Fractal structure of near-threshold quarkonium production off cold nuclear matter

Abstract

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 ...

Near-threshold J/Ψ production in proton–nucleus collisions

“…There are essentially less extensive investigations [12][13][14][15][16][17] of the production and absorption of the charmonium states in antiproton-nucleus reactions at low energies, where they are created with the moderate momenta relative to the target nucleus and where, therefore, the J/Ψ formation length effects play a minor role. Finally, the production of J/Ψ mesons on nuclei in proton-induced reactions at low energies [18][19][20] and, especially, at energies close to their kinematic threshold (the threshold kinetic energy for J/Ψ production in pp collisions being 11.3 GeV) [11,21] has up to now received very little consideration, probably, because of the lack of suitable facilities and associated detectors. Since the cross sections of (p, J/Ψ) reaction at near-threshold energies are expected to be extremely low, high intensity proton beams are needed to perform accurate measurements of J/Ψ creation on nuclear targets in the threshold region.…”

Charmonium interaction in nuclear matter at FAIR

“…This assumption is debatable, see Refs. [43,44,45], for alternative approaches of J/ψ production at near threshold beam energies. However, the validity of QCD factorization, in the near threshold quarkonium production can only be tested with data for FAIR energies.…”

Ψ(2S) production in p + A collisions

“…An alternative approach based on scaling arguments for near-threshold quarkonium production can be found in ref. [28]. Moreover, the model assumes propagation of the perturbatively produced cc pairs through the nucleus and the non-perturbative transition from cc → ψ(2S) occurs outside the nucleus.…”