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Rare decay of the Higgs boson is a powerful tool to probe new physics beyondthe standard model. The rare decays occur through quantum loops in which thestandard model and new physics contributions might cancel each other out. Weconsider a faked-no-new-physics scenario that the new physics contributions areabout minus two times the standard model contribution such that partial widthsof Higgs boson rare decays are the same as the standard model predictions. Wepropose to measure the $HZ\gamma$ and $H\gamma\gamma$ anomalous couplings inthe process of $e^+ e^- \to H\gamma$ that is strongly correlated to Higgs bosonrare decays. We show that the faked-no-new-physics scenario can be fully probedat a high energy electron-positron collider.

Probing $HZ\gamma$ and $H\gamma\gamma$ anomalous couplings in the process of $e^+e^- \to H\gamma$