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

Abstract

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.

Comments: 8 pages, 2 figures