Parametrized uncertainties in the spectral function model of neutrino charged-current quasielastic interactions for oscillation analyses

A substantial fraction of systematic uncertainties in neutrino oscillation experiments stem from the lack of precision in modeling the nuclear target in neutrino-nucleus interactions. Whilst this has driven significant progress in the development of improved nuclear models for neutrino scattering, it is crucial that the models used in neutrino data analyses be accompanied by parameters and associated uncertainties that allow the coverage of plausible nuclear physics. Based on constraints from electron scattering data, we propose such a set of parameters, which can be applied to nuclear shell models, and test their application to the Benhar et al. [Nucl. Phys. A579, 493 (1994)] spectral function model. The parametrization is validated through a series of maximum likelihood fits to cross section measurements made by the T2K and MINERvA experiments, which also permit an exploration of the power of near-detector data to provide constraints on the parameters in neutrino oscillation analyses.

Figure 1

Simulations of the two-dimensional distribution of the removal energy $E_{\mathrm{rmv}}$, and the initial-state nucleon momentum $p_N$, for carbon using the RFG (blue), LFG (green), and SF (red) model simulated with the NEUT neutrino interaction generator.

Figure 2

Comparison between the distribution of the initial-state nucleon momentum (left) and the neutrino energy bias (right) for CCQE interactions for the RFG (blue), LFG (green), and SF (red) model generated by NEUT using the T2K muon neutrino flux.

Figure 3

The prediction of the two-dimensional distribution of removal energy and initial-state nucleon momentum for carbon (left) and oxygen (right) for NEUT. The brightness of the color represents the probability of finding an initial-state nucleon with a particular removal energy and momentum state. The white lines indicate the cuts used to separate the MF region (low $E_{\mathrm{rmv}}$, $p_N$) from the SRC region (high $E_{\mathrm{rmv}}$, $p_N$) in the NuWro (dashed) and NEUT (solid) neutrino interaction generators.

Figure 4

The distributions for removal energy (top) and transverse momentum imbalance (bottom) as given by the SF model implemented in NEUT, showing the impact of the shell normalization parameters ($N_{\text{shell}}$) from $-1.5\sigma$ (pink) to $+1.5\sigma$ (cyan), compared to the nominal (black). The interactions were generated on a carbon target using the T2K flux.

Figure 5

Distribution of the initial-state nucleon momentum within each nuclear shell for carbon as given by the SF model implemented in NEUT generated using the T2K flux.

Figure 6

The impact of the shell normalization parameters ($N_{\text{shell}}$) on the total CCQE cross section when applied to the SF model implemented in NEUT for each shell in carbon (top) and oxygen (bottom). The dashed horizontal lines indicate the $\pm 10\%$ variations, chosen to correspond to the $1\sigma$ uncertainty for these parameters. The interactions were generated using the T2K flux.

Figure 7

Distributions of the initial-state nucleon momentum from the NEUT SF inputs (black) compared to electron scattering measurements [20] (blue and red), made for different nucleon and lepton kinematics for carbon in the $p$-shell (left) and the $s$-shell (right).

Figure 8

The distributions for the angle between the outgoing lepton and neutrino (left) and the transverse momentum imbalance (right) as given by the SF model implemented in NEUT, showing the impact of variations of the $p$-shell shape uncertainty from $-2\sigma$ (pink) to $2\sigma$ (cyan), compared to the nominal (black). The interactions were generated on a carbon target using the T2K flux.

Figure 9

Distribution of the initial-state nucleon momentum in the SF model in NEUT (left) and NuWro (right) for carbon with the MF and SRC contributions.

Figure 10

The distributions of the angle between the outgoing muon and neutrino (top) and the muon momentum in the $\cos {\theta }_{\mu }>0.9$ region (bottom), showing the impact of varying the PB threshold from $-1.5\sigma$ (cyan) to $+1.5\sigma$ (pink), compared to the nominal (black). The interactions were generated on a carbon target using the T2K flux.

Figure 11

The distributions of the angle between the outgoing muon and neutrino (top) and the muon momentum in the $\cos {\theta }_{\mu }>0.9$ region (bottom), showing the impact of varying the PB threshold from 0%, i.e., nominal, (black) to 100% (orange), compared to the nominal (black).

