Fragmentation, factorization and infrared poles in heavy quarkonium production

Abstract

We explore the role of soft gluon exchange in heavy quarkonium production at large transverse momentum. We find uncanceled infrared poles at NNLO that are not matched by conventional NRQCD matrix elements. We show, however, that gauge invariance and factorization require that conventional NRQCD production operators be modified to include nonabelian phases or Wilson lines. With appropriately modified operators, factorization is restored at NNLO. We also argue that, in the absence of special cancellations, infrared poles at yet higher orders may require the inclusion of additional nonlocal operators, not present in the NRQCD expansion in relative veloctiy.

Factorization for Hadronic Heavy Quarkonium Production

“…4(I) and (II), for which two gluons are exchanged between the quarks and the Wilson line, satisfy the infrared cancellation conjecture of Ref. [11], by summing over the possible cuts and connections to quark and antiquark lines, as do diagrams that have three gluon-eikonal vertices on the quark pair and one on the Wilson line [4]. For Fig.…”

“…When p T ≫ m Q , heavy quarkonium production is similar to the single light hadron production, and is dominated by parton fragmentation. The cross section is proportional to the universal parton-to-hadron fragmentation functions [4],…”

“…4(III) type of diagrams, however, with a three-gluon interaction, this cancellation fails. By summing over all contributions to second order in the relative momentum q, it was found that the fragmentation function has a noncanceling real pole [4] …”

Color-transfer enhancement for heavy quarkonium production

“…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.…”

“…More specifically, NRQCD factorization and matching for production cross sections require the cancellation of all infrared gluons that are not "topologically factorized" into factors equivalent to the perturbative expansions of matrix elements in the effective theory [1,16]. The allowed, topologically factorized, soft gluons are those that can be absorbed either into the interaction of the active pair with "the vacuum", or that do not couple to either of the heavy quarks that form the quarkonium.…”