analysis. Note that the Nieves 2p2h model included $\pi$-less $\Delta$ decay contributions, where a nucleon excited into a $\Delta(1232)$ resonance decays without producing a pion [@oset-fsi; @singh_1998]. Contributions from $\pi$-less $\Delta$ decay were previously implemented in [<span style="font-variant:small-caps;">NEUT</span>]{}and other generators, and have been treated as an intrinsic background in CCQE selections and corrected for. This leads to complications when comparing the full Nieves model to CCQE cross section measurements.

[0.9]{} ![The ratio of the [CCQE]{}cross section including the non-relativistic RPA model to the [CCQE]{}cross section without RPA, shown for both muon neutrino and muon antineutrino interactions on carbon. An enhancement of the ratio can be seen at high [$Q^{2}$]{}, and a suppression can be seen at low [$Q^{2}$]{}(and close to the kinematic boundary for antineutrinos). These [$E_{\nu}$]{}and [$Q^{2}$]{}dependent tables are used in [<span style="font-variant:small-caps;">NEUT</span>]{}to apply the RPA model. For these plots, an axial mass value of [$M_{\textrm{A}}$]{}= 1.01 GeV$/c^{2}$ was used.[]{data-label="fig:RPA_ratio_NEUT"}](figures/NU_2D-RPA_ratio.pdf "fig:"){width="\textwidth"}

[0.9]{} ![The ratio of the [CCQE]{}cross section including the non-relativistic RPA model to the [CCQE]{}cross section without RPA, shown for both muon neutrino and muon antineutrino interactions on carbon. An enhancement of the ratio can be seen at high [$Q^{2}$]{}, and a suppression can be seen at low 