Higgs portal to dark matter and $$B\rightarrow K^{(*)}$$ decays
Aliaksei Kachanovich, Ulrich Nierste, Ivan Nišandžić
Abstract
Abstract We consider a Higgs portal model in which the 125-GeV Higgs boson mixes with a light singlet mediator $$h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> coupling to particles of a Dark Sector and study potential $$b\rightarrow s h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>b</mml:mi><mml:mo>→</mml:mo><mml:mi>s</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> 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 - $$h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> vertex. We clarify this issue by calculating the b - s - $$h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> vertex in an arbitrary $$R_\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>R</mml:mi><mml:mi>ξ</mml:mi></mml:msub></mml:math> gauge and demonstrate how the $$\xi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>ξ</mml:mi></mml:math> dependence cancels from physical decay rates involving an on-shell or off-shell $$h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> . Then we revisit the $$b\rightarrow s h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>b</mml:mi><mml:mo>→</mml:mo><mml:mi>s</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> phenomenology and point out that a simultaneous study of $$B\rightarrow K^* h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:msup><mml:mi>K</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> and $$B\rightarrow K h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>B</mml:mi><mml:mo>→</mml:mo><mml:mi>K</mml:mi><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math> helps to discriminate between the Higgs portal and alternative models of the Dark Sector. We further advocate for the use of the $$h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> lifetime information contained in displaced-vertex data with $$h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> decaying back to Standard-Model particles to better constrain the $$h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> mass or to reveal additional $$h_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>h</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:math> decay modes into long-lived particles.