the pnc πNN coupling constant, the role of collective effects in nuclei and new contributions to the pnc NN force, yet undetermined. Experiments, which may provide the missing information, are discussed.

Isovector meson-exchange currents in the light-front dynamics

In the light-front dynamics, there is no pair term that plays the role of the dominant isovector pion exchange current. This current gives rise to the large and experimentally observed contribution to the deuteron electrodisintegration cross-section near threshold for pseudo-scalar πNN coupling. We show analytically that in leading 1m order the amplitude in the light-front dynamics coincides, however, with the one given by the pair term. At high Q2, it consists of two equal parts. One comes from extra components of the deuteron and final state relativistic wave functions. The other results from the contact NNπγ interaction which appears in the light-front dynamics. This provides a transparent link between relativistic and non-relativistic approaches.

Are all models of the NN interaction independent of each other

Abstract Models of the NN interaction are most often considered as independent of each other, and it is generally believed that experiments could allow one to discriminate them. It has, however, been shown that there may be some relationship between models designed to be used in momentum and configuration spaces. This relationship is expressed by a unitary transformation. Its consequences for the charge and quadrupole deuteron form factors were investigated in the case of the π-exchange contribution to the NN interaction. For this interaction, the Bonn (Q b ) and Paris models were considered as representative models of momentum and configuration spaces respectively. The above work is extended to the ϱ-exchange contribution on the one hand and to the deuteron magnetic form factor and the form factor for deuteron electrodisintegration near threshold on the other hand. Sensitivity to various inputs is discussed.

Form factors in RQM approaches : Constraints from space-time translations

Different relativistic quantum-mechanic approaches have recently been used to calculate properties of various systems, form factors in particular. It is known that predictions, which most often rely on a single-particle current approximation, can lead to predictions with a very large range. It was shown that accounting for constraints related to space-time translations could considerably reduce this range. It is shown here that predictions can be made identical for a large range of cases. These ones include the following approaches: instant form, front form, and “point form” in arbitrary momentum configurations and a dispersion-relation approach which can be considered as the approach which the other ones should converge to. This important result supposes both an implementation of the above constraints and an appropriate single-particle-like current. The change of variables that allows one to establish the equivalence of the approaches is given. Some points are illustrated with numerical results for the ground state of a system consisting of scalar particles.

Parity non-conservation at the peak of p-resonances in low-energy neutron-nucleus scattering

Abstract Parity-non-conserving effects at the top of ρ-wave resonances in low-energy neutron-nucleus scattering are revisited in view of recent measurements in 238 U and 232 Th. This is done in the framework of the valence model. A quite simple expression in terms of the strength of the neutron-nucleus parity-non-conserving force is derived for the P ( E p ) asymmetry. The result, which is independent on the nucleus, can usefully be considered as a benchmark for those effects. Comparison of experiment to theory confirms earlier conclusions, namely the expected strength of the neutron-nucleus parity-non-conserving force is much too low to account for observations in this approach, even if the sign is well reproduced. Clues to explain discrepancies with other recent works are given.

RQM description of the charge form factor of the pion and its asymptotic behavior

The pion charge and scalar form factors, F1(Q2) and F0(Q2) , are first calculated in different forms of relativistic quantum mechanics. This is done using the solution of a mass operator that contains both confinement and one-gluon exchange interactions. Results of calculations, based on a one-body current, are compared to experiment for the first one. As could be expected, those point form, and instant and front-form ones in a parallel momentum configuration fail to reproduce experiment. The other results corresponding to a perpendicular momentum configuration (instant form in the Breit frame and front form with q+ = 0 do much better. The comparison of charge and scalar form factors shows that the spin-1/2 nature of the constituents plays an important role. Taking into account that only the last set of results represents a reasonable basis for improving the description of the charge form factor, this one is then discussed with regard to the asymptotic QCD power law behavior Q-2. The contribution of two-body currents in achieving the right power law is considered while the scalar form factor, F0(Q2) , is shown to have the right power law behavior in any case. The low-Q2 behavior of the charge form factor and the pion decay constant are also discussed.

PNC effects in neutron-232Th scattering: a window to class II or new states of nuclei?

Abstract The sign correlation of parity-non-conserving ( pnc ) asymmetries observed in neutron 232 Th scattering at the peak of p-wave resonances is examined. Assuming that it is a real effect, the conditions that this implies for a theoretical explanation are determined. It is shown that it has to rely on the existence of two states of opposite parity, which act as “doorway states”, different from those recently considered in the present field. The location of these states, their energy difference and their spreading width are estimated. It is shown that experimental data on 232 Th favor the location of both “doorway states” in the low energy region ( E s 0 , E p 0 ∼0–1 keV). In this case, the asymmetry exhibits a different sign depending on whether the energy of the p-wave resonance is below or above E s 0 . Candidates for such states are then considered, including the well known parity doublet built on a pear-shape nucleus, a more exotic one based on a structure where spins of nucleons align along their momentum ( σ · p correlation), and finally an accidental one in the second well of the potential energy surface. The evidence for a sign correlation in a limited energy range partly depends on the size of the random contribution to the observed pnc effects. The examination of the root mean square value of the pnc matrix element between states of the compound nucleus shows that the range of predictions is quite large and does not provide any constraint at present.

Parity non-conservation in the pp system at low energy: Critical remarks about direct quark approaches

Abstract Several papers dealing with predictions for the parity-non-conserving longitudinal asymmetry in pp scattering at low energy, using either a quark-model approach or the concept of parity admixture of vector mesons, are reviewed. About 10 papers which are concerned with the determination of the sign are discussed here. It is shown that they predict a sign for the asymmetry which is likely to be incorrect and, in any case, in contradiction with the standard theoretical understanding of the sign actually determined by experiment. The relationship of these approaches with that based on the old factorization approximation is emphasized. In this order, many details are given, and obviously special attention is given to the sign prediction (conventions, definitions, phases, etc.).