Implementation of a relativistic distorted wave impulse approximation model into the NEUT event generator

We describe the implementation of a model for charged-current quasi-elastic (CCQE) neutrino-nucleus scattering in the NEUT Monte Carlo event generator. This model employs relativistic momentum distributions obtained from mean field theory and relativistic distorted waves to describe the initial and final nucleon states. Final state interactions, both elastic and inelastic, are modelled by combining distorted waves with the NEUT intranuclear cascade, offering a more accurate representation of the interactions experienced by scattered nucleons. The model and its implementation in NEUT are described in detail and benchmarked against $\nu_{\mu}$-$^{12}$C scattering cross-section measurements from T2K and MINER$\nu$A, as well as $\nu_{\mu}$-$^{40}$Ar measurements from MicroBooNE. Results, including transverse kinematic imbalance variables and scattered nucleon kinematics, show improved $\chi^2$ values compared to other CCQE models in NEUT. Furthermore, the model consistently predicts lower cross sections in CCQE-dominated regions, indicating potential for further refinement, such as incorporating two-body currents or the use of more advanced nucleon axial form factors consistent with lattice QCD calculations.