Deuterium target data for precision neutrino-nucleus cross sections

Amplitudes derived from scattering data on elementary targets are basic inputs to neutrino-nucleus cross section predictions. A prominent example is the isovector axial nucleon form factor, $F_A(q^2)$, which controls charged current signal processes at accelerator-based neutrino oscillation experiments. Previous extractions of $F_A$ from neutrino-deuteron scattering data rely on a dipole shape assumption that introduces an unquantified error. A new analysis of world data for neutrino-deuteron scattering is performed using a model-independent, and systematically improvable, representation of $F_A$. A complete error budget for the nucleon isovector axial radius leads to $r_A^2=0.46(22){\mathrm{fm}}^2$, with a much larger uncertainty than determined in the original analyses. The quasielastic neutrino-neutron cross section is determined as $\sigma ({\nu }_{\mu }n\to {\mu }^{-}p){|}_{E_{\nu }=1\mathrm{GeV}}=10.1(0.9)\times {10}^{-39}{\mathrm{cm}}^2$. The propagation of nucleon-level constraints and uncertainties to nuclear cross sections is illustrated using MINERvA data and the GENIE event generator. These techniques can be readily extended to other amplitudes and processes.

Figure 1

Experimental data and best fit curves corresponding to dipole and $N_a=4$ $z$ expansion in Table 4, for BNL1981 (top pane), ANL1982 (middle pane) and FNAL1983 (bottom pane).

Figure 2

Best fit curves and errors propagated from deuterium to free-neutron cross section, for BNL1981 (top pane), ANL1982 (middle pane) and FNAL1983 (bottom pane). Blue (horizontal stripes) corresponds to dipole and red (vertical stripes) to $N_a=4$ $z$ expansion in Table 4.

Figure 3

Absolutely normalized $d{\sigma }^n/d{Q}^2$ at $E_{\nu }=10\mathrm{GeV}$ for dipole (blue) and $z$-expansion axial form factor central values as in the FNAL1983 results of Fig. 1 and Fig. 2.

Figure 4

Data divided by best fit prediction for the $Q^2$ distributions displayed in Fig. 1, for BNL (blue) ANL (red), and FNAL (green). Calculated ${\chi }^2/N_{\mathrm{bins}}$ are $35.3/22$, $41.2/25$, and $10.7/14$ for BNL, ANL, and FNAL respectively.

Figure 5

Same as Fig. 1, but with $Q^2\le 1{\mathrm{GeV}}^2$. These fits correspond to the $N_a=4$ $z$ expansion in Table 5.

Figure 6

Differential scattering cross sections for neutrino-deuteron scattering at 1 GeV neutrino energy, employing different nuclear models. The solid (red) curve is the free-neutron result. The dashed (blue) curve is obtained from the free-neutron result using the model from Ref. [65], as in the original deuterium analyses. The top dot-dashed (black) curve is extracted at $E_{\nu }=1\mathrm{GeV}$ from Ref. [70]. The charged lepton mass is neglected in this plot.

Figure 7

Final form factor from Eqs. (31), (32) and (33). Also shown is the dipole axial form factor with axial mass $m_A=1.014(14)\mathrm{GeV}$ [55].

Figure 8

Free nucleon CCQE cross section computed from Eqs. (31), (32) and (33), for neutrino-neutron (top) and antineutrino-proton (bottom) scattering. Also shown are results using dipole axial form factor with axial mass $m_A=1.014(14)\mathrm{GeV}$ [55].

Figure 9

Cross section for charged-current quasielastic events from the MINERvA experiment [56] as a function of reconstructed $Q^2$, compared with prediction using relativistic Fermi gas (RFG) nuclear model with $z$ expansion axial form factor extracted from deuterium data. MINERvA data uses an updated flux prediction from [82]. Also shown are results using the same nuclear model but dipole form factor with axial mass $m_A=1.014(14)\mathrm{GeV}$ [55].