Quantum Monte Carlo calculation of neutral-current $\nu -{}^{12}\mathrm{C}$ inclusive quasielastic scattering

Quasielastic neutrino scattering is an important aspect of the experimental program to study fundamental neutrino properties including neutrino masses, mixing angles, mass hierarchy, and charge-conjugation parity (CP)- violating phase. Proper interpretation of the experiments requires reliable theoretical calculations of neutrino-nucleus scattering. In this paper we present calculations of response functions and cross sections by neutral-current scattering of neutrinos off ${}^{12}\mathrm{C}$. These calculations are based on realistic treatments of nuclear interactions and currents, the latter including the axial, vector, and vector-axial interference terms crucial for determining the difference between neutrino and antineutrino scattering and the CP-violating phase. We find that the strength and energy dependence of two-nucleon processes induced by correlation effects and interaction currents are crucial in providing the most accurate description of neutrino-nucleus scattering in the quasielastic regime.

Figure 1

Neutral-current response functions in ${}^{12}\mathrm{C}$ at momentum transfer $q=570$ MeV/$c$, corresponding to the AV18/IL7 Hamiltonian and obtained with one-body only (dashed lines) and one- and two-body (solid lines) currents. The narrow bands indicate the uncertainty in the maximum-entropy inversion. The vector and axial contributions are shown separately in all cases but for $R_{xy}$. See text for further explanations.

Figure 2

Weak neutral $\nu$ (black curves) and $\overline{\nu }$ (red curves) differential cross sections in ${}^{12}\mathrm{C}$ at $q=570$ MeV/$c$, obtained with one-body only and one- and two-body terms in the NC. The final neutrino angle is indicated in each panel. The insets show ratios of the $\nu$ to $\overline{\nu }$ (central-value) cross sections. Also shown are the PWIA results.