Higgs portal to dark matter and $$B\rightarrow K^{(*)}$$ B→K(∗) decays

Abstract

Abstract We consider a Higgs portal model in which the 125-GeV Higgs boson mixes with a light singlet mediator $$h_2$$ h2 coupling to particles of a Dark Sector and study potential $$b\rightarrow s h_2$$ b→sh2 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-$$h_2$$ h2 vertex. We clarify this issue by calculating the b-s-$$h_2$$ h2 vertex in an arbitrary $$R_\xi $$ Rξ gauge and demonstrate how the $$\xi $$ ξ dependence cancels from physical decay rates involving an on-shell or off-shell $$h_2$$ h2 . Then we revisit the $$b\rightarrow s h_2$$ b→sh2 phenomenology and point out that a simultaneous study of $$B\rightarrow K^* h_2$$ B→K∗h2 and $$B\rightarrow K h_2$$ B→Kh2 helps to discriminate between the Higgs portal and alternative models of the Dark Sector. We further advocate for the use of the $$h_2$$ h2 lifetime information contained in displaced-vertex data with $$h_2$$ h2 decaying back to Standard-Model particles to better constrain the $$h_2$$ h2 mass or to reveal additional $$h_2$$ h2 decay modes into long-lived particles.