Impact of $N^*$ and $\Lambda^*$ resonances on $CP$ violation in $\Lambda_b^0$ decays

The four-body decay $\Lambda_b^0\to pK^-\pi^+\pi^-$ has led to the first observation of baryonic $CP$ violation. However, the underlying subprocesses $\Lambda_b^0\to N^* M$ and $\Lambda_b^0\to \Lambda^* M$, as well as the roles of excited nucleon ($N^*$) and hyperon ($\Lambda^*$) resonances, remain largely unexplored. Within the constituent quark model, we identify the relevant resonant states contributing to these underlying two-body transitions, including $N(1535)$, $N(1520)$, $\Lambda(1670)$, $\Lambda(1690)$, together with the remaining $1P$-wave baryon states. We obtain the resonant branching fraction ${\cal B}(\Lambda_b^0\to pK^-\pi^+\pi^-) =(30.0^{+2.8+4.0}_{-1.3-3.4}\pm1.8)\times10^{-6}$, while the resulting ${\cal A}_{CP}(\Lambda_b^0\to pK^-\pi^+\pi^-)=(3.18\pm0.11\pm0.13\pm0.11)\%$ provides a natural interpretation of the first observed baryonic $CP$ asymmetry. Our analysis establishes the first comprehensive framework for quantifying the impact of excited baryon resonances in multi-body beauty-baryon decays, with the associated mechanism generally applicable to baryonic $CP$ asymmetries.