Reduced cross sections of electron and neutrino charged current quasielastic scattering on nuclei

The semiexclusive averaged reduced cross sections for (anti)neutrino charged current quasielastic scattering on carbon, oxygen, and argon are analyzed within the relativistic distorted wave impulse approximation. One finds that these cross sections as functions of missing nucleon energy are similar to those of electron scattering and are in agreement with electron scattering data for the three nuclei. The difference between the electron and neutrino cross sections can be attributed to Coulomb distortion on the electron wave function. The averaged reduced cross sections depend slowly upon incoming lepton energy. The approach presented in this paper provides novel constraints on nuclear models of quasielastic neutrino-nucleus scattering and can be easily applied to test spectral functions and final state interactions employed in neutrino event generators.

Figure 1

Proton momentum distributions for the $1p_{1/2}$ (dashed line) and $1s_{1/2}$ (dotted line) single-particle states in the ${}^{12}\mathrm{C}$ nucleus. Also shown is the total proton momentum distribution (solid line).

Figure 2

Same as Fig. 1 but for $1p_{1/2}$ (dashed-dotted line), $1p_{3/2}$ (dashed line), and $1s_{1/2}$ (dotted line) single-particle states in the ${}^{16}\mathrm{O}$ nucleus.

Figure 3

Total proton and neutron momentum distributions in the ${}^{40}\mathrm{Ar}$ nucleus.

Figure 4

Comparison of the RDWIA calculations for electron, neutrino, and antineutrino reduced cross sections for the removal of nucleons from $1s$ and $1p$ shells of ${}^{12}\mathrm{C}$ as functions of the missing momentum. JLab data [41] are for beam energy $E_{\mathrm{beam}}=2.455$ GeV, proton kinetic energy $T_p=350$ MeV, and $Q^2=0.64$ (GeV/${c)}^2$. The RDWIA calculations are shown for electron scattering (dashed line) and neutrino (solid line) and antineutrino (dashed-dotted line) scattering. This figure was taken from Ref. [7].

Figure 5

The RDWIA calculation of neutrino (solid line) and antineutrino (dashed-dotted line) averaged reduced cross sections compared with measured exclusive cross section data for the removal of nucleons from $1p$ and $1s+1p$ shells of ${}^{12}\mathrm{C}$ as functions of the missing momentum. The data are from Saclay [53] for $1p$ and the beam energy $E_{\mathrm{beam}}=500$ MeV, from SLAC [56] for $1s+1p$ shells and $E_{\mathrm{beam}}=2015$ MeV, and from JLab [41] for $1s+1p$ shells and $E_{\mathrm{beam}}$=2455 MeV.

Figure 6

The RDWIA neutrino averaged reduced cross section for removal of nucleons from the $1s+1p$ shells of ${}^{12}\mathrm{C}$ as a function of neutrino energy and missing momentum $p_m$.

Figure 7

Comparison of the RDWIA calculations for neutrino (dashed line) and antineutrino (dashed-dotted line) averaged reduced cross sections for the removal of nucleons from the$1p$ shell of ${}^{16}\mathrm{O}$ with Saclay [53] and NIKHEF [59] data as functions of $p_m$. Also shown are the RDWIA calculations of the reduced cross section for electron scattering (solid line) from Ref. [7].

Figure 8

Same as Fig. 6 but for ${}^{16}\mathrm{O}$.

Figure 9

Comparison of the RDWIA calculations for electron (solid line), neutrino (dashed line), and antineutrino (dashed-dotted line) reduced cross sections for the removal of nucleons from $1d_{3/2}$, $2s_{1/2}$, and $1d_{5/2}$ shells of ${}^{40}\mathrm{Ca}$ with NIKHEF data [49]. The cross sections are presented as functions of missing momentum $p_m$. The figure was taken from Ref. [12].

Figure 10

Missing momentum distribution in argon obtained by integrating over the missing energy ranges of 0–30 MeV (left panel) and 30–54 MeV (right panel), presented with the geometrical factor of $4\pi p_m^2$. The gray band shows the measured spectral function including the full error.

Figure 11

Missing momentum distribution in titanium obtained by integrating over the missing energy range of 0–30 MeV, presented with the geometrical factor of $4\pi p_m^2$. The gray band shows the measured spectral function including the full error.

Figure 12

Same as Fig. 6 but for ${}^{40}\mathrm{Ar}$.