Golden probe of the top Yukuwa coupling

We perform a preliminary study of the ability of the Higgs decay to four leptons to shed light on the top quark Yukawa couplings. In particular we examine whether the $h\to 4\ell$ `golden channel' is sensitive to the $CP$ properties of the top quark couplings to the Higgs boson. We show that kinematic distributions are sensitive to interference of the next-to-leading order electroweak corrections with the tree level $ZZ$ contribution. This translates into a sensitivity to the top quark Yukawa couplings such that meaningful constraints on their $CP$ properties can begin to be obtained once $\sim 300$ fb$^{-1}$ of data has been collected at $\sim 14$ TeV, with significant improvements at higher luminosity or with a higher energy hadron collider. This makes the $h\to4\ell$ channel a useful probe of the top quark Yukawa couplings that is qualitatively different from already established searches in $h\to V\gamma$ two body decays, $tth$, and $gg\to h$. We also briefly discuss other potential possibilities for probing the top Yukawa $CP$ properties in $h\to2\ell\gamma$ and $\ell^+\ell^-\to h Z, h\gamma$.