Figure 12

Prefit (red) and postfit (blue) distributions of $p_{\mu }$ in bins of $\cos {\theta }_{\mu }$ from the fit to T2K $\mathrm{CC}0\pi$ joint measurement of lepton kinematics on carbon and oxygen. The usual chi-squares as well as the number of bins are quoted in the legend. The NS chi-square ${\chi }_{\mathrm{NS}}^2$ used in the minimization is reported in Table 3.

Figure 13

Prefit (red) and postfit (blue) values and constraints on the uncertainties from the fit to T2K $\mathrm{CC}0\pi$ joint measurement of lepton kinematics on carbon and oxygen. The displayed central value for each parameter corresponds to the difference with respect to its prior value divided by the prior uncertainty as reported in Table 2.

Figure 14

Postfit correlation matrix from the fit to T2K $\mathrm{CC}0\pi$ joint measurement of lepton kinematics on carbon and oxygen.

Figure 15

True squared four momentum transfer (upper) and neutrino energy (lower) distributions of interactions falling into the $\mathrm{CC}0\pi 0p$ (blue) and $\mathrm{CC}0\pi Np$ (red) topologies in the T2K beam on a carbon target as predicted by NEUT.

Figure 16

Prefit (red) and postfit (blue) distributions of $p_{\mu }$ in bins of $\cos {\theta }_{\mu }$ from fitting T2K $\mathrm{CC}0\pi 0p$ data only. The usual chi-squares as well as the number of bins are quoted in the legend. The NS chi-square ${\chi }_{\mathrm{NS}}^2$ used in the minimization is reported in Table 3.

Figure 17

Prefit (red) and postfit (blue) distributions of $\delta p_{\mathrm{T}}$ from fitting the T2K $\mathrm{CC}0\pi Np$ data only. The usual chi-squares as well as the number of bins are quoted in the legend. The NS chi-square ${\chi }_{\mathrm{NS}}^2$ used in the minimization is reported in Table 3.

Figure 18

Prefit and postfit values and constraints on the uncertainties from the fit to T2K $\mathrm{CC}0\pi 0p$ measurement of lepton kinematics and $\mathrm{CC}0\pi Np$ measurement of $\delta p_{\mathrm{T}}$ on carbon. The displayed central value for each parameter corresponds to the difference with respect to its prior value divided by the prior uncertainty as reported in Table 2.

Figure 19

Postfit correlation matrices from the fit to T2K $\mathrm{CC}0\pi 0p$ measurement of lepton kinematics (top left) and $\mathrm{CC}0\pi Np$ measurement of $\delta p_{\mathrm{T}}$ (top right), as well as the simultaneous fit (bottom).

Figure 20

Prefit (red) and postfit (blue) distributions from the fit to MINERvA $\mathrm{CC}0\pi +Np$ measurement of $\delta p_{\mathrm{T}}$ on carbon. The usual chi-squares as well as the number of bins are quoted in the legend. The NS chi-square ${\chi }_{\mathrm{NS}}^2$ used in the minimization is reported in Table 3.

Figure 21

Prefit (red) and postfit (blue) values and constraints on the uncertainties from the fit to MINERvA $\mathrm{CC}0\pi Np$ measurement of $\delta p_{\mathrm{T}}$ on carbon. The displayed central value for each parameter corresponds to the difference with respect to its prior value divided by the prior uncertainty as reported in Table 2.

Figure 22

Postfit correlation matrix from the fit to MINERvA $\mathrm{CC}0\pi Np$ measurement of $\delta p_{\mathrm{T}}$ on carbon.

Figure 23

Prefit (red) and postfit (blue) constraints on the true neutrino energy (top) and the bias of $E_{\nu }^{\mathrm{QE}}$ (bottom) differential cross sections in the T2K beam on a carbon target following the fit to the T2K $\mathrm{CC}0\pi$ joint measurement of lepton kinematics on carbon and oxygen (Sec. 4b1). The plots on the left show the overall constraint on the differential cross section, whilst the plots on the right indicate the constraint on the shape of the distribution.