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Soft gluon resummation for heavy quark and dijet cross sections

Nikolaos Kidonakis

TL;DR

The paper develops a comprehensive next-to-leading logarithmic (NLL) framework for threshold resummation in hadronic heavy-quark and dijet production using soft anomalous dimension matrices to describe noncollinear soft-gluon emission. By factorizing cross sections into hard, soft, and collinear components and employing Mellin moments, the authors exponentiate the relevant logarithms and diagonalize the soft-gluon evolution in convenient color bases. They provide explicit one-loop soft anomalous dimension matrices for all pertinent partonic subprocesses in heavy-quark and dijet production, along with NLO expansions and numerical results for top-quark production at the Tevatron, demonstrating reduced scale dependence and improved predictions. The methodology is broadly applicable to other processes and cross sections in hadronic collisions, and the work connects to broader threshold-resummation efforts in particle phenomenology.

Abstract

We discuss the resummation of threshold logarithms for heavy quark and dijet cross sections in hadronic collisions. The resummed cross sections are presented at next-to-leading logarithmic accuracy in terms of anomalous dimension matrices which describe the factorization of soft gluons from the hard scattering. We apply our formalism to the calculation of the top quark production cross section at the Fermilab Tevatron.

Soft gluon resummation for heavy quark and dijet cross sections

TL;DR

The paper develops a comprehensive next-to-leading logarithmic (NLL) framework for threshold resummation in hadronic heavy-quark and dijet production using soft anomalous dimension matrices to describe noncollinear soft-gluon emission. By factorizing cross sections into hard, soft, and collinear components and employing Mellin moments, the authors exponentiate the relevant logarithms and diagonalize the soft-gluon evolution in convenient color bases. They provide explicit one-loop soft anomalous dimension matrices for all pertinent partonic subprocesses in heavy-quark and dijet production, along with NLO expansions and numerical results for top-quark production at the Tevatron, demonstrating reduced scale dependence and improved predictions. The methodology is broadly applicable to other processes and cross sections in hadronic collisions, and the work connects to broader threshold-resummation efforts in particle phenomenology.

Abstract

We discuss the resummation of threshold logarithms for heavy quark and dijet cross sections in hadronic collisions. The resummed cross sections are presented at next-to-leading logarithmic accuracy in terms of anomalous dimension matrices which describe the factorization of soft gluons from the hard scattering. We apply our formalism to the calculation of the top quark production cross section at the Fermilab Tevatron.

Paper Structure

This paper contains 18 sections, 86 equations.

Table of Contents

  1. Introduction
  2. Resummation for heavy quark production
  3. Factorized cross section
  4. Resummation
  5. Soft anomalous dimension matrices for heavy quark production
  6. Soft anomalous dimension for $q {\bar{q}} \rightarrow Q {\bar{Q}}$
  7. Soft anomalous dimension for $gg \rightarrow Q {\bar{Q}}$
  8. Diagonalization and numerical results for $q {\bar{q}} \rightarrow t{\bar{t}}$
  9. Resummation for dijet production
  10. Factorized dijet cross section
  11. Resummed dijet cross section
  12. Soft anomalous dimension matrices for dijet production
  13. Soft anomalous dimension for $q \bar{q}\rightarrow q \bar{q}$
  14. Soft anomalous dimension for $q q\rightarrow q q$ and ${\bar{q}}{\bar{q}}\rightarrow {\bar{q}}{\bar{q}}$
  15. Soft anomalous dimension for $q \bar{q}\rightarrow g g$ and $g g \rightarrow q \bar{q}$
  16. ...and 3 more sections