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Microscopic calculation of two-particle-two-hole meson-exchange currents in $^{40}$Ar and asymmetric scaling properties for neutrino and electron scattering

V. L. Martinez-Consentino, J. Segovia, J. E. Amaro

TL;DR

This work tackles the challenge of accurately modeling two-particle-two-hole meson-exchange currents in asymmetric nuclei, focusing on $^{40}$Ar for neutrino experiments. It develops a relativistic framework with separate proton and neutron Fermi momenta, enabling a microscopic calculation of 2p2h responses and revealing modest to substantial asymmetry effects relative to $^{40}$Ca. A key contribution is the asymmetric scaling formulas that predict 2p2h responses for arbitrary nuclei from a $^{12}$C reference, capturing leading phase-space dependencies and reducing reliance on ad hoc proxies. The authors benchmark their approach against inclusive electron scattering and MicroBooNE neutrino data, finding overall good agreement and providing a practical path to reduce systematic uncertainties in argon-based measurements through implementation in neutrino event generators.

Abstract

We present a microscopic calculation of two particle-two hole meson exchange current response functions in asymmetric nuclei, with particular emphasis on the $^{40}$Ar nucleus. Employing a relativistic mean-field and relativistic Fermi gas framework, we compute the nuclear response for $^{40}$Ar and compare it with that of the symmetric $^{40}$Ca nucleus, analyzing the role of proton-neutron imbalance. The model incorporates distinct proton and neutron Fermi momenta to accurately capture the nuclear dynamics of systems with $Z \neq N$. Our results indicate that using $^{40}$Ca as a proxy for $^{40}$Ar leads to a systematic error of approximately 10\%. Additionally, we propose an asymmetric scaling formula to obtain the 2p2h response for arbitrary nuclei from the $^{12}$C response, improving the description of asymmetric nuclei. Finally, we benchmark our predictions against inclusive electron scattering and neutrino cross sections.

Microscopic calculation of two-particle-two-hole meson-exchange currents in $^{40}$Ar and asymmetric scaling properties for neutrino and electron scattering

TL;DR

This work tackles the challenge of accurately modeling two-particle-two-hole meson-exchange currents in asymmetric nuclei, focusing on Ar for neutrino experiments. It develops a relativistic framework with separate proton and neutron Fermi momenta, enabling a microscopic calculation of 2p2h responses and revealing modest to substantial asymmetry effects relative to Ca. A key contribution is the asymmetric scaling formulas that predict 2p2h responses for arbitrary nuclei from a C reference, capturing leading phase-space dependencies and reducing reliance on ad hoc proxies. The authors benchmark their approach against inclusive electron scattering and MicroBooNE neutrino data, finding overall good agreement and providing a practical path to reduce systematic uncertainties in argon-based measurements through implementation in neutrino event generators.

Abstract

We present a microscopic calculation of two particle-two hole meson exchange current response functions in asymmetric nuclei, with particular emphasis on the Ar nucleus. Employing a relativistic mean-field and relativistic Fermi gas framework, we compute the nuclear response for Ar and compare it with that of the symmetric Ca nucleus, analyzing the role of proton-neutron imbalance. The model incorporates distinct proton and neutron Fermi momenta to accurately capture the nuclear dynamics of systems with . Our results indicate that using Ca as a proxy for Ar leads to a systematic error of approximately 10\%. Additionally, we propose an asymmetric scaling formula to obtain the 2p2h response for arbitrary nuclei from the C response, improving the description of asymmetric nuclei. Finally, we benchmark our predictions against inclusive electron scattering and neutrino cross sections.

Paper Structure

This paper contains 8 sections, 20 equations, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Relativistic 2p2h framework for asymmetric nuclei
  3. Comparison of 2p2h responses between $^{12}$C, $^{40}$Ar, and $^{40}$Ca
  4. 2p2h scaling properties
  5. Cross Sections
  6. Inclusive Electron Scattering
  7. Neutrino-Nucleus Scattering
  8. Conclusions

Figures (9)

  • Figure 1: RMF calculation of 2p2h responses for charged-current neutrino scattering at $q=500~\text{MeV}/c$ in the $pp$ and $np$ channels, shown for $^{40}$Ar, $^{40}$Ca, and $^{12}$C.
  • Figure 2: The same as Fig. \ref{['fig1rmf']}, but computed in the RFG framework (free masses, with separation energy, and real part of the free $\Delta$ propagator only).
  • Figure 3: Ratio of the $^{40}$Ar transverse neutrino response to that of $^{40}$Ca (left panels) and $^{12}$C (right panels) in the $pp$, $np$, and $pp+np$ emission channels at $q = 500$ MeV/$c$. Upper panels: RMF model; lower panels: RFG model.
  • Figure 4: Ratio of the 2p2h MEC transverse neutrino response of $^{40}$Ar to that of $^{12}$C in the $pp+np$ emission channel for several momentum transfers ($q=500$, 750, 1000, 1500, 2000 MeV/$c$). Upper panels: RMF model; lower panels: RFG model.
  • Figure 5: Transverse neutrino response in the $pp+pn$ channel. The exact responses for $^{40}$Ar (black) and $^{40}$Ca (red) are compared with the predictions obtained by rescaling from $^{12}$C using the scaling formulas with the parameters of Table \ref{['tablaprop']}, shown as dashed lines of the same color as the target nucleus. Results are displayed for $q=500$, $750$, and $1000$ MeV/$c$ in both the RMF (left column) and RFG (right column) frameworks.
  • ...and 4 more figures