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Scrutinizing the Higgs Signal and Background in the $2e2μ$ Golden Channel

Kinematic distributions in the decays of the newly discovered resonance to four leptons are a powerful test of the tensor structure of its couplings to electroweak gauge bosons. We present an analytic calculation for both signal and background of the fully differential cross section for the `Golden Channel' $e^+e^-μ^+μ^-$ final state. We include all interference effects between intermediate gauge bosons and allow them to be on- or off-shell. For the signal we compute the fully differential cross section for general scalar couplings to $ZZ$, $γγ$, and $Zγ$. For the background we compute the leading order fully differential cross section for the dominant contribution coming from $q\bar{q}$ annihilation into $Z$ and $γ$ gauge bosons, including the contribution from the resonant $Z\rightarrow 2e2μ$ process. We also present singly and doubly differential projections and study the interference effects on the differential spectra. These expressions can be used in a variety of ways to uncover the nature of the newly discovered resonance or any new scalars decaying to neutral gauge bosons which might be discovered in the future.