Heavy quarkonium production at collider energies: Factorization and evolution

Abstract

We present a perturbative QCD factorization formalism for inclusive production of heavy quarkonia of large transverse momentum, pT at collider energies, including both leading power (LP) and next-to-leading power (NLP) behavior in pT . We demonstrate that both LP and NLP contributions can be factorized in terms of perturbatively calculable short-distance partonic coefficient functions and universal non-perturbative fragmentation functions, and derive the evolution equations that are implied by the factorization. We identify projection operators for all channels of the factorized LP and NLP infrared safe short-distance partonic hard parts, and corresponding operator definitions of fragmentation functions. For the NLP, we focus on the contributions involving the production of a heavy quark pair, a necessary condition for producing a heavy quarkonium. We evaluate the first non-trivial order of evolution kernels for all relevant fragmentation functions, and discuss the role of NLP contributions.

Heavy quarkonium production at collider energies: Partonic cross section and polarization

“…For some production channels of the NRQCD calculations, the NLO corrections are orders larger than their corresponding leading order (LO) results, which raises questions as to whether yet higher order contributions can be neglected. Motivated in part by these challenges to existing theory, new approaches based on QCD factorization [18][19][20][21][22] and soft-collinear effective theory [23,24] have been proposed for the systematic study of heavy quarkonium production at collider energies.…”

“…[22], we developed an extended QCD factorization formalism for heavy quarkonium production at large transverse momentum p T ≫ m H ≫ Λ QCD in hadronic collisions (or at a large energy E ≫ m H in e + e − collisions) with heavy quarkonium mass m H . The new QCD factorization formalism includes both collinear-factorized leading power (LP) and collinear-factorized next-to-leading power (NLP) terms in the 1/p T expansion of the production cross section,…”

“…In Eq. (1), the variables z, u, and v, withū = 1 − u andv = 1 − v are light-cone momentum fractions; and D f →H (z; m Q ) and D [QQ(κ)]→H (z, u, v; m Q ) are single-parton and heavy quark-pair fragmentation functions (FFs), respectively [22]. In the factorization formula in Eq.…”

“…(1), we neglect all contributions involving twist-4 multi-parton correlation functions of colliding hadrons, as well as all terms at NLP involving FFs not from a heavy quark pair, because these contributions must create the heavy quark pair non-perturbatively. We thus expect them to be suppressed by powers of heavy quark mass [22], and could be suppressed further by reasons similar to those that lead to the OZI rule in evaluating the decay rates. The QCD factorization formalism in Eq.…”

“…At NLP accuracy, the QCD factorization requires not only the factorized NLP term in Eq. (1), but also a new power suppressed contribution to the DGLAP evolution of heavy quarkonium FFs from a single active parton [22]. The factorized NLP term in Eq.…”