Intercomparison of lepton-nucleus scattering models in the quasielastic region

I present a discussion of the models of nuclear effects used to describe the inclusive electron-nucleus scattering in the quasielastic (QE) peak region, aiming to compare them and to draw conclusions about their reliability when applied in neutrino-nucleus interactions. A basic motivation is to reduce the systematic errors in the neutrino oscillation experiments. I concentrate on the neutrino energy profile of the T2K experiment, which provides me with a region of the greatest importance in terms of the highest contribution to the charge-current quasielastic (CCQE) cross section. Only electron-nucleus data that overlap with this region is chosen. In order to clarify the analysis, I split the data sets into three groups and draw conclusions separately from each one of them. Six models are selected for this comparison: Benhar's spectral function with and without the final-state interactions (Benhar's SF + FSI); the Valencia spectral function (Valencia SF), for higher energy transfers only with the hole spectral function; the Giessen Boltzmann-Uehling-Uhlenbeck (GiBUU) model; and the local and global Fermi gas models. The latter two are included as a benchmark to quantify the roles of various nuclear effects. All six models are often used in neutrino scattering studies. A short theoretical description of each model is given. Although in the selected data sets the QE mechanism dominates, I also discuss the possible impact of the 2p2h and the $\mathrm{\Delta }$ contributions.

Figure 1

The muon neutrino flux in ND280 detector of the T2K experiment, taken from Ref. [16]. The dashed line shows the flux; the solid curve shows flux multiplied by the oscillation probability ${\mathcal{P}}_{{\nu }_{\mu }\to {\nu }_e}$ [17]. Both are normalized to the same area.

Figure 2

${(d\sigma /dqd\omega )}_{\mathrm{T}2\mathrm{K}}^{\text{osc}}$ $[{10}^{-38}{\text{cm}}^2/{\text{GeV}}^2]$ for the T2K flux (using the prediction of the Valencia spectral function); see Eq. (3). The position of the CCQE peak is marked with the solid line. Three typical electron data sets are also shown (experimental points are connected by a line for better legibility): solid line, $E=200$ MeV, $\theta ={60}^{\circ }$; dashed line, $E=1500$ MeV, $\theta =13.{54}^{\circ }$; dot-dashed line, $E=680$ MeV, $\theta ={60}^{\circ }$. Each of them cross the solid line (CCQE line) at different points. The value of ${(d\sigma /dqd\omega )}_{\mathrm{T}2\mathrm{K}}^{\text{osc}}$ in this crossing point is taken as the measure of the importance of the data set.

Figure 3

A profile of the CCQE peak (the profile along the line marked on Fig. 2 projected on the $\omega$ axis).

Figure 4

Comparison of the electron scattering models in region I. For the local Fermi gas, the relativistic kinematics is employed and the difference from the nonrelativistic version is shown as a gray band.

Figure 5

Comparison of the electron scattering models in region II (for which the QE peak position is at $\omega \in (50,125)$ MeV).

Figure 6

The same as Fig. 5.

Figure 7

The same as Figs. 5 and 6.

Figure 8

Comparison of the electron scattering models in region III (for which the QE peak position is at $\omega \in (125,200)$ MeV). The inclusive electron scattering data are shown. In many cases the 2p2h and $\mathrm{\Delta }$ contributions are large and influence the QE peak region. One, thus, does not expect the models of the QE mechanism to reproduce the data.

Figure 9

The same as Fig. 8. The inclusive electron scattering data are shown. In many cases the 2p2h and the $\mathrm{\Delta }$ contributions are large and influence the QE peak region. One, thus, does not expect models of the QE mechanism to reproduce the data.

Figure 10

A comparison of three models, GiBUU, Valencia SF, and Benhar's SF + FSI, with the data. The 2p2h and $\mathrm{\Delta }$ contributions are subtracted using results from Ref. [30] from the data points. Both data sets (before and after subtraction) are shown. Left panel: full Valencia SF is used. Right panel: approximated Valencia SF is used (without FSI).

Figure 11

Ratio ${(d\sigma /d\mathrm{\Omega }d\omega )}^{\mathrm{model}}/{(d\sigma /d\mathrm{\Omega }d\omega )}^{\mathrm{data}}$ in the QE peak for various models. A band above Benhar's SF + FSI line shows the difference from Benhar's SF alone. Two vertical lines at 50 and 125 MeV tentatively mark regions I, II, and III.

Figure 12

Position of the QE peak with respect to the data. Because of the discrete nature of experimental points, an error band of 5 MeV is also shown with a dotted line. The two vertical lines at 50 and 125 MeV tentatively mark regions I, II, and III.

Figure 13

On the left, the ratio ${(d\sigma /d\mathrm{\Omega }d\omega )}^{\mathrm{model}}/{(d\sigma /d\mathrm{\Omega }d\omega )}^{\mathrm{LFG}}$ in the QE peak for the following models: Benhar's SF + FSI, GiBUU, and the Valencia SF. On the right, the ratio $({\omega }_R^{\mathrm{model}}-{\omega }_L^{\mathrm{model}})/({\omega }_R^{\mathrm{LFG}}-{\omega }_L^{\mathrm{LFG}})$, where ${\omega }_R$, ${\omega }_L$ are the energy transfer values in the middle of the peak's height. A band above or below Benhar's SF + FSI line shows the difference from Benhar's SF alone. For $\omega >150$ MeV, the approximated Valencia SF model is used. The two vertical lines at 50 and 125 MeV tentatively mark regions I, II, and III.