Higgs portal to dark matter and B→K(∗) decays.

We consider a Higgs portal model in which the 125-GeV Higgs boson mixes with a light singlet mediator h 2 coupling to particles of a Dark Sector and study potential b → s h 2 decays in the Belle II experiment. Multiplying the gauge-dependent off-shell Standard-Model b-s-Higgs vertex with the sine of the Higgs mixing angle does not give the correct b-s- h 2 vertex. We clarify this issue by calculating the b-s- h 2 vertex in an arbitrary R ξ gauge and demonstrate how the ξ dependence cancels from physical decay rates involving an on-shell or off-shell h 2 . Then we revisit the b → s h 2 phenomenology and point out that a simultaneous study of B → K ∗ h 2 and B → K h 2 helps to discriminate between the Higgs portal and alternative models of the Dark Sector. We further advocate for the use of the h 2 lifetime information contained in displaced-vertex data with h 2 decaying back to Standard-Model particles to better constrain the h 2 mass or to reveal additional h 2 decay modes into long-lived particles. [ABSTRACT FROM AUTHOR]