Lepton polarization dependent angular observables and the polarization asymmetries in the four-fold $Λ_b \rightarrow Λ(\rightarrow N π) \ell^+\ell^-$ decay

TL;DR

This paper develops a polarization-dependent angular analysis for the four-body decay $\Lambda_b \to \Lambda(\to N\pi)\ell^{+}\ell^{-}$ to probe $b \to s \ell^{+}\ell^{-}$ transitions. Using the SM weak effective Hamiltonian and a helicity-transversity formalism, the authors derive the full four-fold angular distributions for unpolarized and polarized (longitudinal, normal, and transverse) leptons, including lepton-mass effects, and express all angular coefficients in terms of helicity and transversity amplitudes. They implement lattice QCD form factors and explore NP scenarios by adopting global fits for vector/axial-vector Wilson coefficients, showing that longitudinal polarization offers the strongest potential NP sensitivity, while normal and transverse polarizations yield additional but SM-suppressed structures. The framework provides a robust baseline for testing the SM and constraining NP in $\Lambda_b$ decays, with improvements in form factors and data expected to enhance sensitivity to polarization-dependent observables.

Abstract

The rare decays mediated by flavor-changing neutral current processes, such as $b \to s \ell^{+}\ell^{-}$, provide powerful probes of the Standard Model and potential windows into new physics. Particularly, the angular observables in these exclusive decays are valuable because of their sensitivity to short-distance dynamics and their reduced dependence on hadronic uncertainties, which mainly arise from form factors. In this work, we analyze the $Λ_b \to Λ(\to Nπ)\ell^{+}\ell^{-}$ (with $Nπ=\{pπ^-,nπ^0\}$) decay with polarized final-state lepton and derive the corresponding four-fold differential decay distributions. For the longitudinal, normal, and transverse polarization states, we systematically identify the additional angular coefficients that emerge relative to the unpolarized case. We find that the longitudinal polarization preserves the structure of the unpolarized distribution, while the normal and transverse polarizations introduce some new additional angular coefficients. The analytical expressions of all polarized and unpolarized angular coefficients are explicitly derived in terms of the helicity and transversity amplitudes. To compare the variation in the polarized and unpolarized angular observables, we have plotted them against the square of the momentum transfer $q^2$. Additionally, the Standard Model predictions of the polarization asymmetry observables are provided and their sensitivity to new physics is explored under different new physics scenarios. The obtained results, in the current study, for longitudinal and transverse polarization cases, provide a baseline for the lepton polarization dependent observables, which may serve as sensitive probes to test the Standard Model in these decays.

Figures (5)

• Figure 1: Differential branching ratios and various observables vs. $q^{2}$ for SM unpolarized and longitudinally polarized final state lepton. Dotted region represent the spin $+\tfrac{1}{2}$ contributions, while the dashed region represent the spin $-\tfrac{1}{2}$ contributions. For all results $\ell=\mu$.
• Figure 2: Differential branching ratios and various observables vs. $q^{2}$ for SM unpolarized and transversely polarized final state lepton. Dotted region represent the spin $+\tfrac{1}{2}$ contributions, while the dashed region represent the spin $-\tfrac{1}{2}$ contributions. For all results $\ell=\mu$.
• Figure 5: SM predictions for polarization asymmetries of the new real angular coefficients, $\overline{\mathcal{K}}_{\text{3cN}}$ and $\overline{\mathcal{K}}_{\text{3N}}$, for the normally polarized muon.
• Figure 6: SM predictions for polarization asymmetries of the new real angular coefficients, $\overline{\mathcal{K}}_{\text{4ssT}}$, $\overline{\mathcal{K}}_{\text{4ccT}}$, $\overline{\mathcal{K}}_{\text{4cT}}$, and $\overline{\mathcal{K}}_{\text{4T}}$, for the transversely polarized muon.
• Figure 7: Kinematics of $\Lambda_{b} \to \Lambda (\rightarrow N \pi) \ell^{+}\ell^{-}$ decays, where $N\pi=\{p\pi^-,n\pi^0\}$.