Impact of Two-Body Currents on Semi-Exclusive Lepton-Nucleus Reactions

TL;DR

This work tackles the challenge of describing MEC-driven two-nucleon knockout in lepton–nucleus scattering at energies up to about $1\,\text{GeV}$, with significant implications for neutrino oscillation analyses. It develops a generalized two-nucleon spectral-function formalism that retains angular correlations via the two-body momentum distribution $\rho_{ST}(\mathbf{q},\mathbf{Q})$ and updates the Delta current using a pure spin-3/2 propagator and consistent couplings. The framework is validated against semi-exclusive electron-scattering data and contrasted with a Relativistic Fermi Gas baseline, underscoring the importance of current structure and correlations. The authors also provide neutrino-scattering predictions on $^{12}$C for mono-energetic and flux-folded inputs, revealing back-to-back emission tendencies and enhanced high-momentum protons in the spectral-function approach, with clear implications for the interpretation of $Np$ final-state topologies in experiments.

Abstract

We generalize the spectral-function formalism to describe two-nucleon knockout processes in exclusive kinematics. Significant improvements are introduced both in the treatment of the current operators entering the $Δ$-current contribution and in the modeling of correlations between the two struck nucleons, including a consistent treatment of isospin dependence and the explicit incorporation of angular correlations. The framework is validated through comparisons with relativistic Fermi-gas calculations and with semi-exclusive electron-nucleus scattering data. Our results demonstrate that an accurate description of nuclear dynamics plays a crucial role in modeling this reaction mechanism. We further present a study of selected electroweak observables relevant to neutrino-scattering experiments.

Figures (9)

• Figure 1: Subset of MEC diagrams contributing to $j^{\mu}_{2b}$. Lines represent nucleons (solid), pions (dashed), $\Delta$s (thick solid), gauge bosons (wavy lines). Diagrams (a), (b), and (c) are respectively the Seagull, Pion-in-flight, and Pion-pole diagrams, while diagrams (d) and (e) are the forwards and backwards $\Delta$ diagrams. Filled circles at vertices represent the insertion of strong form factors which modify the $\pi NN$ and $\pi N \Delta$ vertices.
• Figure 2: Ratio of normalized two-body momentum distributions for $np$ and $pp$ pairs as a function of $q$ and $Q$. Both distributions have been normalized to 1.
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• Figure 6: Fermi Gas differential cross section in the cosine of the outgoing nucleon angles for $np$ (left) and $pp$ (right) pairs