Title: Elucidating the impact of massive neutrinos on halo assembly bias

Abstract: Massive neutrinos have non-negligible impact on the formation of large-scale structures. We investigate the impact of massive neutrinos on the halo assembly bias effect, measured by the relative halo bias $\hat{b}$ as a function of the curvature of the initial density peak $\hat{s}$, neutrino excess $\epsilon_\nu$, or halo concentration $\hat{c}$, using a large suite of $\Sigma M_\nu{=}0.0$ eV and $0.4$ eV simulations with the same initial conditions. By tracing dark matter haloes back to their initial density peaks, we construct a catalogue of halo twins that collapsed from the same peaks but evolved separately with and without massive neutrinos, thereby isolating any effect of neutrinos on halo formation. We detect a $2\%$ weakening of the halo assembly bias as measured by $\hat{b}(\epsilon_\nu)$ in the presence of massive neutrinos. As there exists a significant correlation between $\hat{s}$ and $\epsilon_\nu$ ($r_{cc}{=}0.319$), the impact of neutrinos persists at a reduced level~($0.1\%$) in the halo assembly bias measured by $\hat{b}(\hat{s})$. However, we do not detect any neutrino-induced impact on $\hat{b}(\hat{c})$, consistent with earlier studies and the lack of correlation between $\hat{c}$ and $\epsilon_\nu$ ($r_{cc}{=}0.087$). We also discover an analogous assembly bias effect for the neutrino haloes, whose concentrations are anti-correlated with the large-scale clustering of neutrinos.