Scalar leptoquark contributions to the $gg\rightarrow Zh$ process

In this manuscript, we study the general scalar leptoquark contributions to the $gg\rightarrow Zh$ process at one-loop level. We find that the contributions only show up for the off-diagonal Higgs and $Z$ boson interactions with scalar leptoquarks, which can lead to a new tensor structure different from the standard model. In the one-field and two-field models, the contributions vanish exactly; thus, the contributions are possible at least in the three-field models. We exemplify the contributions in the $S_1+\widetilde{R}_2+S_3$ model, which can appear in the presence of scalar leptoquark mass splittings and $CP$ violation. In view of the heavy scalar leptoquark mass suppression, the leading contributions are typically small and difficult to observe at hadron colliders.