Review of quarkonium production: status and prospects

Abstract

Production cross sections of heavy quarkonia are considered as useful tools to study various aspects of QCD. We have entered a new era of quarkonium production phenomenology, with the help of new measurements from the LHC giving access to more varieties of observables, and recent theoretical developments that provided us a better understanding of the short-distance process in which quarkonia are produced. With a more concrete understanding of perturbative corrections and a prolific collection of data, a satisfactory description of the quarkonium production mechanism might now be within reach. Unfortunately, the exact mechanism of quarkonium production still remains elusive. Even analyses based on the same formalism can lead to different descriptions of the production process and give contradicting predictions of processes involving heavy quarkonia. This implies that there are much more physics yet to be understood and much work yet to be done in quarkonium production phenomenology. In this paper, we review the current status of theoretical approaches and discuss possible strategies that may improve our understanding of heavy quarkonium production.

Inclusive production of heavy quarkonia in pNRQCD

“…(3.12), the Schwinger lines are in the fundamental representation, whereas, in the third one, the Schwinger line has to be understood in the adjoint representation. 6 The condition k = n in the first and second line of eq. (3.12) has been lifted for r = 0 in the third line, since, according to footnote 4, n ∈ S implies that (0) n|Φ bc (0, x 1 )T c |Ω vanishes after taking the color trace.…”

“…(3.12) is valid in any gauge, it can be easily verified in the temporal gauge (A0 = 0) where the Schwinger line becomes unity. 6 Consider an infinitesimal time interval dt and fields located at a same but unspecified position, then it holds…”

“…Therefore, in most phenomenological studies, the long-distance matrix elements have been obtained from fits to cross section data. This approach has resulted in different sets of LDME determinations depending on the choice of data that are used in the fit, which can disagree with one another [6]. These inconsistent sets of LDMEs lead to contradicting predictions, and none of the determinations is able to give a comprehensive description of the most important observables related to heavy quarkonium production at a satisfactory level [6,7].…”

“…This approach has resulted in different sets of LDME determinations depending on the choice of data that are used in the fit, which can disagree with one another [6]. These inconsistent sets of LDMEs lead to contradicting predictions, and none of the determinations is able to give a comprehensive description of the most important observables related to heavy quarkonium production at a satisfactory level [6,7]. It is therefore desirable and to some extent even necessary to have first-principle JHEP09(2021)032 based constraints, or even computations, of the NRQCD LDMEs, in order to enhance significantly our understanding of the heavy quarkonium production mechanism.…”

Quarkonium production in pNRQCD: the P-wave case

“…The LDMEs are however poorly known, as they are inherently non perturbative. They are usually fitted on data, but the inclusion of different set of data in the fit typically leads to different determinations, none of them able to describe all the data in a satisfactory manner [14,15]. From the point of view of figure 1, the LDMEs still contain contributions from the scales mv and mv 2 .…”