Realistic spectral function model for charged-current quasielastic-like neutrino and antineutrino scattering cross sections on ${}^{12}\mathrm{C}$

A detailed study of charged current quasielastic neutrino and antineutrino scattering cross sections on a ${}^{12}\mathrm{C}$ target with no pions in the final state is presented. The initial nucleus is described by means of a realistic spectral function $S(p,\mathcal{E})$ in which nucleon-nucleon correlations are implemented by using natural orbitals through the Jastrow method. The roles played by these correlations and by final-state interactions are analyzed and discussed. The model also includes the contribution of weak two-body currents in the two-particle two-hole sector, evaluated within a fully relativistic Fermi gas. The theoretical predictions are compared with a large set of experimental data for double-differential, single-differential, and total integrated cross sections measured by the MiniBooNE, $\mathrm{MINER}\nu \mathrm{A}$, and T2K experiments. Good agreement with experimental data is found over the whole range of neutrino energies. The results are also in global good agreement with the predictions of the superscaling approach, which is based on the analysis of electron-nucleus scattering data, with only a few differences seen at specific kinematics.

Figure 1

Results for the superscaling function $f\left(\psi \right)$ for ${}^{12}\mathrm{C}$ obtained using HO and NO approaches with (HO+FSI and NO+FSI) and without FSI (HO and NO) are compared with the RFG results, as well as with the longitudinal experimental data.

Figure 2

The predicted ${\nu }_{\mu }$ (${\overline{\nu }}_{\mu }$) fluxes at the MiniBooNE [68], T2K [69], and $\mathrm{MINER}\nu \mathrm{A}$ [70] detectors and corresponding mean energies.

Figure 3

MiniBooNE flux-folded double differential cross section per target neutron for the ${\nu }_{\mu }$ CCQE process on ${}^{12}\mathrm{C}$ displayed versus the ${\mu }^{-}$ kinetic energy $T_{\mu }$ for various bins of $cos{\theta }_{\mu }$ obtained within the SuSAv2, HO+FSI, and NO+FSI approaches including MEC. 2p-2h MEC results are shown separately. The data are from Ref. [36].

Figure 4

As for Fig. 3 but considering more backward kinematics. The data are from Ref. [36].

Figure 5

As for Fig. 3 but now for the ${\overline{\nu }}_{\mu }$ CCQE process on ${}^{12}\mathrm{C}$. The data are from Ref. [37].

Figure 6

As for Fig. 5 but considering more backward kinematics. The data are from Ref. [37].

Figure 7

MiniBooNE flux-averaged CCQE ${\nu }_{\mu }–{}^{12}\mathrm{C}$ (${\overline{\nu }}_{\mu }–{}^{12}\mathrm{C}$) differential cross section per nucleon as a function of the muon kinetic energy [(a) and (c)] and of the muon scattering angle [(b) and (d)]. Panels (a) and (b) correspond to neutrino cross sections and (c) and (d) to antineutrino reactions. The data are from Refs. [36, 37].

Figure 8

CCQE ${\nu }_{\mu }–{}^{12}\mathrm{C}$ (${\overline{\nu }}_{\mu }–{}^{12}\mathrm{C}$) total cross section per neutron (proton) as a function of the neutrino energy. Panel (a) corresponds to neutrino cross sections and (b) to antineutrino reactions. The data are from MiniBooNE [36, 37] and NOMAD [38] experiments.

Figure 9

Flux-folded CCQE ${\overline{\nu }}_{\mu }$–CH scattering cross section per target proton as a function of $Q_{\text{QE}}^2$ and evaluated in the SuSAv2, HO+FSI, and NO+FSI approaches including MEC. The $\mathrm{MINER}\nu \mathrm{A}$ data are from Ref. [42].

Figure 10

T2K flux-folded double differential cross section per target nucleon for the ${\nu }_{\mu }$ CCQE process on ${}^{12}\mathrm{C}$ displayed versus the ${\mu }^{-}$ momentum $p_{\mu }$ for various bins of $cos{\theta }_{\mu }$ obtained within the SuSAv2, HO+FSI, and NO+FSI approaches including MEC. MEC results are shown also separately. The data are from Ref. [39].

Figure 11

MiniBooNE flux-folded double differential cross section per target neutron for the ${\nu }_{\mu }$ CCQE process on ${}^{12}\mathrm{C}$ displayed versus the ${\mu }^{-}$ kinetic energy $T_{\mu }$ for $0.9<cos{\theta }_{\mu }<1.0$ (a) and T2K flux-folded double differential cross section per target neutron for the ${\nu }_{\mu }$ CCQE process on ${}^{12}\mathrm{C}$ displayed versus the ${\mu }^{-}$ momentum $p_{\mu }$ for $0.98<cos{\theta }_{\mu }<1.00$ (b) obtained within the HO, NO, HO+FSI, and NO+FSI approaches including MEC. The data are from Refs. [36, 39].

Figure 12

T2K flux-folded double differential cross section per target neutron for the ${\nu }_{\mu }$ CCQE process on ${}^{12}\mathrm{C}$ displayed versus the ${\mu }^{-}$ momentum $p_{\mu }$ for two bins of $0.98<cos{\theta }_{\mu }<1.00$ and $0.60<cos{\theta }_{\mu }<0.70$ obtained within the HO+FSI and NO+FSI approaches with and without PB effects. Data are from Ref. [39].