Nonrelativistic QCD factorization and the velocity dependence of NNLO poles in heavy quarkonium production

Abstract

We study the transition of a heavy quark pair from octet to singlet color configurations at next-to-next-to-leading order (NNLO) in heavy quarkonium production. We show that the infrared singularities in this process are consistent with NRQCD factorization to all orders in the heavy quark relative velocity v. This factorization requires the gauge-completed matrix elements that we introduced previously to prove NNLO factorization to order v 2 .

Color-transfer enhancement for heavy quarkonium production

“…The underlying factorization that justifies fragmentation analysis extends as well to hadronic scattering, as shown in Ref. [17].…”

“…We will then go on to rederive this result from an effective non-local vertex involving the gluon field strength coupled to the dipole moment of the active pair [16]. This reformulation will enable us to extend our analysis to NNLO in the following section, and also to exhibit the relation of the analysis here to our previous study of NRQCD factorization [17] and to potential NRQCD [5].…”

“…In essence, we will supplement below the calculations of Refs. [16,17], by studying infrared poles in corrections to the production of a heavy quark pair due to the exchange of soft gluons with an additional massive final-state particle. The extension from massless to massive particles in the final state has important consequences for a cross section in which the color of the quark pair is fixed to be in a singlet configuration in the final state.…”

Factorization for Hadronic Heavy Quarkonium Production

“…[14] that with the gauge-completed matrix elements, infrared singularities in the fragmentation function for a color octet pair to a singlet at NNLO are consistent with NRQCD factorization to all orders in v or to a finite v,…”

“…[4], as well as at finite v in Ref. [14]. Consider representative NNLO contributions to the fragmentation process of transforming a color octet heavy quark pair to a singlet, as sketched in Fig.…”