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

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.

💡 Research Summary

In this paper the authors investigate charmless non‑leptonic two‑body decays of the bottom baryon Λ_b^0 into an excited nucleon resonance N*(1535, 1520) and a light meson M, where M can be K_S, K*_0(700), f_0(500, 980), ρ(770), \bar K*^0 or ϕ. The novelty of the work lies in the systematic inclusion of final‑state rescattering (FSR) effects through hadronic triangle diagrams, and in the explicit calculation of both the absorptive (imaginary) and dispersive (real) parts of these loops. By doing so the authors obtain a complete strong‑phase structure that can interfere with the weak phase from the short‑distance weak Hamiltonian, thereby generating direct CP asymmetries.

The theoretical framework is built on the effective weak Hamiltonian for b→u tree‑level and b→q (q=d,s) penguin transitions. Wilson coefficients are taken at μ=m_b at next‑to‑next‑to‑leading order, and the hadronic matrix elements are evaluated under the naive factorization hypothesis, factorizing them into meson decay constants and Λ_b→B transition form factors. The short‑distance amplitudes (A_SD) thus obtained are relatively simple and contain the CKM weak phase.

Long‑distance contributions are modeled by a single‑particle exchange mechanism. After the weak decay Λ_b^0→B_8 V_8 (or B_c D) the intermediate hadrons rescatter into the final N* M pair by exchanging a pseudoscalar, vector or charmed meson. The corresponding triangle loop integrals are evaluated in four‑dimensional momentum space. The absorptive part is extracted using the Cutkosky cutting rules, i.e. by putting the intermediate particles on shell, while the dispersive part is obtained via a dispersion relation that integrates the absorptive contribution over the appropriate kinematic range. To regularize ultraviolet divergences and to account for off‑shell effects, a phenomenological form factor \