Gauge and Lorentz invariant one-pion exchange currents in electron scattering from a relativistic Fermi gas

Abstract

A consistent analysis of relativistic pionic correlations and meson-exchange currents for electroweak quasielastic electron scattering from nuclei is carried out. Fully-relativistic one-pion-exchange electromagnetic operators are developed for use in one-particle emission electronuclear reactions within the context of the relativistic Fermi gas model. Then the exchange and pionic correlation currents are set up fully respecting the gauge invariance of the theory. Emphasis is placed on the self-energy current which, being infinite, needs to be renormalized. This is achieved starting in the Hartree-Fock framework and then expanding the Hartree-Fock current to first order in the square of the pion coupling constant to obtain a truly, gauge invariant, one-pion-exchange current. The model is applied to the calculation of the parity-conserving (PC) and parity-violating (PV) inclusive responses of nuclei. Interestingly, in the pionic correlations terms exist which arise uniquely from relativity, although their impact on the responses is found to be modest.

Final-state interactions in the superscaling analysis of neutral-current quasielastic neutrino scattering

“…Meson-exchange current effects do not scale (see Refs. [36,37]), but they are expected to contribute less than 15% (see for instance Refs. [38,39]) to these inclusive neutrino-nucleus cross sections at intermediate energies.…”

Meson-exchange currents and final-state interactions in quasielastic electron scattering at high momentum transfers

“…An exhaustive analysis of (e, e ) world data demonstrated the scaling at energy transfers ω below the quasielastic (QE) peak [1,2], namely the independence of the reduced cross sections on the momentum transfer (first-kind scaling) and on the nuclear target (second-kind scaling) when plotted versus the appropriate scaling variable. It is well known that at energies above the QE peak scaling is violated in the transverse (T ) channel by effects beyond the impulse approximation: inelastic scattering [3,4], correlations, and meson-exchange currents (MEC) in both the one-particle one-hole (1p-1h) and two-particle two-hole (2p-2h) sectors [5][6][7][8].In contrast, the available data for the longitudinal (L) response are compatible with scaling throughout the QE region and permitted [9] the extraction of a phenomenological scaling function f L . In recent work [10][11][12] it was shown that only a few models [the relativistic mean field (RMF), the semirelativistic (SR) approach with Dirac-equation-based (DEB) and a "BCS-like" model] are capable of reproducing the detailed shape of f L , while other models fail to reproduce the long tail appearing at high ω. Theses models effectively account for the major ingredients needed to describe the (e, e ) responses for intermediate-to-high momentum transfers, namely relativistic effects and an appropriate description of the effective final-state interactions (FSI).…”

“…An exhaustive analysis of (e, e ) world data demonstrated the scaling at energy transfers ω below the quasielastic (QE) peak [1,2], namely the independence of the reduced cross sections on the momentum transfer (first-kind scaling) and on the nuclear target (second-kind scaling) when plotted versus the appropriate scaling variable. It is well known that at energies above the QE peak scaling is violated in the transverse (T ) channel by effects beyond the impulse approximation: inelastic scattering [3,4], correlations, and meson-exchange currents (MEC) in both the one-particle one-hole (1p-1h) and two-particle two-hole (2p-2h) sectors [5][6][7][8].…”

“…Finally, let us mention that in this article, as in past work (see Ref. [7] for details), we use a monopole parametrization for the πNN and πN form factors, giving a smooth dependence on the energy of the pion. Different prescriptions will modify slightly the present results, but they will remain qualitatively the same without changing our conclusions.…”

Final-state interaction and recoil polarization in reactions: comparison with the polarized target case

“…In the particular case of the results for 40 Ca of the next section, we use the potential parameterization of Schwandt [40], the same considered in [25] since we want to compare with the results for polarized nuclei using the same interaction. The present model accounts for relativistic corrections that have proven to be successful in describing intermediate-energy inclusive and exclusive electron scattering observables in the region of the quasielastic peak [41,42,43,44,45]. First we use relativistic kinematics for the nucleons, as these are essential to have a correct description of the position and width of the quasielastic peak.…”