On relation between rest frame and light-front descriptions of quarkonium

TL;DR

This paper explores the relationship between rest frame and light-front descriptions of quarkonium, providing relations between potentials in both frameworks and discussing implications for high-energy processes and weakly bound systems.

Contribution

It introduces a consistent framework connecting rest frame and light-front potentials for quarkonium, applicable to high-energy production and weakly bound systems.

Findings

Derived relations between rest frame and light-front potentials.

Validated results in small coupling and small binding energy regimes.

Potential applications to quarkonium production and weakly bound systems.

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.