Ab Initio Study of $({\nu }_{\ell },{\ell }^{-})$ and $({\overline{\nu }}_{\ell },{\ell }^{+})$ Inclusive Scattering in ${}^{12}\mathrm{C}$: Confronting the MiniBooNE and T2K CCQE Data

We carry out an ab initio calculation of the neutrino flux-folded inclusive cross sections measured on ${}^{12}\mathrm{C}$ by the MiniBooNE and T2K Collaborations in the charged-current quasielastic 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 ${\mathrm{\Lambda }}_A=1.0$ 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.

Popular Summary

Neutrinos are particles shrouded in mystery. Despite nearly a century of investigations, researchers still do not fully understand the masses of neutrinos or the parameters that characterize a bizarre behavior known as flavor oscillations—the ability to morph from one flavor (or type) to another. To measure these flavor oscillations, physicists have mounted a large program of experiments. Interpretation of these experiments depends strongly on a detailed understanding of how neutrinos interact with atomic nuclei over a broad range of energies. Here, we address this problem in the regime where protons and neutrons (or nucleons) are the dominant players in the interaction, a case known as the quasielastic regime.

We model the strong interactions among nucleons by two- and three-body forces, while the weak interactions of neutrinos with the nucleus involve individual nucleons and pairs of nucleons. When coupled to numerically exact methods, this dynamical framework provides a quantitatively accurate description of many nuclear properties, including spectra and reactions. In our study, we use this framework to calculate from first principles the interaction cross section between neutrinos and a carbon nucleus (12C). In contrast to other approaches, we made no approximations beyond those inherent to the dynamical model itself.

We find that available quasielastic cross-section data of neutrinos and antineutrinos on ${}^{12}\mathrm{C}$ are in good accord with theoretical predictions, thus corroborating the validity of the adopted dynamical model and yielding a consistent picture of nuclear electroweak properties across a wide range of energies and momenta.

Figure 1

GFMC response functions at $q=300$ (red), 500 (blue), and 700 (green) MeV. Predictions obtained with one-body (one- and two-body) currents are shown by dash (solid) lines. Shaded areas result from a combination of GFMC statistical errors and uncertainties associated with the maximum-entropy inversion.

Figure 2

Transverse scaling functions obtained from $R_{xx}$ and $R_{xy}$ including only one-body, and one- and two-body terms in the CC denoted, respectively, as $f_{xx}^{1b}$ and $f_{xy}^{1b}$, and $f_{xx}^{12b}$ and $f_{xy}^{12b}$. The different curves are obtained for three different values of the moment transfer.

Figure 3

Normalized ${\nu }_{\mu }$ fluxes of MiniBooNE and T2K, and normalized ${\overline{\nu }}_{\mu }$ flux of MiniBooNE.

Figure 4

MiniBooNE flux-folded double-differential cross sections per target neutron for ${\nu }_{\mu }$-CCQE scattering on ${}^{12}\mathrm{C}$ displayed as a function of the muon kinetic energy ($T_{\mu }$) for different ranges of $\cos {\theta }_{\mu }$. The experimental data and their shape uncertainties are from Ref. [55]. The additional 10.7% normalization uncertainty is not shown here. Calculated cross sections are obtained with ${\mathrm{\Lambda }}_A=1.0\mathrm{GeV}$.

Figure 5

Same as Fig. 4 but for ${\overline{\nu }}_{\mu }$-CCQE scattering. The experimental data and their shape uncertainties are from Ref. [56]. The additional 17.4% normalization uncertainty is not shown here.

Figure 6

T2K flux-folded double-differential cross sections per target neutron for ${\nu }_{\mu }$-CCQE scattering on ${}^{12}\mathrm{C}$ displayed as a function of the muon momentum $p_{\mu }$ for different ranges of $\cos {\theta }_{\mu }$. The experimental data and their shape uncertainties are from Ref. [57]. Calculated cross sections are obtained with ${\mathrm{\Lambda }}_A=1.0\mathrm{GeV}$.

Figure 7

The flux-folded GFMC cross sections for selected bins in $\cos {\theta }_{\mu }$ obtained by replacing in the dipole parametrization the cutoff ${\mathrm{\Lambda }}_A=1\mathrm{GeV}$ with the value ${\tilde{\mathrm{\Lambda }}}_A=1.15\mathrm{GeV}$, more in line with a current LQCD determination [47]. The first two rows correspond to the MiniBooNE flux-folded ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ CCQE cross sections, respectively; the last row corresponds to the T2K ${\nu }_{\mu }$ CCQE data. In the theoretical curves, the total one- plus two-body current contribution to the cross section is displayed.