Electron-neutrino scattering off nuclei from two different theoretical perspectives

We analyze charged-current electron-neutrino cross sections on carbon. We consider two different theoretical approaches, on one hand the continuum random phase approximation (CRPA) which allows a description of giant resonances and quasielastic excitations, on the other hand the RPA-based calculations which are able to describe multinucleon emission and coherent and incoherent pion production as well as quasielastic excitations. We compare the two approaches in the genuine quasielastic channel, and find a satisfactory agreement between them at large energies while at low energies the collective giant resonances show up only in the CRPA approach. We also compare electron-neutrino cross sections with the corresponding muon-neutrino ones in order to investigate the impact of the different charged-lepton masses. Finally, restricting to the RPA-based approach, we compare the sum of quasielastic, multinucleon emission, coherent, and incoherent one-pion production cross sections (folded with the electron-neutrino T2K flux) with the charged-current inclusive electron-neutrino differential cross sections on carbon measured by T2K. We find a good agreement with the data. The multinucleon component is needed in order to reproduce the T2K electron-neutrino inclusive cross sections.

Figure 1

Electron-neutrino CC double differential cross section on carbon for fixed values of scattering angles and incident neutrino energies as a function of the energy transferred to the nucleus. In the upper panels the results obtained in the bare-LRFG approach and in the RPA with and without the EELL effect are displayed. In the lower panels the results obtained in HF and CRPA approaches are displayed. Only genuine quasielastic and giant resonance excitations (given by the CRPA) are considered.

Figure 2

Electron-neutrino CC double differential cross section on carbon for fixed values of scattering angles and incident neutrino energies as a function of the energy transferred to the nucleus. In the upper (lower) panels the results obtained in the bare-LRFG (RPA) and HF (CRPA) approaches are displayed. Only genuine quasielastic and giant resonances excitations (given by the CRPA) are considered. Continuous lines: HF and CRPA results; dashed lines: LRFG and RPA results shifted by 18 MeV.

Figure 3

The three major multipole contributions to the CRPA cross sections in the different kinematical conditions.

Figure 4

Normalized electron-neutrino T2K [54] and MiniBooNE [55] fluxes.

Figure 5

Electron-neutrino T2K and MiniBooNE flux-folded CC single differential cross sections on carbon per nucleon.

Figure 6

Electron- and muon-neutrino CC double differential cross section on carbon for fixed values of scattering angle and incident neutrino energies as a function of the charged lepton kinetic energy calculated in the RPA approach of Ref. [20]. Left panel: genuine quasielastic with and without RPA and EELL effects; middle panel: np-nh excitations; right panel: incoherent one pion production contribution.

Figure 7

Electron- and muon-neutrino CC double differential cross section on carbon calculated in the CRPA approach for fixed values of scattering angles and incident neutrino energies as a function of the energy transferred to the nucleus.

Figure 8

The values of the momentum transfer versus the transferred energy for the ${\nu }_e$ and ${\nu }_{\mu }$ scattering corresponding to the kinematical conditions of Fig. 7.

Figure 9

Coulomb-longitudinal (CL) and transverse (T) contributions to electron- and muon-neutrino CC double differential cross section on carbon calculated in the CRPA approach for incident neutrino energies of 200 MeV and 750 MeV and two fixed values of scattering angles as a function of the transferred energy to the nucleus.

Figure 10

Ratio of the ${\nu }_e$ over ${\nu }_{\mu }$ differential cross section on carbon calculated for two fixed values of incident neutrino energies as a function of the cosine of the lepton scattering angle. The 1p-1h results in the CRPA approach are shown for $E_{\nu }=200$ MeV and $E_{\nu }=750$ MeV. The 1p-1h results in the RPA approach with or without the EELL effect, the $n\text{p}-n\mathrm{h}$ excitations and the one-pion production (via $\mathrm{\Delta }$ excitation) results are shown for $E_{\nu }=750$ MeV.

Figure 11

Electron- and muon-neutrino CC double differential cross section on carbon calculated in the RPA approach of Martini et al. for fixed values of scattering angles and incident neutrino energies as a function of the transferred energy to the nucleus. The genuine quasielastic (QE), multinucleon ($\mathrm{n}\text{p}-\mathrm{n}\mathrm{h}$), and incoherent one-pion production excitations are plotted separately.

Figure 12

T2K flux-integrated inclusive ${\nu }_e$ CC differential cross section on carbon per nucleon as a function of the electron momentum. The different contributions to this inclusive cross section obtained in the Martini et al. RPA model of Ref. [20] are shown. The experimental T2K points are taken from Ref. [37].

Figure 13

T2K flux-integrated inclusive ${\nu }_e$ CC differential cross section on carbon per nucleon as a function of the cosine of the lepton scattering angle. The different contributions to this inclusive cross section obtained in the Martini et al. RPA model of Ref. [20] are shown. The experimental T2K points are taken from Ref. [37].