New Strategies for New Physics Search with $\Lambda_b \to \Lambda \nu \bar\nu$ Decays

We examine the new physics sensitivity of the rare decay $\Lambda_b \to \Lambda \nu\bar\nu$ which can be accessible at future $Z$-pole machines like FCC-ee and CEPC. We find that the longitudinal polarization of $\Lambda_b$ baryons produced in $Z$ decays introduces a novel observable, the forward-backward asymmetry $A_\text{FB}^\uparrow$ in the angle between the outgoing $\Lambda$ momentum and the $\Lambda_b$ spin. We provide Standard Model predictions for the $\Lambda_b \to \Lambda \nu\bar\nu$ branching ratio and $A_\text{FB}^\uparrow$, and show that future precision measurements of these observables are complementary and probe new physics scales comparable to other $b \to s \nu\bar\nu$ and $b \to s \ell^+ \ell^-$ processes. We also show that the zero crossing of the forward-backward asymmetry offers a robust test of form factor calculations independent of new physics.