Next-to-leading-order electroweak corrections to the production of four charged leptons at the LHC

TL;DR

This work delivers a complete NLO electroweak treatment of ZZ production with fully off-shell Z decays to four charged leptons at 13 TeV, using the complex-mass scheme to preserve gauge invariance across resonant and non-resonant regions. By separating virtual and real corrections into purely weak and photonic parts and handling collinear-safe and collinear-unsafe observables, the authors provide precise integrated and differential predictions for two realistic experimental setups, including photon-induced channels. The main findings show ~−5% overall EW corrections from qq̄ channels, with weak corrections rising to tens of percent in high-energy tails, while photonic corrections generate radiative tails near thresholds; interference effects between equal-flavour leptons can reach ~10% in off-shell regions. The results, implemented in a Monte Carlo program, are poised to enhance ZZ background modeling and can be combined with advanced QCD calculations to attain percent-level accuracy for LHC analyses, especially in Higgs studies where off-shell effects are crucial.

Abstract

We present a state-of-the-art calculation of the next-to-leading-order electroweak corrections to ZZ production, including the leptonic decays of the Z bosons into $μ^+μ^-\mathrm{e}^+\mathrm{e}^-$ or $μ^+μ^-μ^+μ^-$ final states. We use complete leading-order and next-to-leading-order matrix elements for four-lepton production, including contributions of virtual photons and all off-shell effects of Z bosons, where the finite Z-boson width is taken into account using the complex-mass scheme. The matrix elements are implemented into Monte Carlo programs allowing for the evaluation of arbitrary differential distributions. We present integrated and differential cross sections for the LHC at 13 TeV both for an inclusive setup where only lepton identification cuts are applied, and for a setup motivated by Higgs-boson analyses in the four-lepton decay channel. The electroweak corrections are divided into photonic and purely weak contributions. The former show the well-known pronounced tails near kinematical thresholds and resonances; the latter are generically at the level of $\sim-5\%$ and reach several $-10\%$ in the high-energy tails of distributions. Comparing the results for $μ^+μ^-\mathrm{e}^+\mathrm{e}^-$ and $μ^+μ^-μ^+μ^-$ final states, we find significant differences mainly in distributions that are sensitive to the $μ^+μ^-$ pairing in the $μ^+μ^-μ^+μ^-$ final state. Differences between $μ^+μ^-\mathrm{e}^+\mathrm{e}^-$ and $μ^+μ^-μ^+μ^-$ channels due to interferences of equal-flavour leptons in the final state can reach up to $10\%$ in off-shell-sensitive regions. Contributions induced by incoming photons, i.e. photon-photon and quark-photon channels, are included, but turn out to be phenomenologically unimportant.

Figures (19)

• Figure 1: Sample tree-level diagrams contributing at $O(\alpha^4)$. The dominant $\bar{q} q$ channel (a,b) defines the LO contribution, while the photon-induced $\gamma\gamma$ channel (c) is counted as a correction.
• Figure 2: Sample diagrams for the virtual EW corrections. Diagram types (a)--(d) are obtained by photon and Z-boson insertions between the fermion lines of the tree-level diagrams in Fig. \ref{['fig:born']}(a). The remaining diagrams may involve couplings (f)--(i) or corrections to vertices (e) that are not present at LO.
• Figure 3: Illustration of the splitting of EW corrections into purely weak (a) and photonic (b)--(d) contributions for the diagram type shown in Fig. \ref{['fig:virtdiagrams']}(d).
• Figure 4: Illustration of real photon radiation off the final-state leptons and off the initial-state quarks.
• Figure 5: Photon-induced contributions with the two initial-state splittings $\gamma \to \bar{q}+q^*$ and $\bar{q} \to \bar{q} + \gamma^\star$. The star indicates the particle belonging to the initial state of the reduced Born matrix element.