Electroweak corrections to lepton pair production in association with two hard jets at the LHC

TL;DR

This work delivers a complete NLO calculation of electroweak corrections to the process ${\rm pp}\to {\rm j}{\rm j}{\rm j}\ell^-\ell^+$, incorporating all off-shell effects and QCD contributions at ${\cal O}(\alpha_s^2\alpha^3)$ using Recola and Collier. It combines a thorough LO framework with a ZZ-pole approximation and analyzes standard as well as vector-boson-fusion cuts, showing percent-level corrections to total cross sections but significant enhancements of high-energy tail distortions due to electroweak Sudakov logarithms. The results highlight the importance of including EW effects for precise SM background modeling in multi-jet, multi-lepton final states at the LHC, particularly in high-$p_T$ and high-$M$ regions where corrections can reach tens of percent. Overall, the paper demonstrates the capabilities of modern automated tools for multiparticle NLO calculations and provides detailed guidance for phenomenology and experimental analyses at 13 TeV and beyond.

Abstract

We compute the next-to-leading order corrections of $O(α_s^2α^3)$ to the hadronic production of two oppositely charged leptons and two hard jets, $p p \to j j l^- l^+$, using Recola and Collier. We include electroweak and QCD corrections at the given order and all off-shell effects. We provide detailed predictions for the LHC operating at 13 TeV and obtain per-cent-level corrections for the total cross section. For differential distributions we find significant non-uniform distortions in high-energy tails at the level of several ten per cent due to electroweak Sudakov logarithms and deformations at the level of a few per cent for angular variables.

Figures (9)

• Figure 1: Sample tree diagrams for the QCD contributions to $q$q$_i\,{\rm g}$ g$\to q$q$_i\,{\rm g}$ g$\,\ell$ℓ$^-\,\ell$ℓ$^+$, $q$q$_i\,{q$q$}_j\to q$q$_i\,q$q$_j\,\ell$ℓ$^-\,\ell$ℓ$^+$, and $q$q$_i\,\bar{q$q$}_i\to q$q$_j\,\bar{q$q$}_j\,\ell$ℓ$^-\,\ell$ℓ$^+$ (first line) the EW contributions to $q$q$_i\,{q$q$}_j\to q$q$_i\,q$q$_j\,\ell$ℓ$^-\,\ell$ℓ$^+$, $q$q$_i\,\bar{q$q$}_i\to q$q$_j\,\bar{q$q$}_j\,\ell$ℓ$^-\,\ell$ℓ$^+$ and $q$q$_i\,\bar{q$q$}_j\to q$q$'_i\,\bar{q$q$}_j'\,\ell$ℓ$^-\,\ell$ℓ$^+$ (second line) and the contributions to ${\rm g}$ g$\,\gamma\to\bar{q$q$_i}\,q$q$_i\,\ell$ℓ$^-\,\ell$ℓ$^+$, $q$q$_i\,\gamma\to q$q$_i\,{\rm g}$ g$\,\ell$ℓ$^-\,\ell$ℓ$^+$ and $\gamma\,\gamma\to q$q$_i\,\bar{q$q$_i}\,\ell$ℓ$^-\,\ell$ℓ$^+$.
• Figure 2: Sample tree diagrams for interferences of QCD and EW diagrams.
• Figure 3: Distributions of the transverse momentum of the harder jet ${\rm j_1}$, the di-jet invariant mass $M_{{\rm j}$ j${\rm j}$ j$}$, the transverse momenta of the negatively charged lepton $\ell$ℓ$^-$ and the lepton pair $\ell$ℓ$^-\ell$ℓ$^+$, the scalar sum of all transverse momenta, and the relative azimuthal angle between the leptons at the $13\,{\rm TeV}$ LHC for basic cuts. The upper panels show the corresponding distributions, the middle ones the composition of the cross section and the lower ones the contributions of the EW diagrams. Further details are described in the text.
• Figure 4: Distributions of the transverse momentum of the harder jet ${\rm j_1}$, the di-jet invariant mass $M_{{\rm j}$ j${\rm j}$ j$}$, the transverse momenta of the negatively charged lepton $\ell$ℓ$^-$ and the lepton pair $\ell$ℓ$^-\ell$ℓ$^+$, the scalar sum of all transverse momenta, and the relative azimuthal angle between the leptons at $13 \,{\rm TeV}$ LHC for the VBF setup. The upper panels show the corresponding distributions, the middle ones the composition of the cross section and the lower ones the contributions of the EW diagrams. Further details are described in the text.
• Figure 5: Sample diagrams for virtual corrections: hexagon of ${\cal O}(g_{{\rm s}}^2 e^4)$ for $q_i\,{\rm g}$ g$\to q_i\,{\rm g}$ g$\,\ell$ℓ$^-\,\ell$ℓ$^+$ (upper left), pentagon of ${\cal O}(g_{{\rm s}}^4 e^2)$ for $q_i\,q_j\to q_i\,q_j\,\ell$ℓ$^-\,\ell$ℓ$^+$ (upper right), hexagon of ${\cal O}(g_{{\rm s}}^2 e^4)$ for $q_i\,q_j\to q_i\,q_j\,\ell$ℓ$^-\,\ell$ℓ$^+$ (lower left), hexagon of ${\cal O}(g_{{\rm s}}^2 e^4)$ for $q_i\,q_j\to q_i^\prime \,q_j^\prime\,\ell$ℓ$^-\,\ell$ℓ$^+$ (lower right).