A cluster-separable Born approximation for the 3D reduction of the three-fermion Bethe-Salpeter equation

We perform a 3D reduction of the two-fermion Bethe-Salpeter equation based on Sazdjian's explicitly covariant propagator, combined with a covariant substitute of the projector on the positive-energy free states. We use this combination in the two fermions in an external potential and in the three-fermion problems. The covariance of the two-fermion propagators insures the covariance of the two-body equations obtained by switching off the external potential, or by switching off all interactions between any pair of two fermions and the third one, even if the series giving the 3D potential is limited to the Born term or more generally truncated. The covariant substitute of the positive energy projector preserves the equations against continuum dissolution without breaking the covariance.Comment: 21 pages, 1 figure This article has been deeply modified after refereeing. The presentation has been improved and examples have been added. Three subsections have been added (transition matrix elements, two-body limits, covariant Salpeter's equation). submitted to Journal of Physics

3D reduction of the N-body Bethe-Salpeter equation

We perform a 3D reduction of the two-fermion Bethe-Salpeter equation, by series expansion around a positive-energy instantaneous approximation of the Bethe-Salpeter kernel, followed by another series expansion at the 3D level in order to get a manifestly hermitian 3D potential. It turns out that this potential does not depend on the choice of the starting approximation of the kernel anymore, and can be written in a very compact form. This result can also be obtained directly by starting with an approximation of the free propagator, based on integrals in the relative energies instead of the more usual delta-constraint. Furthermore, the method can be generalized to a system of N particles, consisting in any combination of bosons and fermions. As an example, we write the 3D equation for systems of two or three fermions exchanging photons, in Feynman or Coulomb's gauge.Comment: 22 pages, 3 figures in one single ps file. In the first revision, the self-energy corrections to the propagator have been taken into account. The three figures were gathered in a single ps file instead of three eps. In this second revision (after submission to Nuclear Physics A and refereeing) some explanations have been added, plus a new subsection about the scattering of a particle by a bound stat

Supersymmetry and superalgebra for the two-body system with a Dirac oscillator interaction

Some years ago, one of the authors~(MM) revived a concept to which he gave the name of single-particle Dirac oscillator, while another~(CQ) showed that it corresponds to a realization of supersymmetric quantum mechanics. The Dirac oscillator in its one- and many-body versions has had a great number of applications. Recently, it included the analytic expression for the eigenstates and eigenvalues of a two-particle system with a new type of Dirac oscillator interaction of frequency~$\omega$. By considering the latter together with its partner corresponding to the replacement of~$\omega$ by~$-\omega$, we are able to get a supersymmetric formulation of the problem and find the superalgebra that explains its degeneracy.Comment: 21 pages, LaTeX, 1 figure (can be obtained from the authors), to appear in J. Phys.

Closed expression of the interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states

The interaction kernel in the Bethe-Salpeter equation for quark-antiquark bound states is derived from the Bethe-Salpeter equations satisfied by the quark-antiquark four-point Green's function. The latter equations are established based on the equations of motion obeyed by the quark and antiquark propagators, the four-point Green's function and some other kinds of Green's functions which follow directly from the QCD generating functional. The B-S kernel derived is given an exact and explicit expression which contains only a few types of Green's functions. This expression is not only convenient for perturbative calculations, but also suitable for nonperturbative investigations.Comment: 27 pages,no figure

Weak Pion Production off the Nucleon

We develop a model for the weak pion production off the nucleon, which besides the Delta pole mechanism (weak excitation of the $\Delta(1232)$ resonance and its subsequent decay into $N\pi$), includes also some background terms required by chiral symmetry. We re-fit the $C_5^A(q^2)$ form factor to the flux averaged $\nu_\mu p \to \mu^-p\pi^+$ ANL $q^2-$differential cross section data, finding a substantially smaller contribution of the Delta pole mechanism than traditionally assumed in the literature. Within this scheme, we calculate several differential and integrated cross sections, including pion angular distributions, induced by neutrinos and antineutrinos and driven both by charged and neutral currents. In all cases we find that the background terms produce quite significant effects and that they lead to an overall improved description of the data, as compared to the case where only the Delta pole mechanism is considered. We also show that the interference between the Delta pole and the background terms produces parity-violating contributions to the pion angular differential cross section, which are intimately linked to $T-$odd correlations in the contraction between the leptonic and hadronic tensors. However, these latter correlations do not imply a genuine violation of time reversal invariance because of the existence of strong final state interaction effects.Comment: Typos corrected; comments adde

Nucleon-to-Delta axial transition form factors in relativistic baryon chiral perturbation theory

We report a theoretical study of the axial Nucleon to Delta(1232) ($N\to\Delta$) transition form factors up to one-loop order in relativistic baryon chiral perturbation theory. We adopt a formalism in which the $\Delta$ couplings obey the spin-3/2 gauge symmetry and, therefore, decouple the unphysical spin-1/2 fields. We compare the results with phenomenological form factors obtained from neutrino bubble chamber data and in quark models.Comment: A few clarifying remarks added; version to appear in Physical Review

N-Delta(1232) axial form factors from weak pion production

The N-Delta axial form factors are determined from neutrino induced pion production ANL & BNL data by using a state of the art theoretical model, which accounts both for background mechanisms and deuteron effects. We find violations of the off diagonal Goldberger-Treiman relation at the level of 2 sigma which might have an impact in background calculations for T2K and MiniBooNE low energy neutrino oscillation precision experiments.Comment: 4 pages, 1 figur