Electron-induced single-pion production to constrain the neutron structure in $^{40}$Ar. A proof of concept

TL;DR

The paper investigates electron-induced single-pion production on $^{40}$Ar via a triple-coincidence reaction $^{40}$Ar$(e,e'p\pi^-)$ as a method to constrain the neutron spectral function in argon, aiming to reduce systematic uncertainties in neutrino experiments using argon detectors. A RPWIA framework with an IPSM ground state and a Ghent-Hybrid single-pion production model is combined with a NuWro intranuclear cascade to predict signal and backgrounds, under kinematics that emphasize $E_m$ and $p_m$ regions tied to the neutron shell structure. Feasibility is shown to be facility-dependent: MAMI's high-resolution, small-acceptance spectrometers can resolve neutron-shell peaks in $E_m$ with $E_m<70$ MeV and $p_m<350$ MeV, while CLAS's large acceptance yields larger cross sections but cannot resolve shell structure due to its energy resolution. The work provides a proof-of-concept that such triple-coincidence measurements can illuminate neutron structure in $^{40}$Ar and inform neutrino-nucleus interaction modeling, with next steps including final-state distortions and uncertainty quantification.

Abstract

We study electron-induced single-pion production as a way to constrain the neutron structure of $^{40}$Ar, information that is necessary for neutrino experiments using argon detectors. The proposed experimental signal consists in detecting in coincidence the scattered electron, a proton and a $π^-$. We performed simulations compatible with the experimental conditions of the MAMI (University of Mainz) and CLAS (Jefferson Lab) facilities. We have computed cross sections and evaluated the main backgrounds. MAMI is a three-spectrometer system with extremely good energy resolution and small acceptances. We found that, by choosing specific values of the final particle's momenta, the shell structure can be well resolved, with negligible background contributions. CLAS is a large solid angle detector with poorer energy resolution. In both cases, the background can be kept under control by performing cuts in missing energy and missing momentum; however, in CLAS, the shell structure cannot be resolved due to the energy resolution. We conclude that MAMI is particularly appropriate for the proposed experiment, whereas CLAS is better suited for other studies.

Figures (12)

• Figure 1: Definition of the the reference frame. The $\hat{z}$-axis is defined by the electron beam. The $\hat{x}$-$\hat{z}$ plane coincides with the floor of the laboratory. The scattering angles ($\theta_l$, $\theta_p$ and $\theta_\pi$) are defined on this plane. Azimuthal angles are the angles with respect to the $\hat{x}$-$\hat{z}$ plane.
• Figure 2: Model prediction for the inclusive electron scattering cross section for $E_i=855$ MeV, $\theta_l=(30.00\pm1.15)$ deg and $\phi_l=(180\pm4)$ deg. The inner plot is a zoom around the Delta peak focusing on the SPP channels.
• Figure 3: The left panel shows the cross sections corresponding to events with at least one proton and one $\pi^-$ in the final state, arose from different reaction channels: $p\pi^-$, $p\pi^0$, $n\pi^+$ and $n\pi^0$. The events from the $p\pi^-$ channel are separated in unscattered and rescattered contributions. The right panel is the same, but only events with $E_m<70$ MeV and $p_m<350$ MeV contribute. The blue line indicates the central energy chosen for the final electron, the band represents the acceptance of Spec. B. In all cases, $E_i=855$ MeV, $\theta_l=(30\pm1.15)$ deg and $\phi_l=(180\pm4)$ deg.
• Figure 4: Left panels: Differential cross sections in terms of different combinations of hadron variables. Right panels: Coverage of the proton (red, Spec. A) and pion (green, Spec. C) spectrometers, the line indicates the central value and the band represents the acceptance. Upper row: proton and pion momenta. Lower row: scattering angles of the proton and pion. The line contours indicate the regions where the unscattered $1p1\pi^-$ cross section are 90%, 70% and 50% of its maximum. Only events with $E_m<70$ MeV and $p_m<350$ MeV contribute. In all cases, $E_i=855$ MeV, $E_l=505 \text{ MeV} \pm7.5\%$, $\theta_l=(30\pm1.15)$ deg, $\phi_l=(180\pm4)$ deg, $\phi_p=(0\pm4)$ deg and $\phi_\pi=(180\pm4)$ deg.
• Figure 5: Differential cross section in terms of missing energy for the signal sample $1p1\pi^-$ within the chosen acceptances for MAMI. Vertical lines represent the RMF eigenvalues for the shells. Only events with $E_m<70$ MeV and $p_m<350$ MeV contribute.