  Investigating the polarization of weak bosons provides an important probe of
the scalar and gauge sector of the Standard Model. This can be done in the
Higgs decay to four leptons, whose Standard-Model leading-order amplitude
enables to generate polarized observables from unpolarized ones via a
fully-differential reweighting method. We study the Z-boson polarization from
the decay of a Higgs boson produced in association with two jets, both in the
gluon-fusion and in the vector-boson fusion channel. We also address the
possibility of extending the results of this work to higher orders in
perturbation theory.
