Exact baryon-meson relation for $b\to s\nu \bar{\nu }$

Abstract

We derive an exact relation among the normalized branching fractions of ${\Lambda }_b\to \Lambda \nu \bar{\nu }$ and $B\to K^{(\ast )}\nu \bar{\nu }$, within the lepton-number-conserving effective Hamiltonian in which only active neutrinos contribute to the invisible final state. Although the effective Hamiltonian contains 18 independent Wilson coefficients, the three normalized rates depend on only two independent combinations of them, leading to an exact algebraic relation. Remarkably, the central values of the coefficients of this baryon-meson relation are close to $1/4$ and $3/4$, which appear in the heavy-to-heavy $b\to c$ 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 active neutrino interactions, thereby providing a clean target prediction for future experiments. This clearly demonstrates that observables in baryonic and mesonic $b\to s\nu \bar{\nu }$ transitions will serve as a compact consistency test and a powerful probe for discriminating among new-physics scenarios.

arXiv comment8 pages, 2 figures; v2: The numerical code has been corrected, resulting in an updated evaluation of the theoretical uncertainties. The final conclusions remain unchanged. References have been added. Version accepted for publication in Physical Review D