Beyond Geolocating: Constraining Higher Dimensional Operators in $H \to 4\ell$ with Off-Shell Production and More

We extend the study of Higgs boson couplings in the "golden" $gg\to H \to ZZ^\ast \to 4\ell$ channel in two important respects. First, we demonstrate the importance of off-shell Higgs boson production ($gg\to H^\ast \to ZZ \to 4\ell$) in determining which operators contribute to the $HZZ$ vertex. Second, we include the five operators of lowest non-trivial dimension, including the $Z_\mu Z^\mu \Box H$ and $H Z_\mu \Box Z^\mu$ operators that are often neglected. We point out that the former operator can be severely constrained by the measurement of the off-shell $H^\ast \to ZZ$ rate and/or unitarity considerations. We provide analytic expressions for the off-peak cross-sections in the presence of these five operators. On-shell, the $Z_\mu Z^\mu \Box H$ operator is indistinguishable from its Standard Model counterpart $H Z_\mu Z^\mu$, while the $H Z_\mu \Box Z^\mu$ operator can be probed, in particular, by the $Z^\ast$ invariant mass distribution.