Study of weak corrections to Drell-Yan, top-quark pair and dijet Production at high energies with MCFM

TL;DR

This paper implements and analyzes electroweak one-loop corrections in the MCFM Monte Carlo framework for three key LHC processes: Neutral-Current Drell-Yan, top-quark pair production, and di-jet production. It provides both exact one-loop weak corrections and Sudakov-logarithm approximations, enabling direct comparison with NLO/NNLO QCD predictions and assessment of approximation validity in high-energy tails. The work validates results against established calculations, explores photon-induced contributions, and examines methods to combine QCD and EW effects, highlighting significant corrections in the high-energy regime and guiding future collider phenomenology. The public MCFM implementation and the detailed Sudakov analyses equip researchers to improve predictions for SM tests and new-physics searches at current and future hadron colliders.

Abstract

Electroweak (EW) corrections can be enhanced at high energies due to the soft or collinear radiation of virtual and real $W$ and $Z$ bosons that result in Sudakov-like corrections of the form $α_W^l\log^n(Q^2/M_{W,Z}^2)$, where $α_W =α/(4π\sin^2θ_W)$ and $n\le 2l-1$. The inclusion of EW corrections in predictions for hadron colliders is therefore especially important when searching for signals of possible new physics in distributions probing the kinematic regime $Q^2 \gg M_V^2$. Next-to-leading order (NLO) EW corrections should also be taken into account when their size ($\mathcal{O}(α)$) is comparable to that of QCD corrections at next-to-next-to-leading order (NNLO) ($\mathcal{O}(α_s^2)$). To this end we have implemented the NLO weak corrections to the Neutral-Current Drell-Yan process, top-quark pair production and di-jet production in the parton-level Monte-Carlo program MCFM. This enables a combined study with the corresponding QCD corrections at NLO and NNLO. We provide both the full NLO weak corrections and their Sudakov approximation since the latter is often used for a fast evaluation of weak effects at high energies and can be extended to higher orders. With both the exact and approximate results at hand, the validity of the Sudakov approximation can be readily quantified

Figures (29)

• Figure 1: Feynman diagrams for the NC DY process at LO.
• Figure 2: Weak vertex corrections of $\mathcal{O}(\alpha)$ to the NC DY process $(V^a=Z,W)$.
• Figure 3: Gauge-boson self-energy correction at ${\cal O}(\alpha)$, where $\hat{\Sigma}_{T}^{V^a\bar{V}^b}$ is the renormalized vector boson self-energy, and $\Gamma_{V^a}$ the width of the gauge boson ($V^a=\gamma,Z)$. The red dot denotes the tree-level coupling to the initial $\mathrm{q\bar{q}}$qq̅$$ pair, $I^{V^a}_{q\bar{q}}$, and $I^{V^b}_{l\bar{l}}$ describes the coupling to the final lepton pair.
• Figure 4: Feynman diagrams for weak one-loop box corrections to the NC DY process ($V^a = Z/W$).
• Figure 5: Feynman diagrams for LO strong $\mathrm{t\bar{t}}$tt̅$$ production at ${\cal O}(\alpha_s^2)$.