Charged-current quasielastic-like neutrino scattering from $^{12}$C in the coherent density fluctuation model with two-nucleon emission

Published 17 Apr 2026 in nucl-th | (2604.15989v1)

Abstract: The quasielastic cross-sections of charged-current neutrino and antineutrino scattering on $^{12}$C are calculated using the coherent density fluctuation model with a relativistic effective mass $m_N^* =0.8 m_N$ (CDFM${M^*}$). The model explicitly considers the modification of the relativistic effective mass of the nucleon within the relativistic mean field (RMF) model of nuclear matter. In addition, our calculations include neutrino-induced two-particle emission processes, which are evaluated within the RMF model of nuclear matter. Utilizing the CDFM${M^*}$, we provide predictions for the neutrino and antineutrino cross sections of $^{12}$C, which have been observed in accelerator experiments, such as MiniBooNE, T2K, and MINERvA. Also, we analyze the axial form factor value for the excitation of the $Δ$ at zero momentum transfer (commonly denoted as $C^A_5 (0)$) which is important for the treatment of the $Δ$ current in the meson-exchange currents (MEC) calculation. In addition, the quasielastic results obtained within CDFM$_{M^*}$ model are thoroughly evaluated for different regions of the momentum transfer.

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Authors (2)

Summary

The paper introduces a unified CDFM_M* approach that integrates two-nucleon emission and MEC to resolve discrepancies in CCQE-like neutrino scattering.
Methodologically, it extends the relativistic Fermi gas model by incorporating effective nucleon mass and local density fluctuations to capture finite-size and correlation effects.
Empirical comparisons with MiniBooNE, T2K, and MINERvA data validate the model’s consistent ~20–30% MEC contribution in reproducing cross sections.

Charged-current Quasielastic-like Neutrino Scattering from $^{12}$ C in the Coherent Density Fluctuation Model with Two-Nucleon Emission

Introduction and Theoretical Context

The paper presents a comprehensive study of charged-current quasielastic-like (CCQE-like) scattering of neutrinos and antineutrinos off $^{12}$ C within the Coherent Density Fluctuation Model with an effective nucleon mass (CDFM $_{M^*}$ ), incorporating two-nucleon (2p-2h) emission. The analysis addresses unresolved challenges in the theoretical modeling of lepton-nucleus reactions relevant to oscillation experiments, particularly the limitations of the relativistic Fermi gas (RFG) model regarding medium modifications, finite-size effects, nuclear correlations, and two-body meson-exchange currents (MEC), which are essential to obtain an accurate description of cross sections in the presence of nucleon-nucleon correlations and multinucleon emission processes.

CDFM $_{M^*}$ employs a generator coordinate method-based extension of the RFG, which enables the description of realistic finite nuclei configurations and incorporates the relativistic effective mass $m_N^* = 0.8 m_N$ arising from mean-field scalar and vector interactions of the RMF framework. The scaling function is constructed from a superposition of RFG response functions, weighted by nucleon density distributions, capturing effects beyond independent-particle models, such as medium-induced modifications and high-momentum tails from short-range correlations.

The crucial innovation in this work is the explicit computation of 2p-2h MEC contributions derived within the RMF model for nuclear matter, using semi-empirical parametric expressions that factor in effective masses and vector energies. This hybrid approach better aligns one- and two-body descriptions, allows for systematic treatment of $\Delta$ -current uncertainties, and is validated against inclusive cross-section data from MiniBooNE, T2K, and MINERvA.

The CDFM $_{M^*}$ Framework

The CDFM $_{M^*}$ approach generates the nuclear scaling function $f^\text{QE}(\psi^*)$ as a convolution of the empirical local density distribution with RFG-based scaling functions, evaluated for an effective mass $m_N^*$ . The scaling variable $^{12}$ 0 and function $^{12}$ 1 are defined according to the RMF theory, incorporating medium effects such as lower components of the nucleon spinors that enhance transverse responses. All kinematic factors, Fermi momentum, and normalization constants are functions of nuclear density, ensuring finite-size and shell effects are reflected in the modeling.

The CCQE-like double differential cross section is calculated as a sum over longitudinal, transverse, and interference nuclear response functions, each weighted by appropriate kinematic coefficients and evaluated using the CDFM $^{12}$ 2 scaling function. The only free parameter in the QE part of the model is $^{12}$ 3, systematically fixed across all calculations.

Two-Nucleon Emission and Meson Exchange Currents

The model accounts for multinucleon (2p-2h) emission induced by MEC, which have proven essential in resolving discrepancies between theory and inclusive $^{12}$ 4, neutrino, and antineutrino cross-section data, especially between the QE peak and $^{12}$ 5-resonance region. In this study, 2p-2h responses are computed within the RMF consistent with the QE sector, using a parametrization developed in [PhysRevD.104.113006], which factors in coupling coefficients, form-factors, phase-space, and averaged $^{12}$ 6 propagators. Two alternative values for the $^{12}$ 7 axial form factor, $^{12}$ 8, are considered ( $^{12}$ 9 and $_{M^*}$ 0) to bracket theoretical uncertainties.

