B → K+ invisible, dark matter, and CP violation in hyperon decays

Recently the Belle II Collaboration has reported a measurement of the B⁺ → K+νν¯ 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.