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

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.