Lorentz-boosted description of a heavy quarkonium

Abstract

In this paper we study the relation between the light-front (infinite momentum) and rest-frame descriptions of quarkonia. While the former is more convenient for high-energy production, the latter is usually used for the evaluation of charmonium properties. In particular, we discuss the dynamics of a relativistically moving system with nonrelativistic internal motion and give relations between rest frame and light-front potentials used for the description of quarkonium states. We consider two approximations, first the small coupling regime, and next the nonperturbative small binding energy approximation. In both cases we get consistent results. Our results could be relevant for the description of final state interactions in a wide class of processes, including quarkonium production on nuclei and plasma. Moreover, they can be extended to the description of final state interactions in the production of weakly bound systems, such as for example the deuteron.

Exclusive photoproduction of excited quarkonia in ultraperipheral collisions

“…A justification of this prescription has been discussed in Ref. [38] and no significant deviation in predictions has been found between the exact calculation and the Terent'ev recipe in the phenomenologically relevant domains of the phase space. The spatial momentum-space wave function ψ V ðpÞ is found by a Fourier transform from the coordinate-space radial wave function ψðRÞ where R ≡ j ⃗…”

Suppression versus enhancement of heavy quarkonia in pA collisions

“…We fixed here α = α = 1/2, because these values are strongly enhanced by the projection into the charmonium wave function [22,24].…”

Production of pentaquarks inpA-collisions

“…In the general case a relation between the two objects is a nontrivial dynamical problem, however, under assumption that a motion of nucleons inside the nucleus is nonrelativistic, we may use the relation suggested in [63,64] whereΦ 2N stands for a Fourier transform of the corresponding wave function. As follows from (38) and is seen from the left pane of the Figure 5 , the α-dependence of the wave function is strongly peaked near a value α ≈ 1/2, for this reason in Equations (1,12,26,30) we do not write a convolution over a light-cone fraction α carried by a nucleon, tacitly assuming that for all physical observableŝ…”

“…In this kinematics, application of perturbative QCD might be questionable due to saturation effects. For this reason, we adopt a dipole model which naturally incorporates all saturation effects and has been applied to the description ofcc production in [36][37][38][39][40]. Since the produced dipoles are small and have a typical size r cc ∼ m −1 c , up to O (1/m c )-corrections this approach is equivalent to a k T -factorization approach suggested in [41][42][43], taking into account the relation of the dipole cross-section and the unintegrated gluon PDF F (x, k ⊥ ) suggested in [44].…”