Study of $CP$ violation in $Λ_b^0\rightarrow N^*M$ decays with the final-state rescattering mechanism

TL;DR

This work addresses CP violation in charmless two-body decays of $\Lambda_b^0$ by modeling long-distance final-state interactions through hadronic triangle (rescattering) diagrams, calculating both absorptive and dispersive parts to obtain strong phases. Short-distance dynamics are treated with the weak effective Hamiltonian under naive factorization, while long-distance effects are captured via a systematic rescattering framework with regulator form factors and two cutoff scales $\Lambda_{\text{charm}}$ and $\Lambda_{\text{charmless}}$, allowing predictions for $\Lambda_b^0\to N^*(1535,1520)M$ with $M=K_S, K^*_0(700), f_0(500,980), \rho(770), \bar{K}^{*0}, \phi$. The authors present branching ratios, direct and partial-wave CP asymmetries, and decay asymmetry parameters for these channels, highlighting charm-loop dominance in several modes and notable CP-violating effects—including sizable partial-wave cancellations in certain channels—and discuss implications for four-body decays such as $\Lambda^0_b\to p\pi^-\pi^+\pi^-$ that can be probed at LHCb. The results depend on the phenomenological cutoffs $\Lambda_{\text{charmless}}$ and $\Lambda_{\text{charm}}$, motivating future refinements of form factors and strong couplings to sharpen predictions and tests of the Standard Model and potential new physics in baryon decays.

Abstract

In this work, we investigate the charmless non-leptonic two-body $Λ_b$ decays within the framework of final-state rescattering mechanism. In contrast to the Cutkosky cutting method, we compute both the absorptive and dispersive parts of the hadronic rescattering triangle diagrams. Based on the established formalism, we analyze the $Λ_b \to N^*(1535,1520)M$ decay processes with $M =K_S, K^*_0(700)$, $f_0(500,980), ρ(770), \bar{K}^{*0}$, $φ$, and predict various physical observables, such as their branching ratios, direct and partial-wave $CP$ asymmetries, as well as decay asymmetry parameters. These two-body decay processes are expected to contribute primarily to the subsequent four-body decay channels, such as $Λ_b^0 \to p\,π^-\,π^+\,π^-$, whose $CP$ asymmetry measurements will be accessible at the LHCb experiment.

Figures (7)

• Figure 1: The diagrams of $\Lambda_b^0 \to N^* M$ with $M =K_S, K^*_0(700)$, $f_0(500,980), \rho(770), \bar{K}^{*0}$, $\phi$, from rescattering mechanism at hadronic level with exchanging one single particle, where the $B_8, B_c, B_{10}, N^*$ denote octet baryons, charmed baryons, decuplet baryons and $N^*(1520,1535)$, respectively, and $P,S,V,D$ and $D^*$ are pseudoscalar, vector, $D$ and $D^*$ mesons, respectively.
• Figure 2: The diagram of $\Lambda_b^0 \to N^* K_S$ with intermediate states octet vector meson $V_8$ and octet baryons $B_8$ rescattering by exchanging a pseudoscalar meson.
• Figure 3: The dependence of the average branching ratios of $\Lambda_b \to N^*(1535, 1520)K_S/\bar{K}^{*0}$ on the model parameters $\Lambda_{\rm charmless}$ and $\Lambda_{\rm charm}$.
• Figure 4: The dependence of the direct $CP$ asymmetries for $\Lambda_b \to N^*(1535, 1520) K_S/\bar{K}^{*0}$ on the model parameters $\Lambda_{\rm charmless}$ and $\Lambda_{\rm charm}$.
• Figure 5: The dependence of the partial wave $CP$ asymmetries for $\Lambda_b \to N^*(1535, 1520)K_S$ on the model parameters $\Lambda_{\rm charmless}$ and $\Lambda_{\rm charm}$.