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Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC

W. J. Stirling, E. Vryonidou

TL;DR

This paper investigates next-to-leading order electroweak corrections to Standard Model 2→2 processes at the LHC, focusing on Sudakov double logarithms and Bloch-Nordsieck violations. It combines analytic leading-log results for real and virtual electroweak corrections with hadronic-level results for γ/Z+jet, comparing eikonal approximations to full 2→3 matrix elements with MCFM. The study finds substantial partial cancellation between virtual DLs and real soft emission, especially for the γ/Z ratio, but BN-violating effects remain due to initial-state W emission and phase-space cuts. It also discusses BN-violating contributions in QCD dijet and purely electroweak processes like W+Z and W+H, highlighting that full beyond-DL accuracy requires including real emissions with experimental cuts. Overall, the work clarifies when electroweak BN violations impact inclusive observables at the LHC and emphasizes the need for complete calculations beyond the double-log approximation.

Abstract

We consider the effect of next-to-leading order (NLO) electroweak corrections to Standard Model 2-to-2 processes, taking into account the potentially large double logarithms originating from both real and virtual corrections. A study of the leading Sudakov logarithms is presented and Bloch-Nordsieck (BN) violations are discussed for processes at the CERN Large Hadron Collider. In particular, we focus on the processes Z/photon+jet and also the ratio of Z to photon production. This ratio is known to be insensitive to NLO QCD corrections but this is not expected to be the case for the electroweak corrections. We also comment on the effect of electroweak corrections and the presence of BN violation for QCD processes, in particular dijet production, and also for purely electroweak processes such as W + H and W + Z associated production.

Electroweak corrections and Bloch-Nordsieck violations in 2-to-2 processes at the LHC

TL;DR

This paper investigates next-to-leading order electroweak corrections to Standard Model 2→2 processes at the LHC, focusing on Sudakov double logarithms and Bloch-Nordsieck violations. It combines analytic leading-log results for real and virtual electroweak corrections with hadronic-level results for γ/Z+jet, comparing eikonal approximations to full 2→3 matrix elements with MCFM. The study finds substantial partial cancellation between virtual DLs and real soft emission, especially for the γ/Z ratio, but BN-violating effects remain due to initial-state W emission and phase-space cuts. It also discusses BN-violating contributions in QCD dijet and purely electroweak processes like W+Z and W+H, highlighting that full beyond-DL accuracy requires including real emissions with experimental cuts. Overall, the work clarifies when electroweak BN violations impact inclusive observables at the LHC and emphasizes the need for complete calculations beyond the double-log approximation.

Abstract

We consider the effect of next-to-leading order (NLO) electroweak corrections to Standard Model 2-to-2 processes, taking into account the potentially large double logarithms originating from both real and virtual corrections. A study of the leading Sudakov logarithms is presented and Bloch-Nordsieck (BN) violations are discussed for processes at the CERN Large Hadron Collider. In particular, we focus on the processes Z/photon+jet and also the ratio of Z to photon production. This ratio is known to be insensitive to NLO QCD corrections but this is not expected to be the case for the electroweak corrections. We also comment on the effect of electroweak corrections and the presence of BN violation for QCD processes, in particular dijet production, and also for purely electroweak processes such as W + H and W + Z associated production.

Paper Structure

This paper contains 16 sections, 21 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Sudakov Double Logs in real and virtual corrections
  3. $\gamma/Z$ plus jet production
  4. Partonic results
  5. Initial state: $q\bar{q}$
  6. Initial state: $qg$
  7. Isospin averaging -- cancellation of double logarithms
  8. Hadronic results
  9. Comparison with numerical calculation of full real corrections
  10. The $\gamma$ to $Z$ ratio
  11. Bloch-Nordsieck violations in other hard-scattering processes
  12. QCD dijet production
  13. Electroweak processes
  14. W $+$ Z production
  15. W $+$ H production
  16. ...and 1 more sections

Figures (11)

  • Figure 1: Feynman diagrams for $u(p_1)\bar{u}(p_2)\rightarrow A(p_3) g(p_4) Z(p_5)$.
  • Figure 2: Feynman diagrams for $qg\rightarrow \gamma q$.
  • Figure 3: Relative contribution of single logarithms to the virtual corrections in $\gamma+1$ jet production.
  • Figure 4: Virtual and real electroweak corrections to $\gamma+1$ jet production at 14 TeV.
  • Figure 5: Virtual and real electroweak corrections to $Z+1$ jet production at 14 TeV.
  • ...and 6 more figures