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Electroweak corrections to Z + 2 jets production at the LHC

Ansgar Denner, Lars Hofer, Andreas Scharf, Sandro Uccirati

TL;DR

This paper computes the complete electroweak radiative corrections at NLO for pp to ZZ + 2 jets with leptonic Z decays, using Recola for amplitude generation and Collier for tensor integrals. The calculation employs a complex-mass scheme for resonances and adheres to a G_mu–based definition of the electromagnetic coupling, addressing both EW corrections to LO QCD diagrams and QCD corrections to LO EW interferences. The results show modest corrections for inclusive cross sections (about a few percent) but large negative corrections in high-energy tails due to Sudakov logarithms, with up to ~20% suppression in appropriate kinematic regions. The work demonstrates the practicality of automated EW NLO calculations for multi-jet final states and provides precise SM background predictions relevant to Higgs physics and beyond-Standard-Model searches at the LHC.

Abstract

We present results for the electroweak radiative corrections to the production of a leptonically decaying Z boson in association with two jets at the LHC. Tree-level and one-loop amplitudes have been obtained with the computer code Recola for the recursive generation of tree-level and one-loop amplitudes in the Standard Model. The one-loop integrals have been calculated with the tensor-integral library Collier. The electroweak corrections turn out to be small for inclusive cross sections but can become large in tails of distributions.

Electroweak corrections to Z + 2 jets production at the LHC

TL;DR

This paper computes the complete electroweak radiative corrections at NLO for pp to ZZ + 2 jets with leptonic Z decays, using Recola for amplitude generation and Collier for tensor integrals. The calculation employs a complex-mass scheme for resonances and adheres to a G_mu–based definition of the electromagnetic coupling, addressing both EW corrections to LO QCD diagrams and QCD corrections to LO EW interferences. The results show modest corrections for inclusive cross sections (about a few percent) but large negative corrections in high-energy tails due to Sudakov logarithms, with up to ~20% suppression in appropriate kinematic regions. The work demonstrates the practicality of automated EW NLO calculations for multi-jet final states and provides precise SM background predictions relevant to Higgs physics and beyond-Standard-Model searches at the LHC.

Abstract

We present results for the electroweak radiative corrections to the production of a leptonically decaying Z boson in association with two jets at the LHC. Tree-level and one-loop amplitudes have been obtained with the computer code Recola for the recursive generation of tree-level and one-loop amplitudes in the Standard Model. The one-loop integrals have been calculated with the tensor-integral library Collier. The electroweak corrections turn out to be small for inclusive cross sections but can become large in tails of distributions.

Paper Structure

This paper contains 10 sections, 9 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Collier, a Fortran library for tensor one-loop integrals
  3. $\mathrm{Z}$Z$+2\,$jets production at the LHC
  4. Leading-order contributions
  5. Setup of NLO calculation
  6. Virtual corrections
  7. Real corrections
  8. Implementation
  9. Numerical results
  10. Conclusions

Figures (3)

  • Figure 1: From left to right: Sample tree diagrams for the QCD contributions to $q$q$_i\,\mathrm{g}$g$\to q$q$_i\,\mathrm{g}$g$\,{l$l$^+}\,{l$l$^-}$ and to $q$q$_i\,\bar{q$q$}_i\to q$q$_j\,\bar{q$q$}_j\,{l$l$^+}\,{l$l$^-}$, and the EW contributions to $q$q$_i\,\bar{q$q$}_j\to q$q$'_i\,\bar{q$q$}_j'\,{l$l$^+}\,{l$l$^-}$.
  • Figure 2: Box diagram involving potentially resonant $\mathrm{Z}$Z$$-boson propagators (left) and hexagon diagram involving a 6-point tensor integral of rank 4 (right).
  • Figure 3: Distributions of the transverse momenta of the harder jet ${\mathrm{j}$j$_1}$ (left) and the negatively charged lepton ${{l$l$^-}}$ (right) at the $8\,\mathrm{TeV}$ LHC at LO (black). The central panels show the relative contributions of gluonic (red), four-quark (blue) and bottom (magenta, dashed) channels. In the lower panels we show the total relative corrections (black) from ${\@fontswitch\mathcal{O}}(\alpha_{\mathrm{s}}^2\alpha^3)$ contributions, the included real photonic (red) and real gluonic (blue) corrections together with the statistical error (green, dashed).