Electron versus Muon Neutrino Induced Cross Sections in Charged Current Quasielastic Processes

Differences between ${\nu }_e$ and ${\nu }_{\mu }$ quasielastic cross sections are essential in neutrino oscillation analyses and $CP$ violation searches for experiments such as DUNE and T2HK. The ratio of these is however poorly known experimentally and for certain kinematic regions theoretical models give contradictory answers. We use two independent mean-field based models to investigate this ratio using ${}^{40}\mathrm{Ar}$ and ${}^{12}\mathrm{C}$ targets. We demonstrate that a proper treatment of the final nucleon’s wave function confirms the dominance of ${\nu }_{\mu }$ over ${\nu }_e$ induced cross sections at forward lepton scattering.

Figure 1

CRPA (full lines) and RMF (dashed) cross sections for different incoming neutrino energies for a lepton scattering angle of ${\theta }_l=5°$ for muon (thick lines) and electron neutrino (thin lines) induced interactions with ${}^{12}\mathrm{C}$.

Figure 2

HF (full line) and HF-PWIA (dashed) cross section for scattering off ${}^{40}\mathrm{Ar}$ for different lepton scattering angles at a fixed neutrino energy of 200 MeV, for neutrinos in panels (a)–(c) and antineutrinos in panels (d)–(f). The momentum transferred to the nucleus as a function of the energy transfer for both muon and electron neutrinos at the same kinematics is shown in panels (g)–(i). To better represent the cross section at the most forward angles the HF-PWIA cross sections have been scaled down in some panels.

Figure 3

Comparison of the ${\nu }_e$ (thin lines) and ${\nu }_{\mu }$ (thick lines) cross sections on carbon for RPWIA (dashed) and PB-RPWIA (solid), in which the nonorthogonal contributions of the plane wave have been projected out. The lepton scattering angle is ${\theta }_l=5°$.

Figure 4

Ratio of ${}^{12}\mathrm{C}$ cross sections as a function of incoming energy and lepton scattering angle, combined with relative strength of the cross section at the same kinematics (normalized such that the maximum in this kinematic region is 1). Results shown here were obtained within the CRPA approach, RMF ratios are very similar [30].