Higgs decays to four leptons to $\mathcal{O}(1/\Lambda^4)$ in SMEFT

We study the decays $h \to \ell \bar{\ell} \left(Z \to \ell' \bar{\ell'}\right)$ and $h\to\ell\bar{\nu}_\ell\nu_{\ell'}\bar{\ell'}$ within the SMEFT framework and including effects up to $\mathcal O(1/\Lambda^4)$, where $\Lambda$ is the new physics scale suppressing higher dimensional operators. To work to this order, we must include the square of dimension-six operators and the interference of dimension-eight operators with the Standard Model. We study angular asymmetries and other differential decay observables and determine which are most sensitive to $\mathcal O(1/\Lambda^4)$ effects. While new kinematic structures arising in higher dimensional operators have the potential to induce novel angular dependency, we find this does not occur for $h\to\ell\bar{\ell}\left(Z\xrightarrow{}\ell'\bar{\ell'}\right)$. For $h \to \ell \bar{\nu}_\ell \nu_{\ell'} \bar{\ell'}$, new angular dependencies do arise at $\mathcal O(1/\Lambda^4)$, though they require a fully reconstructible (meaning we can go to the Higgs rest frame) final state. For non-reconstructible final states such as $\ell \bar{\nu}_\ell \nu_{\ell'} \bar{\ell'}$, we must study Higgs production and decay together with the appropriate observables, which we find obscures the new angular effects.