$B\to K^* M_X$ vs $B\to K M_X$ as a probe of a scalar-mediator dark matter scenario

TL;DR

This paper proposes that analyzing the decays $B o K M_X$ and $B o K^* M_X$ can effectively probe scalar-mediator dark matter scenarios, especially given recent experimental hints of excess missing mass events at Belle II.

Contribution

It introduces a method to use combined decay analysis to test scalar mediator dark matter models, providing model-independent upper limits based on current experimental data.

Findings

Observed $B o K M_X$ branching ratio exceeds SM expectations.

Derived an upper limit on $B o K^* M_X$ based on current data.

Proposed a clean probe for scalar-mediator dark matter scenarios.

Abstract

Recently, Belle II reported the observation of the decay $B\to K M_X$, $M_X$ the missing mass, with the branching ratio much exceeding ${\cal B}(B\to K \nu\bar\nu)$ which is the only Standard Model (SM) process contributing to this reaction. If confirmed, this might be an indication of new nonSM particles produced in this decay. One of the possible explanations of the observed effect could be light dark-matter (DM) particles produced via a scalar mediator field. We give simple arguments, that a combined analysis of the $B\to K M_X$ and $B\to K^* M_X$ reactions would be a clean probe of the scalar mediator scenario: (i) making use of an observed value ${\cal B}(B\to K M_X)\simeq 5.4\, {\cal B}(B\to K \nu\bar\nu)_{\rm SM}$ and (ii) assuming that the effect is due to the light dark matter coupling to the top quark via a {\it scalar} mediator field, one finds an upper limit ${\cal B}(B\to K^* M_X) < 2.8 \, {\cal B}(B\to K^* \nu\bar\nu)_{\rm SM}$. Within the discussed scenario, this upper limit does not depend on the mass of the scalar mediator nor on the specific details of the unobserved dark-matter particles in the final state.