A Challenge for Discrimination of Color-Singlet versus Color-Octet Quarkonium Production

TL;DR

This paper investigates the challenge of distinguishing between color-singlet and color-octet mechanisms in quarkonium production at hadron colliders, highlighting the dependence of discrimination observables on the quantum state of the heavy quark pair.

Contribution

It demonstrates that the likelihood ratio for discriminating production mechanisms strongly depends on the angular momentum state, complicating universal classification.

Findings

Likelihood ratio varies with quantum state

Discrimination observable is not universal

Obstruction to a single robust observable

Abstract

The precise mechanism for production of quarkonium at hadron colliders is still an open question. Within non-relativistic quantum chromodynamics, quarkonium production cross sections can be factorized into short-distance, perturbative contributions and universal, non-perturbative, long-distance matrix elements, and then summed over quantum numbers of the heavy quark pair. In principle, at short-distances, the heavy quark pair can be either in a color-singlet or color-octet state, and it is desirable to establish the relative contributions to compare with data and to make predictions in different experimental environments. From the explicit form of the lowest-order perturbative matrix elements for color-singlet and color-octet production, we show that the structure of the optimal observable for discrimination on phase space, the likelihood ratio, has strong dependence on the angular momentum state of the heavy quark pair. This presents an obstruction for construction of a single, robust discrimination observable that can be applied to production of an arbitrary quarkonium state.