Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Fragmentation, Factorization and Infrared Poles in Heavy Quarkonium Production

Gouranga C. Nayak, Jian-Wei Qiu, George Sterman

TL;DR

This paper analyzes heavy quarkonium production at large transverse momentum and reveals uncancelled infrared poles at NNLO that challenge conventional NRQCD factorization. By introducing gauge-completed NRQCD operators that include nonabelian Wilson lines, the authors show that factorization can be restored at NNLO, aligning infrared structure with the fragmentation function through an eikonal treatment of soft gluons. A key finding is that at NNLO there exist nontopological infrared poles that are precisely accounted for by the gauge-completed operators, while rotational invariance in the quarkonium rest frame serves as a crucial consistency check. The work suggests that, beyond NNLO, additional nonlocal operators may be required and underscores the need for further study of NRQCD factorization in heavy-quarkonium production and its evolution.

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.

Fragmentation, Factorization and Infrared Poles in Heavy Quarkonium Production

TL;DR

This paper analyzes heavy quarkonium production at large transverse momentum and reveals uncancelled infrared poles at NNLO that challenge conventional NRQCD factorization. By introducing gauge-completed NRQCD operators that include nonabelian Wilson lines, the authors show that factorization can be restored at NNLO, aligning infrared structure with the fragmentation function through an eikonal treatment of soft gluons. A key finding is that at NNLO there exist nontopological infrared poles that are precisely accounted for by the gauge-completed operators, while rotational invariance in the quarkonium rest frame serves as a crucial consistency check. The work suggests that, beyond NNLO, additional nonlocal operators may be required and underscores the need for further study of NRQCD factorization in heavy-quarkonium production and its evolution.

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.

Paper Structure

This paper contains 6 sections, 9 equations, 2 figures.

Table of Contents

  1. Introduction
  2. NRQCD in Fragmentation
  3. Gauge Invariance and Wilson Lines
  4. Eikonal Approximation for $g\to H$
  5. Fragmentation Function at NNLO
  6. Summary and Future Studies

Figures (2)

  • Figure 1: a) Lowest-order fragmentation function for $g\to c\bar{c}$. There are no interactions on the eikonal quark pair or the Wilson line that corresponds to an eikonal gluon of four-velocity $l$. b,c) Representative NLO contributions to $g\to c\bar{c}$ fragmentation in eikonal approximation. In these figures the parent gluon is contracted to a point, represented by the dark circle, because it is off-shell by order $m_c$
  • Figure 2: Representative NNLO contributions to $g\to c\bar{c}$ fragmentation in eikonal approximation.