  In this paper, we show that multiplicity spectra of direct photons in A+A and
d+Au collisions at different centrality classes and different energies exhibit
geometrical scaling, {\em i.e.}, they depend on a specific combination of
number of participants $N_{\rm part}$, collisions energy $W$, and transverse
momentum $p_{T}$ -- called saturation scale -- rather than on all these three
variables separately. In particular, the dependence on the geometry of
collisions encoded in the dependence on $N_{\rm part}$ is in agreement with the
expectations based on the Color Glass Condensate theory.
