Can dd excitations mediate pairing ?

The Cu-$3d$ states in the high-$T_c$ cuprates are often described as a single band of $3d_{x^2-y^2}$ states, with the other four $3d$ states having about 2 to 3 eV higher energy due to the lower-than-octahedral crystal field at the copper sites. However, excitations to these higher energy states observed with RIXS show indications of strong coupling to doped holes in the $3d_{x^2-y^2}$ band. This relaunches a decades-old question of the possible role of the orbital degrees of freedom that once motivated Bednorz and Müller to search for superconductivity in these systems. Here we explore a direction different from the Jahn-Teller electron-phonon coupling considered by Bednorz and Müller, namely the interaction between holes mediated by $dd$ excitations.