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Recent advances in momentum-resolved electron energy-loss spectroscopy(MEELS) and resonant inelastic X-ray scattering (RIXS) now allow one to accessthe charge response function with unprecedented versatility and accuracy. Thisallows for the study of excitations which were inaccessible recently, such aslow-energy and finite momentum collective modes. The SU(2) theory of thecuprates is based on a composite order parameter with SU(2) symmetryfluctuating between superconductivity and charge order. The phase where itfluctuates is a candidate for the pseudogap phase of the cuprates. This theoryhas a signature, enabling its strict experimental test, which is thefluctuation between these two orders, corresponding to a charge 2 spin 0 modeat the charge ordering wave-vector. Here we derive the influence of this SU(2)collective mode on the charge susceptibility in both strong and weak couplinglimits, and discuss its relation to MEELS, RIXS and Raman experiments. We findtwo peaks in the charge susceptibility at finite energy, whose middle is thecharge ordering wave-vector, and discuss their evolution in the phase diagram.

Collective mode in the SU(2) theory of cuprates