Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Approximate N$^2$LO and N$^3$LO QCD Predictions for $tW$ Production

Jia-Le Ding, Hai Tao Li, Jian Wang

Abstract

We report a calculation of approximate next-to-next-to-leading-order (N$^2$LO) and next-to-N$^2$LO (N$^3$LO) QCD corrections to associated $tW$ production at the LHC, which constitute the dominant contributions to full perturbative predictions. The approximate N$^2$LO corrections consist of the large logarithmic terms $\ln^n (1-Q^2/\hat{s})$ (with $\sqrt{\hat{s}}$ being the partonic center-of-mass energy and $Q$ the invariant mass of the $tW$ system) and the terms proportional to $δ(1-Q^2/\hat{s})$ at $\mathcal{O}(α_s^2)$, which are obtained by utilizing the newly obtained two-loop hard and soft functions. The approximate N$^3$LO corrections further include the large logarithms at $\mathcal{O}(α_s^3)$ by using renormalization group evolution equations and the three-loop soft anomalous dimension, while the $δ(1-Q^2/\hat{s})$ term is only partially accurate at this order. Numerical evaluation reveals that they increase the NLO cross section by more than $10\%$. The inclusion of these higher-order corrections leads to improved agreement with the experimental data at the LHC, resulting in a direct determination of the CKM matrix element $|V_{tb}|=0.99\pm 0.03({\rm exp.})\pm 0.03({\rm theo.})$ without assuming unitarity of the matrix.

Approximate N$^2$LO and N$^3$LO QCD Predictions for $tW$ Production

Abstract

We report a calculation of approximate next-to-next-to-leading-order (NLO) and next-to-NLO (NLO) QCD corrections to associated production at the LHC, which constitute the dominant contributions to full perturbative predictions. The approximate NLO corrections consist of the large logarithmic terms (with being the partonic center-of-mass energy and the invariant mass of the system) and the terms proportional to at , which are obtained by utilizing the newly obtained two-loop hard and soft functions. The approximate NLO corrections further include the large logarithms at by using renormalization group evolution equations and the three-loop soft anomalous dimension, while the term is only partially accurate at this order. Numerical evaluation reveals that they increase the NLO cross section by more than . The inclusion of these higher-order corrections leads to improved agreement with the experimental data at the LHC, resulting in a direct determination of the CKM matrix element without assuming unitarity of the matrix.

Paper Structure

This paper contains 5 sections, 20 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Factorization formalism
  3. Numerical results
  4. Conclusion
  5. Anomalous Dimensions

Figures (4)

  • Figure 1: LO Feynman diagrams for $tW^-$ production.
  • Figure 2: Scale dependence of the inclusive $tW^-/\bar{t} W^+$ cross section with $\mu_r=\mu_f=\mu$ at the 14 TeV LHC. Both panels display exact LO (red) and NLO (black) results. The top panel also shows the LP predictions at NLO$_{\rm LP}$ (yellow), N$^2$LO$_{\rm LP}$ (blue) and N$^3$LO$_{\rm LP}$ (green). The bottom panel also shows the approximate N$^2$LO (blue) and N$^3$LO (green) results.
  • Figure 3: Comparison between measured cross sections for $tW^-/\bar{t} W^+$ production at the LHC ATLAS:2012bqtATLAS:2020cwjATLAS:2024pppCMS:2012pxdCMS:2014futCMS:2022ytwCMS:2024okz and theoretical predictions. The bands in theoretical predictions denote the scale uncertainties.
  • Figure 4: Top quark $p_T$ distribution (left) and rapidity distribution (right) at the 14 TeV LHC. The top panels show results at different perturbative orders. The bottom panels show the K-factor as the ratio of the aN$^2$LO (aN$^3$LO) over the NLO results.