  Recent advances in momentum-resolved electron energy-loss spectroscopy
(MEELS) and resonant inelastic X-ray scattering (RIXS) now allow one to access
the charge response function with unprecedented versatility and accuracy. This
allows for the study of excitations which were inaccessible recently, such as
low-energy and finite momentum collective modes. The SU(2) theory of the
cuprates is based on a composite order parameter with SU(2) symmetry
fluctuating between superconductivity and charge order. The phase where it
fluctuates is a candidate for the pseudogap phase of the cuprates. This theory
has a signature, enabling its strict experimental test, which is the
fluctuation between these two orders, corresponding to a charge 2 spin 0 mode
at 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 coupling
limits, and discuss its relation to MEELS, RIXS and Raman experiments. We find
two peaks in the charge susceptibility at finite energy, whose middle is the
charge ordering wave-vector, and discuss their evolution in the phase diagram.
