Centre-of-momentum Variables in $\nu_\mu$CC1p1$\pi$

This study introduces a novel set of variables, namely the centre-of-momentum variables, $\theta_{\textrm{COM}}$ and $E_{\textrm{COM}}$, designed to isolate final-state interactions (FSI) from other aspects of neutrino-nucleus interactions. Through detailed simulation studies, this work demonstrates the ability of these variables to distinguish FSI contributions with minimal dependence on the nuclear initial state and, practically, on the neutrino flux, highlighting their potential for advancing FSI modelling. With high-purity neutrino-hydrogen interaction selections, $\theta_{\textrm{COM}}$ offers the first opportunity for a direct cross-comparison among different neutrino cross-section experiments.