Relating High-Energy Lepton-Hadron, Proton-Nucleus, and Nucleus-Nucleus Collisions through Geometric Scaling

A characteristic feature of small-$x$ lepton-proton data from HERA is geometric scaling: the fact that in the region of small Bjorken variable $x$, $x\lesssim 0.01$, all data can be described by a single variable $Q^2/Q_{s,p}^2(x)$, with all $x$ dependence encoded in the so-called saturation momentum $Q_{s,p}(x)$. Here, we observe that the same scaling ansatz accounts for nuclear photoabsorption cross sections and favors the nuclear dependence $Q_{s,A}^2\propto A^{\alpha }{Q}_{s,p}^2$, $\alpha \simeq 4/9$. We then make the empirical finding that the same $A$ dependence accounts for the centrality evolution of the multiplicities measured in $\mathrm{A}\mathrm{u}+\mathrm{A}\mathrm{u}$ collisions at RHIC. It also allows one to parametrize the high-$p_t$ particle suppression in $d+\mathrm{A}\mathrm{u}$ collisions at forward rapidities. If these geometric scaling properties have a common dynamical origin, then this $A$ dependence of $Q_{s,A}^2$ should emerge as a consequence of the underlying dynamical model.