Inclusive electron scattering and the genie neutrino event generator

The extraction of neutrino mixing parameters from accelerator-based neutrino-oscillation experiments relies on proper modeling of neutrino-nucleus scattering processes using neutrino interaction event generators. Experimental tests of these generators are difficult due to the broad range of neutrino energies produced in accelerator-based beams and the low statistics of current experiments. Here we overcome these difficulties by exploiting the similarity of neutrino and electron interactions with nuclei to test neutrino event generators using high-precision inclusive electron-scattering data. To this end, we revised the electron-scattering mode of the genie event generator ($e$-genie) to include electron-nucleus bremsstrahlung radiation effects and to use, when relevant, the exact same physics models and model parameters, as the standard neutrino-scattering version. We also implemented new models for quasielastic (QE) scattering and meson exchange currents (MECs) based on the theory-inspired super scaling approach SuSAv2. Comparing the new $e$-genie predictions with inclusive electron-scattering data, we find an overall adequate description of the data in the QE- and MEC-dominated lower energy transfer regime, especially when using the SuSAv2 models. Higher energy transfer interactions, which are dominated by resonance production, are still not well modeled by $e$-genie.

Figure 1

Charged-current cross sections as a function of neutrino energy obtained using genie for muon neutrino scattering using the DUNE near detector (left) and far detector (right) oscillated fluxes [6]. The shaded bands show the fractional contribution for each interaction mechanism, quasielastic (QE) scattering, meson-exchange currents (MECs), resonance excitation (RES), and deep inelastic scattering (DIS). See text for details of the interaction mechanisms. The numbers in parentheses indicate the percentage of the cross section due to each interaction mechanism.

Figure 2

Left: electron-nucleus inclusive scattering via one-photon exchange. Right: charged-current neutrino-nucleus inclusive scattering via $W$ exchange with a final-state charged lepton.

Figure 3

Comparison between genie v2 and v3 descriptions of inclusive $\mathrm{C}(e,e^{\prime })$ scattering cross sections at $E_0=0.56\mathrm{GeV}$, ${\theta }_e=60°$, and $Q_{QE}^2\approx 0.24{\mathrm{GeV}}^2$ [17]. Black points show the data, solid black line shows the genie v3 results, and dashed black line shows the genie v2 results.

Figure 4

Reaction mechanisms for lepton-nucleus scattering. (a) QE scattering where one nucleon is knocked out of the nucleus, (b) $2p2h$ (MEC) where two nucleons are knocked out of the nucleus, (c) resonance production where a nucleon is excited to a resonance which decays to a nucleon plus meson(s), and (d) DIS where the lepton interacts with a quark in the nucleon.

Figure 5

Number of events vs $E_{\mathrm{cal}}=E_{e^{\prime }}+T_p$ the scattered electron energy plus proton kinetic energy for 4.32 GeV $\mathrm{H}(e,e^{\prime }p)$. Black points are data [46], black histogram shows the unradiated genie prediction, and blue histogram shows the genie prediction with electron radiation. The genie calculations have been scaled to have the same integral as the data.

Figure 6

Comparison of inclusive $\mathrm{C}(e,e^{\prime })$ scattering cross sections for data and for genie. Left: data vs GSuSAv2. Right: data vs G2018. Top: $E_0=0.24\mathrm{GeV}$, ${\theta }_e=60°$, and $Q_{\mathrm{QE}}^2\approx 0.05{\mathrm{GeV}}^2$ [17]. Middle: $E_0=0.56\mathrm{GeV}$, ${\theta }_e=36°$, and $Q_{\mathrm{QE}}^2\approx 0.11{\mathrm{GeV}}^2$ [17]. Bottom: $E_0=0.56\mathrm{GeV}$, ${\theta }_e=60°$, and $Q_{\mathrm{QE}}^2\approx 0.24{\mathrm{GeV}}^2$ [17]. Black points show the data, solid black lines show the total genie prediction, colored lines show the contribution of the different reaction mechanisms: blue, QE; red, MEC; green, RES; and orange, DIS.

Figure 7

Comparison of inclusive $\mathrm{C}(e,e^{\prime })$ scattering cross sections for data and for genie. Left: data vs GSuSAv2. Right: data vs G2018. Top: $E_0=0.96\mathrm{GeV}$, ${\theta }_e=37.5°$, and $Q_{\mathrm{QE}}^2\approx 0.32{\mathrm{GeV}}^2$ [47]. Middle: $E_0=1.30\mathrm{GeV}$, ${\theta }_e=37.5°$, and $Q_{\mathrm{QE}}^2\approx 0.54{\mathrm{GeV}}^2$ [47]. Bottom: $E_0=2.22\mathrm{GeV}$, ${\theta }_e=15.5°$, and $Q_{\mathrm{QE}}^2\approx 0.33{\mathrm{GeV}}^2$ [48]. Black points show the data, solid black lines show the total genie prediction, colored lines show the contribution of the different reaction mechanisms: blue, QE; red, MEC; green, RES; and orange, DIS.

Figure 8

Comparison of inclusive $\mathrm{C}(e,e^{\prime })$ scattering cross sections for data and for genie. Left: data vs GSuSAv2. Right: data vs G2018. Top: $E_0=1.501\mathrm{GeV}$, ${\theta }_e=37.5°$, and $Q_{\mathrm{QE}}^2\approx 0.92{\mathrm{GeV}}^2$ [47]. Middle: $E_0=3.595\mathrm{GeV}$, ${\theta }_e=16°$, and $Q_{\mathrm{QE}}^2\approx 1.04{\mathrm{GeV}}^2$ [49]. Bottom: $E_0=3.595\mathrm{GeV}$, ${\theta }_e=20°$, and $Q_{\mathrm{QE}}^2\approx 1.3{\mathrm{GeV}}^2$ [49]. Black points show the data, solid black lines show the total genie prediction, colored lines show the contribution of the different reaction mechanisms: blue, QE; red, MEC; green, RES; and orange, DIS.

