Differential observables for the Higgs-strahlung process to all orders in EFT

We develop methods to obtain the fully differential cross-section for the $f \bar{f} \to Z(\ell\ell)\,h$ process to any desired order in effective field theory (EFT). To achieve this, we first derive a mapping between the partial wave expansion and the EFT expansion to all orders. We find that at lower orders, EFT predicts correlations between the different partial wave coefficients. This allows us to construct linear combinations of partial wave coefficients that get their leading contributions from a higher dimension EFT operator. We then introduce experimental observables, the so called angular moments -- that probe these linear combinations of partial wave coefficients -- and can be determined from a fully differential analysis of the angular distribution of the leptons arising from the $Z$ decay. We show that analysing the dependence of these angular moments on the $Zh$ invariant mass allows us to systematically probe all higher dimension EFT operators contributing to this process. While we take the Higgs-strahlung process as an example, the methods developed here are completely general and can be applied to other 2-to-2 collider processes.