$B\to K{+}$invisible, dark matter, and $CP$ violation in hyperon decays

TL;DR

This paper explores a new physics model involving dark matter and CP violation that could explain the excess in $B^+ o K^+ u ar{ u}$ decays observed by Belle II, predicting significant hyperon CP violation detectable in current and future experiments.

Contribution

It introduces a two-Higgs-doublet model with a scalar dark matter candidate that links dark matter, $CP$ violation, and rare hyperon decays, providing testable predictions.

Findings

Dark matter can account for the $B^+ o K^+ u ar{ u}$ excess.

Hyperon $CP$ violation can reach current experimental bounds.

Hyperon and kaon processes serve as complementary probes of new physics.

Abstract

Recently the Belle II Collaboration has reported a measurement of the $B^+\to K^+\nu\bar\nu$ rate that is higher than the standard-model expectation. Since the emitted neutrinos are unobserved, the excess could be due to the $B^+$ decaying into a $K^+$ and a dark-matter pair. We entertain this possibility in a two-Higgs-doublet model supplemented with a real singlet scalar boson acting as the dark matter. This model also accommodates strangeness-changing interactions providing new sources of $CP$ violation which can affect hyperon and kaon nonleptonic transitions. We find that the resulting $CP$ violation in the hyperon sector can be significant, reaching the current empirical bounds, after taking into account constraints from kaon mixing and decay and from dark-matter relic-density data and direct searches including the Migdal effect. We demonstrate that the hyperon and kaon processes are complementary probes of this new-physics scenario. Its prediction for sizable hyperon $CP$ violation is potentially testable in ongoing experiments, such as BESIII, Belle II, and LHCb, and in next-generation ones like PANDA and at the Super Tau Charm Facility.