[Paper Review] Vector-boson pair production at the LHC: Electroweak corrections in HERWIG++

Stefan Gieseke, Tobias Kasprzik+1 more|arXiv (Cornell University)|Oct 10, 2013

Particle physics theoretical and experimental studies16 references3 citations

TL;DR

This paper presents a practical method to implement next-to-leading-order (NLO) electroweak (EW) corrections in vector-boson pair production at the LHC using the HERWIG++ Monte Carlo event generator, combining them with QCD corrections and parton showers. The approach enables accurate, a posteriori inclusion of EW effects in any event sample by leveraging four-lepton kinematics and assuming factorization of QCD and EW corrections, with results showing significant distortions in angular distributions at high energies—critical for avoiding misinterpretation as new physics.

ABSTRACT

Vector-boson pair production is of great phenomenological importance at the LHC. These processes will help to validate the Standard Model at highest energies, and they may also open the door for the discovery of new physics potentially showing up in subtle modifications of the non-abelian structure of weak interactions. In this letter, we review the status of the corresponding theory predictions, focusing on the higher-order electroweak corrections. We present a NLO analysis of electroweak corrections to W-pair, W$^+$Z and Z-pair production at the LHC, including all mass effects as well as leptonic decays. Contributions of photon-induced processes and massive-boson radiation are also discussed. The electroweak corrections are implemented in the HERWIG++ Monte Carlo generator, where they are combined with QCD corrections. We also propose a simple and straight-forward method allowing for an \emph{a posteriori} implementation of electroweak corrections to vector-boson pair production in any Monte Carlo event sample.

Motivation & Objective

• To address the lack of NLO electroweak corrections in phenomenological studies of Z-pair and WZ production at the LHC, particularly including full mass effects and leptonic decays.
• To provide a reliable, flexible framework for incorporating electroweak corrections into existing Monte Carlo event samples without requiring re-simulation.
• To demonstrate that photon-induced and weak corrections significantly distort angular distributions at high invariant masses, potentially mimicking anomalous couplings.
• To validate the method using HERWIG++ event samples, ensuring consistency with direct NLO calculations.

Proposed method

• A factorization assumption is made between QCD and electroweak corrections, where the combined cross section is modeled as a product of QCD-corrected partonic cross sections and an EW correction factor $ K_{q\bar{q}'}^{V_1V_2} $.
• The Mandelstam variables $ \hat{s} $ and $ \hat{t} $ are reconstructed from the final-state lepton four-momenta by boosting into the four-lepton center-of-mass frame and defining the effective scattering axis from the initial-state quark directions.
• The effective scattering angle $ \theta^* $ is computed from the vector boson momentum direction relative to the scattering axis, enabling $ \hat{t} $ reconstruction under on-shell kinematics.
• The method is designed for a posteriori application: it requires only final-state lepton momenta and initial-state quark flavor information, making it compatible with any existing Monte Carlo sample.
• A kinematic cut $ \left|\sum \mathbf{p}_{\mathrm{T},l}^{i}\right| < 0.3 \sum |\mathbf{p}_{\mathrm{T},l}^{i}| $ is applied to ensure back-to-back vector bosons and avoid large QCD $ K $-factors.
• The implementation is validated by comparing HERWIG++ results with direct NLO calculations, showing good agreement across differential distributions for ZZ, WW, and WZ production.

Experimental results

Research questions

• RQ1 How do NLO electroweak corrections affect the differential cross sections and angular distributions in vector-boson pair production at the LHC?
• RQ2 To what extent do photon-induced processes distort high-energy observables, and how sensitive are they to uncertainties in the proton's photon PDF?
• RQ3 Can electroweak corrections be reliably applied a posteriori to existing Monte Carlo event samples without re-simulation?
• RQ4 What is the impact of massive-boson radiation and weak corrections on the kinematic distributions of W-pair, WZ, and Z-pair final states?
• RQ5 How do full mass effects and leptonic decays modify the interplay between QCD and electroweak corrections in V-pair production?

Key findings

• Electroweak corrections induce large, logarithmically enhanced negative corrections to the W-pair invariant-mass distribution, while photon-induced processes (γγ and γq) provide positive contributions that counteract this effect.
• At high invariant masses ($ M_{\mathrm{WW}} > 1 $ TeV), the interplay between EW and photon-induced corrections leads to a dramatic distortion of the W-pair rapidity gap distribution, with strong suppression at small gaps and enhancement at large gaps.
• For Z-pair production, large negative electroweak corrections dominate at high transverse momenta, significantly reducing cross sections and potentially affecting signal-background separation.
• The photon-induced contributions suffer from a ±50% systematic uncertainty at 1 TeV due to uncertainties in the proton's photon PDF, highlighting the need for improved PDF determinations.
• The proposed a posteriori method successfully reproduces direct NLO results in HERWIG++ samples, validating its reliability for phenomenological applications.
• The method enables consistent inclusion of EW corrections in any Monte Carlo sample with accessible lepton four-momenta and initial-state quark information, offering a scalable solution for high-precision LHC analyses.