This paper asks how well a 10 tera‑electronvolt (TeV) lepton collider — in practice a muon collider — could measure the mass of the W boson and the strength of its couplings to quarks (the CKM matrix elements). The authors find that the most common way to make W bosons at 10 TeV is an “effective” photon hitting a lepton and producing a W. They show that the clean leptonic W decays (W→lepton+neutrino) give too few events to beat today’s best W mass measurements. By contrast, hadronic W decays (W→quark+antiquark) offer much higher rates and could improve on the current roughly 10 MeV uncertainty from hadron collider results — but only if the detector measures jets and hadronic energy with very high precision.

To reach these conclusions the authors examined several W production channels at lepton colliders and focused on the dominant one at 10 TeV, namely ℓ+ℓ−→W±νℓ∓. This channel is driven by an effective collision of a photon with a beam lepton (µγ→W±ν). They used the Effective Photon Approximation and simulated events with the MG5_AMC@NLO program. The study compared two detector concepts developed for a muon collider and used one of them (called MAIA) in detail. MAIA is a conventional multipurpose detector with a 5 tesla solenoid, silicon trackers, electromagnetic and hadronic calorimeters, and a muon system.

For the leptonic W decay channel the team tried a template fit to the charged‑lepton energy in the laboratory frame. They applied realistic selections — charged leptons with transverse momentum above 20 GeV and angles inside the detector acceptance (10° to 170°) — and simulated the main reducible backgrounds. The result was that the leptonic channel lacks enough rate at 10 TeV to be competitive with current precision determinations of mW.

The hadronic channel looks more promising because it produces many more W decays into jets. Measuring the W mass from those jets could beat the present ≈10 MeV uncertainty from hadron colliders. The same high‑precision hadronic measurements would also let the collider determine CKM matrix elements directly from W→qq′ decays. Because these decays occur at high momentum transfer (high q2), they avoid the main theoretical bottleneck of low-energy flavor experiments, which is poor knowledge of non‑perturbative hadronic matrix elements. The authors expect especially large improvements for elements involving heavy quarks, for example Vcb, provided the experimental systematics are controlled.