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The hidden order in URu$_2$Si$_2$ remains a compelling mystery after morethan thirty years, with the order parameter still unidentified. One intriguingproposal for the phase has been hastatic order: a symmetry breaking heavy Fermiliquid with a spinorial hybridization that breaks both single and doubletime-reversal symmetry. Hastatic order is the first spinorial, rather thanvectorial order in materials, but previous work has not yet found directconsequences of the spinorial nature. In this paper, we revisit the hastaticproposal within Landau-Ginzburg theory. Rather than a single spinorial orderparameter breaking double-time-reversal symmetry, we find two gauge invariantvectorial orders: the expected composite order with on-site moments, and a newquantity capturing symmetries broken solely by the spinorial nature. We addressthe effect of fluctuations and disorder on the tetragonal symmetry breaking,explaining the absence of in-plane moments in URu$_2$Si$_2$ and predicting anew transition in transverse field.

Signatures of spinorial order in URu$_2$Si$_2$: Landau-Ginzburg theory of hastatic order