Single pion-production and pion propagation in Achilles

TL;DR

This paper extends the Achilles neutrino event generator to exclusive single-pion production by integrating a Dynamical Coupled-Channels description of the electroweak vertex with realistic nuclear spectral functions and by modeling final-state interactions through a semi-classical intranuclear cascade. Two cascade modes—Virtual Resonances and Propagating Resonances—are implemented to probe resonance propagation versus absorption and to quantify modeling uncertainties. The approach is validated against pion-nucleon and pion-nucleus data and benchmarked against exclusive electron- and neutrino-nucleus measurements from e4ν, T2K, MINERνA, and MicroBooNE, showing generally good agreement with identifiable gaps due to missing MEC and DIS. The work advances neutrino-nucleus modeling by enabling exclusive final-state predictions, which are crucial for DUNE and other oscillation experiments, and sets the stage for future inclusion of MEC, DIS, and comprehensive error analyses.

Abstract

We extend the applicability of Achilles (A CHIcagoLand Lepton Event Simulator) by incorporating the single-pion production mechanism in a fully exclusive fashion. The electroweak interaction vertex is modeled by combining the state-of-the-art Dynamical Coupled-Channels approach with realistic hole spectral functions, which account for correlations in both the initial target state and the residual spectator system. Final-state interactions are treated using a semi-classical intranuclear cascade that leverages nuclear configurations to determine the correlated spatial distribution of protons and neutrons. The meson-baryon scattering amplitudes used in the cascade are computed within the Dynamical Coupled-Channels framework, consistent with the electroweak vertex. To model pion absorption, we employ the optical potential approach of Oset and Salcedo. As an alternative approach, we explicitly model the production and propagation of resonances which mediate pion-nucleon scattering and pion absorption. We validate out approach against pion-nucleon and pion-nucleus scattering data, and present comparisons with electron- and neutrino-nucleus measurements from e4$ν$, T2K, MINER$ν$A, and MicroBooNE.

Figures (17)

• Figure 1: Achilles comparison to inclusive electron scattering data on ${}^{40}\rm{Ar}$ (left) and ${}^{12}\rm{C}$ (right) from JLab at $E_{\rm{beam}} = 2.222$ GeV and $\theta_{e^{\prime}} = 15.541^\circ$Murphy:2019wed as a function of energy transfer ($\omega$). The data and predictions have been normalized to the number of nucleons in each respective nucleus. The total prediction from Achilles is in blue, while the quasi-elastic component is in orange and the pion production component is in green. Gaps between the data and Achilles' prediction for the differential cross section are expected to be largely filled by the eventual inclusion of contributions from meson exchange currents and deep inelastic scattering.
• Figure 2: Comparison of total pion-production cross sections for $\nu_\mu$ scattering on nucleons. The data are from measurements at Argonne and Brookhaven National Laboratories reanalyzed in Ref. Wilkinson:2014yfa.
• Figure 3: Validation of the pion modes in Achilles INC against experimental data. Achilles results are shown using both the Propagating Resonances model (solid line) and the Virtual Resonances model (dotted line). Left: Absorption cross section for $\pi^{+}$ on carbon (top) and $\pi^{+}$ on argon (bottom). Experimental data are for $\pi^+$ absorption measurements on carbon (DUET DUET and Ashery ASHERY) and on argon (LADS LADS:2000pzh). Right: Total reaction cross section for $\pi^{+}$ on carbon (top) and $\pi^{+}$ on argon (bottom). Data for carbon are from Ref. Dytman:2021ohr.
• Figure 4: Comparison of the electron-carbon $0\pi$ differential cross section with respect to $E_{QE}$ measured by e4$\nu$ and CLAS CLAS:2021neh compared to predictions by Achilles. The black vertical dashed line shows the true incoming beam energy.
• Figure 5: Comparison of the electron-carbon $1p0\pi$ differential cross section with respect to $E_{cal}$ measured by e4$\nu$ and CLAS CLAS:2021neh compared to predictions by Achilles. The black vertical dashed line shows the true incoming beam energy.