Neutrino versus antineutrino cross sections and $\mathit{CP}$ violation

We discuss the nuclear interactions of neutrinos versus those of antineutrinos, a relevant comparison for $\mathit{CP}$ violation experiments in the neutrino sector. We consider the MiniBooNE quasielastic-like double-differential neutrino and antineutrino cross sections that are dependent on the energy profiles of the neutrino fluxes and hence specific to the MiniBooNE setup. We combine them introducing their sum $(\nu +\overline{\nu })$ and their difference $(\nu -\overline{\nu })$. We show that the last combination gives general information on the multinucleon content of the axial-vector interference term. Our theoretical model reproduces well the two cross-section combinations, confirming the need for a sizable multinucleon component.

Figure 1

Normalized MiniBooNE ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ fluxes derived from Refs. [3] and [17], respectively. Their half sum $\left({\Phi }_{+}\right)$ and half difference $\left({\Phi }_{-}\right)$ are also shown.

Figure 2

Difference of the $\nu$ and $\overline{\nu }$ flux-folded double-differential cross sections on carbon per active nucleon plotted as a function of the $cos\theta$ for different values of the emitted muon kinetic energies. Continuous line: evaluation (RPA + np-nh) with the real $\nu$ and $\overline{\nu }$ MiniBooNE fluxes; dot-dashed line: evaluation (RPA + np-nh) with the mean flux ${\Phi }_{+}$.

Figure 3

Sum $S$ of the $\nu$ and $\overline{\nu }$ MiniBooNE flux-folded double-differential cross sections on carbon per active nucleon plotted as a function of the $cos\theta$ for different values of the emitted muon kinetic energies. Continuous line: our complete RPA evaluation including the multinucleon emission channel; dashed line: genuine quasielastic contribution calculated in RPA; dot-dashed line: quasielastic contribution in the bare case. The points are the combination of the MiniBooNE experimental results [3, 17]. For the neutrino and antineutrino data there are additional normalization uncertainties of 10% and 17.2%, respectively, not taken into account here.

Figure 4

The same as Fig. 3 but for the difference $D$.

Figure 5

Sum and difference of the $\nu$ and $\overline{\nu }$ flux-folded differential cross sections $\frac{d\sigma }{dcos\theta }$ and $\frac{d\sigma }{d{T}_{\mu }}$ on carbon per active nucleon. Continuous line: complete RPA evaluation including the multinucleon emission channel with the real $\nu$ and $\overline{\nu }$ MiniBooNE fluxes; dashed line: genuine quasielastic contribution calculated using the RPA with the real $\nu$ and $\overline{\nu }$ MiniBooNE fluxes; dot-dashed line: complete RPA evaluation including the multinucleon emission channel with the mean flux ${\Phi }_{+}$; dotted line: contribution of the isovector response only.

Figure 6

Sum and difference of the $\nu$ and $\overline{\nu }$ flux-folded $Q^2$ distributions on carbon per active nucleon. Continuous line: complete RPA evaluation including the multinucleon emission channel with the real $\nu$ and $\overline{\nu }$ MiniBooNE fluxes; dashed line: genuine quasielastic contribution calculated in RPA with the real $\nu$ and $\overline{\nu }$ MiniBooNE fluxes; thin dot-dashed line: quasielastic contribution calculated in the bare case with the real $\nu$ and $\overline{\nu }$ MiniBooNE fluxes; thick dot-dashed line: complete RPA evaluation including the multinucleon emission channel with the mean flux ${\Phi }_{+}$.