Neutral current quasielastic (anti)neutrino scattering beyond the Fermi gas model at MiniBooNE and BNL kinematics

Neutral current quasielastic (anti)neutrino scattering cross sections on a ${}^{12}\mathrm{C}$ target are analyzed using a realistic spectral function $S(p,E)$ that gives a scaling function in accordance with the $(e,e^{\prime })$ scattering data. The spectral function accounts for the nucleon-nucleon (NN) correlations by using natural orbitals from the Jastrow correlation method and has a realistic energy dependence. The standard value of the axial mass $M_A=1.032$ GeV is used in all calculations. The effect of the final-state interaction on the spectral and scaling functions, as well as on the cross sections, is accounted for. A comparison of the calculations with the empirical data of the MiniBooNE and BNL experiments is performed. Our results are analyzed in comparison with those when NN correlations are not included and, also, with results from other theoretical approaches, such as the relativistic Fermi gas, the relativistic mean field, and the relativistic Green's function, as well as with the SuperScaling Approach based on the analysis of quasielastic electron scattering.

Figure 1

Kinematics for semileptonic nucleon knockout reactions in the one-boson-exchange approximation.

Figure 2

The ${}^{12}\mathrm{C}$ realistic spectral function $S(p,\mathcal{E})$, which is constructed using natural orbit single-particle momentum distributions from the Jastrow correlation method and Lorentzian function for the energy dependence (see text).

Figure 3

NCQE neutrino [(a) $\nu N\to \nu N$] and antineutrino [(b) $\overline{\nu }N\to \overline{\nu }N$] flux-averaged differential cross section computed using the RFG, HO + FSI, NO + FSI, and SUSA scaling functions in the RGF and RMF models and compared with the MiniBooNE data [43, 46]. Results correspond to the world-average axial mass $M_A=1.032$ GeV and strangeness $\Delta s=0$. Error bars do not account for the normalization uncertainty of 18.1% (19.5%) in the $\nu \left(\overline{\nu }\right)$ case.

Figure 4

Differential cross section $d\sigma /d{Q}^2$ for $\nu \mathrm{NCQE}$ scattering per bound nucleon in the ${}^{12}\mathrm{C}$ nucleus calculated within the RMF model and multiplied by the MiniBooNE flux. Results are given at several fixed values of four-momentum transfer squared $\left(Q^2\right)$.

Figure 5

Ratio of the antineutrino-to-neutrino NCQE scattering cross section computed using the RFG, HO + FSI, NO + FSI, SUSA, RGF, and RMF approaches and compared with the MiniBooNE data [46].

Figure 6

RFG, HO + FSI, NO + FSI, SUSA, RGF, and RMF predictions, after the folding procedure, compared with the histograms of the numerator (top left) and denominator (bottom left) of the ratio. Error bars in the left panel represent only the statistical uncertainty, computed as the square root of the event number. The corresponding ratio is shown in the right panel. The axial mass and strangeness are assumed to be the standard axial mass value and zero strangeness. Data are taken from [43, 89, 90].

Figure 7

NCQE flux-averaged cross section: (a) $\nu p\to \nu p$ and (b) $\overline{\nu }p\to \overline{\nu }p$ compared with the BNL E734 experimental data [44]. Our results are evaluated using the RFG, HO + FSI, NO + FSI, and SUSA scaling functions in the RMF model with the standard value of the axial-vector dipole mass $M_A=1.032{\mathrm{GeV}}^2$ and strangeness $\Delta s=0$. Error bars do not include the normalization uncertainty of 11.2% (10.4%) in the $\nu \left(\overline{\nu }\right)$ case.