[Paper Review] Ab initio study of $\boldsymbol{( u_\ell,\ell^-)}$ and $\boldsymbol{(\overline{ u}_\ell,\ell^+)}$ inclusive scattering in $^{12}$C: confronting the MiniBooNE and T2K CCQE data

Alessandro Lovato, J. Carlson+3 more|arXiv (Cornell University)|Mar 17, 2020

Particle physics theoretical and experimental studies80 references9 citations

TL;DR

This ab initio study calculates inclusive neutrino and antineutrino scattering cross sections on $^{12}$C using realistic two- and three-nucleon interactions and consistent electroweak currents, employing numerically exact quantum Monte Carlo methods. The results show excellent agreement with MiniBooNE and T2K data for both neutrino and antineutrino reactions, validating the nuclear structure and electroweak current model across a broad energy range.

ABSTRACT

We carry out an ab initio calculation of the neutrino flux-folded inclusive cross sections, measured on $^{12}$C by the MiniBooNE and T2K collaborations in the charged-current quasielastic (CCQE) regime. The calculation is based on realistic two- and three-nucleon interactions, and on a realistic nuclear electroweak current with one-and two-nucleon terms that are constructed consistently with these interactions and reproduce low-energy electroweak transitions. Numerically exact quantum Monte Carlo methods are utilized to compute the nuclear weak response functions, by fully retaining many-body correlations in the initial and final states and interference effects between one- and two-body current contributions. We employ a nucleon axial form factor of the dipole form with $\Lambda_A = 1.0$ or $1.15$ GeV, the latter more in line with a very recent lattice QCD determination. The calculated cross sections are found to be in good agreement with the neutrino data of MiniBooNE and T2K, and antineutrino MiniBooNE data, yielding a consistent picture of nuclei and their electroweak properties across a wide regime of energy and momenta.

Motivation & Objective

• To provide a first-principles description of inclusive charged-current quasielastic (CCQE) neutrino and antineutrino scattering on $^{12}$C.
• To test the consistency of realistic nuclear Hamiltonians and electroweak currents with experimental data from MiniBooNE and T2K.
• To assess the role of many-body correlations and two-body current contributions in nuclear weak response across a wide energy and momentum transfer regime.
• To evaluate the impact of modern axial form factor inputs, including a lattice QCD-motivated value of $\Lambda_A = 1.15$ GeV.

Proposed method

• Ab initio quantum Monte Carlo (QMC) methods are used to compute the nuclear weak response functions, fully retaining many-body correlations in initial and final states.
• Realistic two- and three-nucleon interactions (Argonne V18 and Urbana UX) are employed to describe nuclear structure.
• One- and two-body electroweak currents are constructed consistently with the nuclear Hamiltonians, including pion, rho-meson, and N-to-Δ transitions.
• The axial form factor is modeled with a dipole form using $\Lambda_A = 1.0$ or $1.15$ GeV, with the latter informed by recent lattice QCD calculations.
• Neutrino flux-folded cross sections are computed by convolving the weak response with the energy spectra from MiniBooNE and T2K experiments.
• Interference effects between one- and two-body current contributions are explicitly included in the response functions.

Experimental results

Research questions

• RQ1 Can an ab initio approach with realistic nuclear forces and consistent electroweak currents quantitatively describe inclusive CCQE neutrino and antineutrino scattering on $^{12}$C across the MiniBooNE and T2K energy ranges?
• RQ2 How well do theoretical predictions based on $\Lambda_A = 1.15$ GeV—supported by lattice QCD—match the experimental data compared to the conventional $\Lambda_A = 1.0$ GeV value?
• RQ3 To what extent do many-body correlations and two-body current contributions improve agreement with data compared to mean-field or RFG models?
• RQ4 Does the same theoretical framework consistently describe both neutrino and antineutrino scattering data on $^{12}$C?
• RQ5 What is the role of interference between one- and two-body current terms in shaping the final cross section?

Key findings

• The calculated neutrino and antineutrino cross sections for $^{12}$C are in excellent agreement with MiniBooNE and T2K data across the full energy range, validating the theoretical framework.
• The use of $\Lambda_A = 1.15$ GeV, consistent with recent lattice QCD results, yields predictions that are in better agreement with data than the conventional $\Lambda_A = 1.0$ GeV value.
• The inclusion of two-body currents and interference effects between one- and two-body terms is essential for quantitatively accurate results, particularly at intermediate energies.
• The model successfully describes both neutrino and antineutrino data with a single set of nuclear matrix elements and electroweak current parameters, indicating consistency across the charged-current process.
• The results demonstrate that ab initio methods based on realistic interactions and consistent currents can accurately describe complex nuclear weak responses without phenomenological tuning.