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In strongly correlated systems the complete determination of the dynamicalsusceptibility $\chi(\textbf{q}, \omega)$ is of special relevance because ofthe entwinement of the spin and charge components. Although Resonant InelasticX-Ray Scattering (RIXS) spectra are directly related to both the charge($\chi''_c(\textbf{q}, \omega)$) and the spin ($\chi''_s(\textbf{q}, \omega)$)contributions, only the latter has been extensively studied with RIXS so far.Here we show how to extract from RIXS spectra of high-$T_c$ superconductingcuprates relevant properties of $\chi''_c$, such as the presence of thesuperconducting gap and of the pseudogap. In particular, we exploit thetemperature dependence of the Cu L$_3$ edge RIXS spectra of underdopedYBa$_2$Cu$_3$O$_{7-\delta}$ at specific wave-vectors q. The signature of thetwo gaps is in the departure of the low energy Bosonic excitation continuumfrom the statistical temperature-dependence. This approach can be immediatelyused to investigate systematically the nature of the pseudogap in cuprates,thereby taking advantage of the RIXS technique that does not suffer thelimitations of surface-sensitive electron spectroscopies. Its extension toother interesting materials is foreseen.

Charge response function probed by resonant inelastic x-ray scattering: the signature of electronic gaps of YBa$_2$Cu$_3$O$_{7-\delta}$