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Factorization and resummation of t-channel single top quark production

Jian Wang, Chong Sheng Li, Hua Xing Zhu, Jia Jun Zhang

TL;DR

The paper develops a soft-collinear effective theory (SCET) framework to factorize and resum threshold logarithms in t-channel single top quark production at the Tevatron and LHC. It decomposes the partonic cross section into hard, jet, and soft functions, deriving NLO expressions and performing RG evolution to achieve NNLL-like resummation. Numerical studies show resummation reduces the cross section slightly (about 3% at the Tevatron and 2% at the LHC) and dramatically decreases scale dependence, yielding more stable predictions across scale variations. When s- and t-channel results are combined, the predicted cross sections align more closely with experimental measurements than previous literature, underscoring the utility of SCET resummation for precise SM predictions in top-quark production.

Abstract

We investigate the factorization and resummation of t-channel single top (antitop) quark production in the SM at both the Tevatron and the LHC in SCET. We find that the resummation effects decrease the NLO cross sections by about 3% at the Tevatron and about 2% at the LHC. And the resummation effects significantly reduce the factorization scale dependence of the total cross section. The transfer momentum cut dependence and other matching scale dependencies are also discussed. We also show that when our numerical results for s- and t-channel single top production at the Tevatron are combined, it is closer to the experimental result than the one reported in previous literatures.

Factorization and resummation of t-channel single top quark production

TL;DR

The paper develops a soft-collinear effective theory (SCET) framework to factorize and resum threshold logarithms in t-channel single top quark production at the Tevatron and LHC. It decomposes the partonic cross section into hard, jet, and soft functions, deriving NLO expressions and performing RG evolution to achieve NNLL-like resummation. Numerical studies show resummation reduces the cross section slightly (about 3% at the Tevatron and 2% at the LHC) and dramatically decreases scale dependence, yielding more stable predictions across scale variations. When s- and t-channel results are combined, the predicted cross sections align more closely with experimental measurements than previous literature, underscoring the utility of SCET resummation for precise SM predictions in top-quark production.

Abstract

We investigate the factorization and resummation of t-channel single top (antitop) quark production in the SM at both the Tevatron and the LHC in SCET. We find that the resummation effects decrease the NLO cross sections by about 3% at the Tevatron and about 2% at the LHC. And the resummation effects significantly reduce the factorization scale dependence of the total cross section. The transfer momentum cut dependence and other matching scale dependencies are also discussed. We also show that when our numerical results for s- and t-channel single top production at the Tevatron are combined, it is closer to the experimental result than the one reported in previous literatures.

Paper Structure

This paper contains 14 sections, 42 equations, 4 figures, 7 tables.

Table of Contents

  1. Introduction
  2. Factorization and Resummation Formalism
  3. The Hard, Jet and Soft Functions at NLO
  4. Hard functions
  5. Jet function
  6. Soft function
  7. Final resummed differential cross section
  8. Numerical Discussion
  9. Scale choices and uncertainties
  10. Resummed cross sections
  11. Combined s and t channel cross sections
  12. Conclusion
  13. Relevant anomalous dimensions and matching coefficients
  14. Calculation of the soft functions

Figures (4)

  • Figure 1: The LO Feynman diagram of the t-channel single top production.
  • Figure 2: Non-vanishing diagrams contributing to the soft function at NLO. The contribution from the left and right diagrams are denoted as $S_{bt}$ and $S_{tt}$, respectively.
  • Figure 3: The variations of $H_{up}(\mu_{h,up})$ and $H_{dn}(\mu_{h,dn})$ with $\mu_{h,up}$ and $\mu_{h,dn}$, respectively.
  • Figure 4: The variations of $J(\mu_{j})$ and $S(\mu_{s})$ with $\mu_{j}$ and $\mu_{s}$, respectively.