We investigate near-threshold production of quarkonium resonances in cold nuclear matter through a scaling theory with two exponents which are fixed by existing data on near-threshold J/ψ production in proton-nucleus collisions. Interestingly, it seems possible to extend one of the multifractal dimensions to the production of other mesons in cold nuclear matter. The scaling theory can be tested and refined in experiments at the upcoming high-intensity FAIR accelerator complex in GSI.PACS numbers: 25.40. Ep,14.40.Pq,24.85.+p. TIFR/TH/13-09There are unexplored systematics for the production of quarkonia close to threshold. For the J/ψ, a few experimental studies were carried out in the days before the understanding of QCD was mature. Attention shifted to the high-energy frontier, since perturbative QCD turned out to be the tool appropriate to that region, and weakcoupling theory was applied successfully to higher-energy production of quarkonium in pA collisions [1][2][3][4]. However, the planned FAIR in GSI presents a grand opportunity for the study of near-threshold particle production in cold nuclear matter, and test and refine a scaling theory which is developed here. This is interesting for several reasons. First, as we argue here, testing the limits of such a scaling theory shows where the crossover between hadron and quark descriptions of matter lie. Second, this measurement can be used to test factorization where it cannot be proved, and therefore has implications on the understanding of CP violations. Third, a detailed understanding of cold nuclear effects in quarkonium production is important to tests of the formation of the QCD plasma in heavy-ion collisions. Finally, the discovery of scaling laws, which is our main result, is of fundamental interest since the exponents can define universality classes across very broad ranges of physical phenomena.The basic toolkit which we bring to this study is the modern understanding that the renormalization group is expressed via scaling. We wish to ascertain whether there is a dynamical symmetry of cold nuclear matter so that a small change in the amount of nuclear matter can be compensated for by a corresponding change in the energy of the probe. Invariance under such scaling would manifest itself in the form of exponents which are eigenvalues of renormalization group transformations [5]. These scaling exponents are also called fractal dimensions or anomalous dimensions. At high energies they can be computed in perturbation theory. Near the threshold of particle production, they have to be discovered in data and understood non-perturbatively. Discovery of scaling exponents, which is our main result, conversely implies the scaling symmetries.We are interested in the production of a quarkonium state, H, in pA collisions near the threshold energy √ S 0 , which is the minimum energy in the center of mass required to produce H. We follow the convention of writing the CM energy, √ S, in the equivalent pp system; for a fixed target configuration this means S = 2M p (E ...