The consistency of using the same effective mass in both the one-body (QE) and two-body (MEC) sectors is explicitly enforced. The impact of nuclear-medium modifications of the $_{M^*}$ 1 is shown to be negligible for the kinematics of MiniBooNE, T2K, and MINERvA.

Confrontation with Experimental Data

MiniBooNE

Cross sections for $_{M^*}$ 2 and $_{M^*}$ 3 on $_{M^*}$ 4C are compared with MiniBooNE double-differential data. The combined QElike+MEC results provide good agreement across most bins. The inclusion of 2p-2h MEC yields a peak response increase of $_{M^*}$ 520–25%, with a near-constant contribution for neutrinos and angle-dependent enhancement for antineutrinos due to interference in the $_{M^*}$ 6 and $_{M^*}$ 7 channels.

At very forward angles ( $_{M^*}$ 8), the model overshoots the data, reflecting limitations at low $_{M^*}$ 9 ( $_{M^*}$ 0 GeV/c), where scaling approaches fail to capture collective and finite-size effects; RPA or microscopic corrections are recommended for such regions.

T2K

The T2K data show a narrower flux peaked at $_{M^*}$ 1 GeV, reducing the relative importance of 2p-2h MEC (10–25% depending on angle). The CDFM $_{M^*}$ 2+MEC calculations agree well with all experimental angular bins. The cross-section decomposition with respect to momentum transfer demonstrates model reliability except at the lowest $_{M^*}$ 3, reinforcing the need for refined treatments at low momenta.

MINERvA

MINERvA measurements with higher energy neutrino flux ( $_{M^*}$ 4 GeV) show substantial 2p-2h MEC contributions (20–30% at maximum). The CDFM $_{M^*}$ 5+MEC results reproduce the observed double-differential cross sections for both neutrino and antineutrino scattering. Comparisons with older RFG-based MEC calculations confirm the magnitude and shape agreement, but the RMF-based inclusion of effective masses and $_{M^*}$ 6-propagators provides a more theoretically consistent framework.

Interpretation, Numerical Results, and Uncertainties

Theoretical predictions are generally in good agreement with available CCQE-like data, with the dominant sources of uncertainty arising from the value of $_{M^*}$ 7, the modeling of MEC, and the low- $_{M^*}$ 8 region. Results with $_{M^*}$ 9 systematically match the data better than those with $m_N^* = 0.8 m_N$ 0, suggesting support for the higher value. Deviations are primarily confined to forward angles and low- $m_N^* = 0.8 m_N$ 1, consistent with known limitations of scaling-based approaches.

The magnitude of the 2p-2h MEC enhancement is process- and kinematics-dependent: approximately 20–30% for MiniBooNE, up to 25% for T2K at very forward angles, and 20–30% for MINERvA. The explicit demonstration that these contributions are needed for accurate data reproduction reinforces the necessity of including multinucleon mechanisms in all cross-section modeling for neutrino-nucleus interactions.

Implications and Prospects

This work demonstrates that with a single effective mass parameter ( $m_N^* = 0.8 m_N$ 2) and consistent CDFM $m_N^* = 0.8 m_N$ 3+MEC treatment, a broad range of inclusive cross-section data can be reproduced for light nuclei. The findings underline the non-negligible role of 2p-2h final states in oscillation experiment analyses and strongly suggest that CCQE-like cross section modeling without multinucleon effects is incomplete. This has direct implications for the extraction of oscillation parameters and the assessment of fundamental neutrino properties from experimental data.

The approach is scalable and can be systematically extended to heavier nuclei (such as $m_N^* = 0.8 m_N$ 4Ar, relevant for MicroBooNE and DUNE). However, limitations persist at low momenta due to the scaling assumption breakdown, and future work should address these with hybrid or fully microscopic corrections at small $m_N^* = 0.8 m_N$ 5.

Conclusion

This study establishes that the CDFM $m_N^* = 0.8 m_N$ 6 superscaling framework with RMF-consistent MEC contributions yields an accurate and reliable description of CCQE-like neutrino and antineutrino scattering on $m_N^* = 0.8 m_N$ 7C. The work provides explicit quantitative support for a $m_N^* = 0.8 m_N$ 820–30% 2p-2h MEC contribution to the cross section in relevant experimental setups. The need to assume a higher $m_N^* = 0.8 m_N$ 9 value to best match data is highlighted. The model's success demonstrates the necessity of a consistent treatment of nuclear correlations, mean-field modifications, and multinucleon emission in neutrino-nucleus interaction theory.

The methodology and results have clear immediate applications in current and forthcoming oscillation analyses that rely on precision modeling of nuclear effects, and delineate a path toward unified treatment of QE and multinucleon response in finite nuclei. Extensions to larger systems and the integration with microscopic low- $\Delta$ 0 modeling will further enhance the scope and predictive capability of the approach.

Reference: "Charged-current quasielastic-like neutrino scattering from $\Delta$ 1C in the coherent density fluctuation model with two-nucleon emission" (2604.15989).