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

TL;DR

The paper derives an exact sum rule linking branching fractions of baryonic and mesonic decays involving neutrinos, providing a model-independent way to probe new physics in $b o s u ar{ u}$ transitions.

Contribution

It establishes a novel, exact sum rule relating baryon and meson decay rates that remains valid despite multiple Wilson coefficients, aiding new physics discrimination.

Findings

Sum rule relates $ ext{BR}( ext{}\Lambda_b o ext{ }\Lambda u ar u)$ and $ ext{BR}(B o K^{( ext{ast})} u ar u$.

Coefficients of the sum rule match those of a similar $b o c$ semileptonic sum rule.

Measurement of $B o K^{ ext{ast}} u ar u$ enables model-independent prediction of $ ext{BR}( ext}\Lambda_b o ext{ }\Lambda u ar u)$.

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.