Complementarity of $B\to K^{(*)} \mu \bar \mu$ and $B\to K^{(*)} + \mathrm{inv}$ for searches of GeV-scale Higgs-like scalars

TL;DR

This paper explores how combining searches for $B$ meson decays into muons and invisible particles can improve constraints on GeV-scale Higgs-like scalars, highlighting the complementarity of these channels and proposing models with invisible decay modes.

Contribution

It demonstrates the complementarity of muonic and invisible decay channels in constraining light scalars and introduces two simple models with sizeable invisible widths involving heavy neutral leptons.

Findings

Current constraints depend on muonic branching ratios.

Invisible decay channels can weaken existing bounds.

Proposed models include a real scalar and a $U(1)_{B-L}$ gauge symmetry.

Abstract

The rare decays $B^+\to K^+ \mu\bar \mu$ and $B^0\to K^{*0} \mu\bar\mu$ provide the strongest constraints on the mixing of a light scalar with the Higgs boson for GeV-scale masses. The constraints sensitively depend on the branching ratio to muons. Additional decay channels like an invisible partial width may substantially weaken the constraints. This scenario will be probed at Belle II in $B\to K^{(*)} + \mathrm{inv}$. We illustrate the complementarity of scalar decays to muons and invisible decays using the currently available results of LHCb and BaBar. We provide two simple model realisations providing a sizeable invisible scalar width, one based on a real scalar and one based on a $U(1)_{B-L}$ gauge symmetry. In both examples the scalar decays into heavy neutral leptons which can be motivated by the seesaw mechanism for neutrino masses.