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 \(b\rightarrow s h_2\) 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 \(R_\xi \) gauge and demonstrate how the \(\xi \) dependence cancels from physical decay rates involving an on-shell or off-shell \(h_2\). Then we revisit the \(b\rightarrow s h_2\) phenomenology and point out that a simultaneous study of \(B\rightarrow K^* h_2\) and \(B\rightarrow K h_2\) 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.

中文翻译：

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暗物质和$ B \ rightarrow K ^ {（*）} $$ B→K（∗）衰变的希格斯门户

我们考虑了一个希格斯门户模型，其中的125 GeV希格斯玻色子与耦合到暗区粒子的轻单线态调解剂\（h_2 \）混合，并在Belle II实验中研究潜在的\（b \ rightarrow s h_2 \）衰减。 。将规范相关的壳外标准模型b - s - Higgs顶点与希格斯混合角的正弦相乘不会得到正确的b - s - \（h_2 \）顶点。我们通过在任意\（R_ \ xi \）量表中计算b - s - \（h_2 \）顶点来澄清此问题，并演示如何使用\（\ xi \）依赖消除了涉及壳上或壳下\（h_2 \）的物理衰减率。然后，我们回顾\（b \ rightarrow s h_2 \）现象，并指出\（B \ rightarrow K ^ * h_2 \）和\（B \ rightarrow K h_2 \）的同时研究有助于区分希格斯门户和黑暗领域的替代模型。我们进一步主张使用包含在位移顶点数据中的\（h_2 \）寿命信息，并将\（h_2 \）衰减回标准模型粒子，以更好地约束\（h_2 \）质量或揭示其他\（ h_2 \）衰减模式变成长寿命的粒子。