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Transverse-Momentum-Dependent Gluon Distributions and Semi-inclusive Processes at Hadron Colliders

Xiangdong Ji, Jian-Ping Ma, Feng Yuan

TL;DR

The paper develops gauge-invariant TMD gluon distributions and a factorization framework for gluon-initiated semi-inclusive processes at hadron colliders, focusing on low transverse momentum where resummation is essential. It establishes one-loop factorization for scalar production via gluon fusion, derives the soft factor, and demonstrates Collins-Soper evolution that enables Sudakov resummation. Matching to integrated PDFs is performed via perturbative coefficient functions, and small-b factorization is shown with explicit C_{gg} coefficients. The work compares its resummation results with prior calculations, clarifying the role of the Higgs-gluon coupling in the C coefficients and outlining extensions to broader processes and higher orders.

Abstract

We study transverse-momentum-dependent (TMD) gluon distributions and factorization theorems for the gluon-initiated semi-inclusive processes at hadron colliders. Gauge-invariant TMD gluon distributions are defined, and their relations to the integrated (Feynman) parton distributions are explored when the transverse momentum is large. Through explicit calculations, soft-collinear factorization is verified at one-loop order for scalar particle production. Summation over large double logarithms is made through solving the Collins-Soper equation. We reproduce the known result in the limit that the transverse momentum of the scalar is large.

Transverse-Momentum-Dependent Gluon Distributions and Semi-inclusive Processes at Hadron Colliders

TL;DR

The paper develops gauge-invariant TMD gluon distributions and a factorization framework for gluon-initiated semi-inclusive processes at hadron colliders, focusing on low transverse momentum where resummation is essential. It establishes one-loop factorization for scalar production via gluon fusion, derives the soft factor, and demonstrates Collins-Soper evolution that enables Sudakov resummation. Matching to integrated PDFs is performed via perturbative coefficient functions, and small-b factorization is shown with explicit C_{gg} coefficients. The work compares its resummation results with prior calculations, clarifying the role of the Higgs-gluon coupling in the C coefficients and outlining extensions to broader processes and higher orders.

Abstract

We study transverse-momentum-dependent (TMD) gluon distributions and factorization theorems for the gluon-initiated semi-inclusive processes at hadron colliders. Gauge-invariant TMD gluon distributions are defined, and their relations to the integrated (Feynman) parton distributions are explored when the transverse momentum is large. Through explicit calculations, soft-collinear factorization is verified at one-loop order for scalar particle production. Summation over large double logarithms is made through solving the Collins-Soper equation. We reproduce the known result in the limit that the transverse momentum of the scalar is large.

Paper Structure

This paper contains 15 sections, 75 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Transverse-momentum-dependent gluon distributions
  3. Gauge-Invariant Definition
  4. One-loop Calculations Without Soft Factor
  5. Soft Factor
  6. TMD Gluon Distribution at One-Loop
  7. Collins-Soper Evolution in Hadron Energy
  8. TMD Parton Distributions at Large Transverse Momentum
  9. Scalar-particle production through gluon fusion
  10. Factorization At One Loop
  11. Factorization at Small $b\ll 1/ \Lambda_{\rm QCD}$
  12. Resummation of Large Double Logarithms
  13. Collins-Soper-Sterman Resummation at Small b
  14. Comparison with Previous Calculations
  15. Conclusion

Figures (12)

  • Figure 1: The Feynman rule for the TMD vertices. The first comes from the eikonal line and the second comes from the non-abelian term in the field strength tensor. In this calculation, the sum of the two will be lumped together and labelled by the gauge link.
  • Figure 2: Virtual corrections to the TMD gluon distribution at one-loop order. The mirror diagrams are not shown.
  • Figure 3: Same as Fig. 2 but for the real contributions.
  • Figure 4: Soft contributions to the TMD gluon distribution at one-loop order.
  • Figure 5: Quark splitting to gluon contribution to $\tilde{C}_{g/q}$ (a) and gluon splitting to quark $\tilde{C}_{q/g}$ (b).
  • ...and 7 more figures