Probing Direct $CP$ Violation in $Λ_b^0 \to P_c^+ h^-$ $(h=π,K)$ with Final-State Rescattering

TL;DR

This work probes direct CP violation in two-body decays $\Lambda_b^0 \to P_c^+ h^-$ (with $h=\pi,K$) under a final-state rescattering mechanism, treating the $P_c$ states as hadronic molecules $P_c(4312)$, $P_c(4440)$, and $P_c(4457)$ with two possible spin assignments for the latter. The decays are modeled as triangle diagrams with intermediate hadrons, where naive factorization governs weak vertices and effective hadronic Lagrangians govern strong interactions, and two cutoff scales $\\Lambda_{ m charm}$ and $\\Lambda_{ m charmless}$ are introduced to capture off-shell effects. Using inputs for the $P_c$ masses, CKM parameters, form factors, decay constants, and couplings, the authors predict branching fractions and direct CP asymmetries: ${\rm BR}(\Lambda_b^0 \to P_c^+ \pi^-)$ is $\mathcal{O}(10^{-6})$ with ${\rm a}^{\rm dir}_{CP}$ up to $\mathcal{O}(10^{-2})$, while ${\rm BR}(\Lambda_b^0 \to P_c^+ K^-)$ is more sensitive to the $P_c$ spin and typically $\mathcal{O}(10^{-5})$ for $J^P=\tfrac{1}{2}^-$ but $\mathcal{O}(10^{-6})$ for $J^P=\tfrac{3}{2}^-$, with CP asymmetries in this channel being very small. The results indicate that CP measurements in the $\pi$ channel could help determine the spin ordering of $P_c(4440)$ and $P_c(4457)$ and provide guidance for amplitude analyses near the $P_c$ region, though the observed $\Delta A_{CP}$ in related decays may require additional contributions beyond the current rescattering picture.

Abstract

The LHCb collaboration has recently reported a measurement of the difference in direct CP asymmetries for the decays $Λ_b^0 \to J/ψ\, p \, h^-$ (with $h = K, π$), offering new experimental constraints on the decay dynamics of heavy baryons into charmonium final states. Inspired by these findings, we explore the branching ratios and direct CP violations for the decays $Λ_b^0 \to P_c^+(4312, 4440, 4457)\,h^-$ within the framework of final-state rescattering. Our analysis indicates that the branching fractions for $Λ_b^0 \to P_c^+ π^-$ lie around the $10^{-6}$ level, with the corresponding direct CP asymmetries approaching approximately $1\%$. In contrast, the direct CP violation for the decay $Λ_b^0 \to P_c^+ K^-$ is found to be very small, while its branching ratios show a strong dependence on the spin assignments of the $P_c$ states. These predictions may provide useful guidance for more precise CP measurements and amplitude analyses in the $P_c$ region in future experiments.

Figures (1)

• Figure 1: The triangle diagrams of $\Lambda^{0}_{b}\to P_{c}^+h^{-}$ considered in this work, where the $B_{c},B_{8}$ represent charmed and octet light baryons, and $P,V,D,D^{*}$ are pseudo-scalar and vector octet, $D$ and $D^{*}$ mesons, respectively.