$b \to c$ semileptonic sum rule: exploring a sterile neutrino loophole

TL;DR

This paper examines how a massive sterile neutrino could affect the $b o c$ semileptonic sum rule, finding that current effects are small and the sum rule remains a useful consistency check for experimental data.

Contribution

It introduces sterile neutrino interactions into the sum rule analysis, assessing their impact on decay rates and the sum rule's validity.

Findings

Sterile neutrino effects on the sum rule are minimal within current uncertainties.

The sum rule remains a reliable consistency check despite potential new physics.

No significant violation of the sum rule is induced by sterile neutrinos at present.

Abstract

We investigate the $b\to c$ semileptonic sum rule in the presence of a massive sterile neutrino. Recent measurements of charged-current semitauonic $B$-meson decays exhibit a $\sim4\sigma$ deviation from the Standard Model predictions, whereas no such tension has been reported for the lowest-lying baryonic counterpart, the $\Lambda_b$ decay. Since these decay rates are related through the sum rule, accommodating such a mismatch beyond the level of uncertainties is nontrivial. We revisit this issue by introducing new interactions involving a sterile neutrino. As the differential decay rates are modified by these new contributions, we evaluate the violation of the sum rule in the presence of a massive sterile neutrino. We find that the induced effect remains small compared with the current experimental uncertainties. Therefore, the sum rule provides a useful consistency check for the experimental data.