Study of $CP$ violation in $Λ_b^0/Ξ^-_b\rightarrow Λ(1520)M$ decays with the final-state rescattering mechanism

TL;DR

This work extends the final-state rescattering framework to CP violation in baryon decays, focusing on $\Lambda_b^0$ and $\Xi_b^-$ transitions to $\Lambda(1520)$ with various light mesons. By combining naive factorization for short-distance effects with triangle-diagram rescattering calibrated by two model parameters $Λ_{charm}$ and $Λ_{charmless}$, the authors compute helicity amplitudes, branching ratios, and CP asymmetries, and they analyze interference among decay channels and full decay chains using Breit–Wigner propagation and a Legendre-based kinematic expansion. The results show that long-distance rescattering dominates CP-violating effects, with significant sensitivity to CKM structure, form factors, and the regulator parameters, yielding predictions that can guide future experimental tests and potentially generalize to higher excited or multiquark baryons. The study highlights channels with pronounced CP violation and emphasizes the need for precise hadronic inputs and a thorough treatment of interference in full decay processes for robust experimental comparisons.

Abstract

Recently, the LHCb collaboration reported the first observation of $CP$ violation in baryon decays, with a significance of more than $5σ$. This strongly motivates us to investigate the $CP$ violation in more baryon decay processes. In this work, we employ the final-state rescattering mechanism with introducing two model parameters, $Λ_{charm}$ and $Λ_{charmless}$, and calculate two-body non-leptonic baryon decays $Λ^0_b \rightarrow Λ(1520)\,π^0/κ(700)/f_0(500, 980)/ρ^0/K^{*0}/φ$ and $Ξ^-_b \rightarrow Λ(1520)\,K^-$. Consequently, we evaluate the corresponding branching ratios, $CP$ asymmetries, and interference effects between different decay amplitudes. Our theoretical predictions for certain decay channels are in good agreement with current experimental measurements, while the remaining processes--particularly the remarkably large $CP$ violation observable revealed by the kinematic analysis are expected to be tested in future experiments.

Figures (5)

• Figure 1: Feynman diagrams for $\mathcal{B}_b\to f_1 +f_2$ process with the final-state interaction Wolfenstein:1990ksSuzuki:1999ucCheng:2004ruJia:2024pyb.
• Figure 2: The long-distance rescattering contributions to $\mathcal{B}_{b}$ decays at hadron level in single-particle exchange approximation, where the $\mathcal{B}_{b},B_{c},B_{8},\Lambda^*$ denote bottom, charm ,octet baryons and $\Lambda(1520)$, and $P,V,S,D,D^*$ are pseudoscalar octet, vector octet, scalar mesons, $D$ and $D^{*}$ mesons, respectively.
• Figure 3: The dependence of the branching ratios of all decay channels on the model parameters $\Lambda_{\rm charmless}$ and $\Lambda_{\rm charm}$.
• Figure 4: The dependence of the $CP$ violations of $\Lambda_b^0 \to \Lambda(1520)+ \pi^0/\rho^0/\kappa(700)$and $\Xi^-_b \to \Lambda(1520)+K-$ on the model parameters $\Lambda_{\rm charmless}$ and $\Lambda_{\rm charm}$.
• Figure 5: The dependence of the $CP$ violations of $\Lambda_b \to f_0(980,500)/\phi/K^{*0}$ on the model parameters $\Lambda_{\rm charmless}$ and $\Lambda_{\rm charm}$.