What is the order parameter of hidden order in $\mathrm{URu_2Si_2}$?
In plain words
Below 17.5 K, $\mathrm{URu_2Si_2}$ enters an ordered phase that releases a large amount of entropy, yet nearly forty years of experiments have not identified what orders.
Precise statement
Identify the order parameter of the phase below $T_{\mathrm{HO}} = 17.5\ \mathrm{K}$ in $\mathrm{URu_2Si_2}$, which has no ordered magnetic moment of matching size and doubles the unit cell along c (wavevector $(0,0,1)$). Candidates include higher-rank multipoles (hexadecapole, dotriacontapole), hastatic order and chirality density waves. An answer gives the symmetry (irreducible representation) and microscopic character, confirmed by a probe that couples directly to it (resonant x-ray scattering, Raman, NMR).
What would settle it
A direct detection of the proposed order parameter whose temperature dependence follows $T_{\mathrm{HO}}$ and vanishes under pressure-induced antiferromagnetism.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Raman data (2015) show an $A_2g$ mode suggesting chirality-density-wave order, while reports of in-plane fourfold symmetry breaking disagree between probes.
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