EW corrections and Heavy Boson Radiation at a high-energy muon collider

In this work we investigate several phenomenological and technical aspects related to electroweak (EW) corrections at a high-energy muon collider, focusing on direct production processes (no VBF configurations). We study in detail the accuracy of the Sudakov approximation, in particular the Denner-Pozzorini algorithm, comparing it with exact calculations at NLO EW accuracy. We also assess the relevance of resumming EW Sudakov logarithms (EWSL) at 3 and 10 TeV collisions. Furthermore, we scrutinise the impact of additional Heavy Boson Radiation (HBR), namely the weak emission of $W, Z$, and Higgs bosons in inclusive and semi-inclusive configurations. All results are obtained via the fully automated and publicly available code MadGraph5_aMC@NLO.

💡 Research Summary

This paper presents a comprehensive study of electroweak (EW) corrections and heavy boson radiation (HBR) for direct production processes at high‑energy muon colliders operating at √s = 3 TeV and 10 TeV. Using the fully automated MadGraph5_aMC@NLO framework, the authors first describe the implementation of exact next‑to‑leading order EW (NLO EW) calculations, including the treatment of lepton PDFs and initial‑state radiation. They then focus on the Sudakov approximation, specifically the Denner‑Pozzorini (DP) algorithm, and compare two schemes: the original SDK 0 and the refined SDK weak. Detailed comparisons with exact NLO EW results reveal that SDK weak generally outperforms SDK 0 when photons are recombined with charged final‑state particles, but both schemes can fail in kinematic regions where logarithms of the form log²(s/|t|) or log²(s/|u|) become large, or where the leading‑order amplitude is dominated by mass‑suppressed contributions (e.g. μ⁺μ⁻ → Z H H).

The authors then implement a simple exponentiation of EW Sudakov logarithms to achieve next‑to‑leading logarithmic (NLL) resummation, matching this resummed result to the exact NLO EW calculation. They demonstrate that at 10 TeV the resummation is essential: without it, the fixed‑order prediction can become negative or wildly inaccurate, whereas at 3 TeV the fixed‑order result remains reliable.

Finally, the impact of heavy‑boson radiation—real emission of W, Z, and Higgs bosons—is examined in both semi‑inclusive (bosons not recombined) and inclusive (bosons clustered into EW jets) configurations for processes such as μ⁺μ⁻ → t t̄ and μ⁺μ⁻ → W⁺W⁻. While HBR contributions are generally smaller than virtual EW corrections, they become non‑negligible in high‑p_T regions and can partially cancel virtual effects. The study quantifies these effects and shows that, for realistic analyses, both resummed Sudakov logarithms and explicit HBR must be incorporated to obtain physically sensible predictions.

Overall, the work establishes the accuracy limits of the Sudakov approximation, underscores the necessity of logarithmic resummation at multi‑TeV muon colliders, and provides a detailed assessment of heavy‑boson radiation, thereby delivering essential tools for precision phenomenology and new‑physics searches at future muon‑collider experiments.