Baryon-Meson Sum Rule for $b \to s \nu\bar\nu$

We derive a robust sum rule among the branching fractions of $\Lambda_b \to \Lambda \nu \bar\nu$ and $B \to K^{(\ast)} \nu\bar\nu$, assuming that right-handed neutrinos are decoupled. Despite the presence of 18 independent Wilson coefficients in the effective Hamiltonian, this relation remains exact. Remarkably, it is found that the coefficients of this baryon-meson sum rule are numerically identical to those of the $b\to c$ semileptonic sum rule among the branching fractions of $\Lambda_b \to \Lambda_c \tau \bar\nu$ and $B \to D^{(\ast)}\tau\bar{\nu}$. Once the decay rate of $B \to K^{\ast} \nu \bar\nu$ is measured, the decay rate of $\Lambda_b \to \Lambda \nu\bar\nu$ can be determined in a model-independent manner for new-physics scenarios involving only left-handed neutrino interactions. This clearly demonstrates that observables in baryonic and mesonic $b \to s \nu \bar{\nu}$ transitions will serve as a powerful probe for discriminating among new-physics scenarios.