Figure 9

Comparison of inclusive $\mathrm{Fe}(e,e^{\prime })$ scattering cross sections for data and for genie. Left: data vs GSuSAv2. Right: data vs G2018. Top: $\mathrm{Fe}(e,e^{\prime })$, $E_0=0.56\mathrm{GeV}$, ${\theta }_e=60°$, and $Q_{\mathrm{QE}}^2\approx 0.24{\mathrm{GeV}}^2$ [17]. Middle: $\mathrm{Fe}(e,e^{\prime })$, $E_0=0.96\mathrm{GeV}$, ${\theta }_e=37.5°$, and $Q_{\mathrm{QE}}^2\approx 0.32{\mathrm{GeV}}^2$ [47]. Bottom: $\mathrm{Fe}(e,e^{\prime })$, $E_0=1.30\mathrm{GeV}$, ${\theta }_e=37.5°$, and $Q_{\mathrm{QE}}^2\approx 0.54{\mathrm{GeV}}^2$ [47]. Black points show the data, solid black lines show the total genie prediction, colored lines show the contribution of the different reaction mechanisms: blue, QE; red, MEC; green, RES; and orange, DIS.

Figure 10

Comparison of inclusive $\mathrm{Ar}(e,e^{\prime })$ scattering cross sections for data and for genie at $E_0=2.22\mathrm{GeV}$, ${\theta }_e=15.5°$, and $Q_{\mathrm{QE}}^2\approx 0.33{\mathrm{GeV}}^2$ [50]. Left: data vs GSuSAv2. Right: data vs G2018. Black points show the data, solid black lines show the total genie prediction, colored lines show the contribution of the different reaction mechanisms: blue, QE; red, MEC; green, RES; and orange, DIS.

Figure 11

Comparison of inclusive proton (left) and deuterium (right) $(e,e^{\prime })$ scattering cross sections for data and for genie using G2018. Top: $E_0=2.445\mathrm{GeV}$ and ${\theta }_e=20°$. Middle: $E_0=3.245\mathrm{GeV}$ and ${\theta }_e=26.98°$. Bottom: $E_0=5.5\mathrm{GeV}$ and ${\theta }_e=41°$ [51, 52, 53]. Black points show the data, solid black lines show the total genie prediction, colored lines show the contribution of the different reaction mechanisms: green, RES; orange, DIS. The first peak at lowest energy transfer is the $\mathrm{\Delta }(1232)$ resonance.

Figure 12

Comparison of inclusive proton (left) and deuterium (right) $(e,e^{\prime })$ scattering cross sections for data and for genie using G2018. Top: $E_0=4.499\mathrm{GeV}$ and ${\theta }_e=4°$. Middle: $E_0=6.699\mathrm{GeV}$ and ${\theta }_e=4°$. Bottom: $E_0=9.993\mathrm{GeV}$ and ${\theta }_e=4°$ [54]. Black points show the data, solid black lines show the total genie prediction, colored lines show the contribution of the different reaction mechanisms: green, RES; orange, DIS. The first peak at lowest energy transfer is the $\mathrm{\Delta }(1232)$ resonance.

Figure 13

Comparison of semiexclusive 1.16 GeV lepton-carbon scattering for $Q^2\ge 0.1{\mathrm{GeV}}^2$. The number of generated events is plotted versus energy transfer (left) and four-momentum transfer squared (right) for events with exactly one proton with $P_p\ge 300\mathrm{MeV}/\mathrm{c}$, no charged pions with $P_{\pi }\ge 70\mathrm{MeV}/\mathrm{c}$ and no neutral pions or photons of any momentum for $e$-genie electrons (orange) and genie CC ${\nu }_{\mu }$ (blue). The electron events have been weighted by $Q^4$. Both curves are area normalized.

Figure 14

Number of simulated events for QE scattering on ${}^{12}\mathrm{C}$ at 1.161 GeV with $Q^2\ge 0.1$ shown as a function of the energy transfer $\omega$ and the momentum transfer $q_3=|\overrightarrow{q}|$ for all the available nuclear models in genie for neutrinos (top) and for electrons (bottom). Left: the GSuSAv2 model which uses a relativistic mean field (RMF) momentum distribution. Middle: the Nieves or Rosenbluth cross section with the local Fermi gas (LFG) momentum distribution. Right: the Llewellyn-Smith or Rosenbluth cross section with the relativistic Fermi gas momentum distribution. The electron events have been weighted by $Q^4$.

Figure 15

Initial momentum distribution of protons in simulated QE $\mathrm{C}(e,e^{\prime }p)$ events at $E=1.161\mathrm{GeV}$ for the local Fermi gas (solid histogram) and relativistic Fermi gas (dotted histogram) models. The two curves are normalized to have the same area.

Figure 16

Number of simulated events as a function of the energy transfer $\omega$ and of the momentum transfer $q_3=|\overrightarrow{q}|$ for neutrinos (left) and for electrons (right) using GSuSav2 for MEC interactions. The electron events have been scaled by $Q^4$ and all the samples have been generated with $Q^2\ge 0.1$.