Neutral current neutrino and antineutrino scattering off the polarized nucleon

The elastic and inelastic neutral current $\nu$ ($\overline{\nu }$) scattering off the polarized nucleon is discussed. The inelastic scattering concerns the single-pion production process. We show that the spin asymmetries’ measurement can help to distinguish between neutrino and antineutrino neutral current scattering processes. The spin asymmetries also encode information about a type of target. Eventually, detailed studies of the inelastic spin asymmetries can improve understanding of the resonant-nonresonant pion production mechanism.

Figure 1

In the top figure: neutrino scattering off the longitudinally (along the neutrino beam) polarized nucleon. In the bottom figure: the neutrino scattering off the nucleon polarized perpendicularly to the beam. The scattering plane has green color. The normal plane to the perpendicular polarization is gray. The red vector denotes the polarization of the nucleon. The polarization vectors ${\chi }_{L,T,N}$ are drawn in both panels.

Figure 2

Target-spin asymmetry for NCEl. The solid/dashed line denotes the spin asymmetries computed for the neutrino/antineutrino-proton (black line), -neutron (blue line), and isoscalar target (red line) scattering. In the top/bottom panel ${\mathcal{T}}^L(E)/{\mathcal{T}}^T(E)$ is plotted.

Figure 3

Target-spin asymmetry for NC SPP (full model). The solid/dotted line corresponds to the ${\mathcal{T}}_{L/T}$ component of the spin asymmetries. The black/red line denotes the spin asymmetries computed for $\nu /\overline{\nu }$ scattering off the nucleon. In the top panels, we plot the corresponding NCEl target spin asymmetries in the background.

Figure 4

Target-spin asymmetry for NC SPP but only $\mathcal{N}\to \mathrm{\Delta }$ contribution described by DP and CDP diagrams. The solid/dotted line corresponds to the ${\mathcal{T}}_{L/T}$ component of the spin asymmetries. The black/red line denotes the spin asymmetries computed for $\nu /\overline{\nu }$ scattering off the nucleon. In the background, the corresponding full SPP model-spin asymmetries are shown.

Figure 5

Target-spin asymmetry for NC SPP but only nucleon-pole contribution described by NP and CNP diagrams. The solid/dotted line corresponds to the ${\mathcal{T}}_{L/T}$ component of the spin asymmetries. The black/red line denotes the spin asymmetries computed for $\nu /\overline{\nu }$ scattering off the nucleon. In the background, the corresponding full SPP model-spin asymmetries are shown.