Impact of $N^{\ast }$ and ${\Lambda }^{\ast }$ resonances on $CP$ violation in ${\Lambda }_b^0$ decays

Abstract

The four-body decay ${\Lambda }_b^0\to p{K}^{-}{\pi }^{+}{\pi }^{-}$ has led to the first observation of baryonic $CP$ violation. However, the underlying subprocesses ${\Lambda }_b^0\to N^{\ast }M$ and ${\Lambda }_b^0\to {\Lambda }^{\ast }M$, as well as the roles of excited nucleon ($N^{\ast }$) and hyperon (${\Lambda }^{\ast }$) 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 $\mathcal{B}({\Lambda }_b^0\to p{K}^{-}{\pi }^{+}{\pi }^{-})=(30.0_{-1.3-3.4}^{+2.8+4.0}\pm 1.8)\times 10^{-6}$, while the resulting ${\mathcal{A}}_{CP}({\Lambda }_b^0\to p{K}^{-}{\pi }^{+}{\pi }^{-})=(3.18\pm 0.11\pm 0.13\pm 0.11)\%$ 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.

Comments: 13 pages, 2 figures, 2 tables