Impact of New Physics on Momentum-Dependent Particle Widths and Propagators

We investigate the impact of momentum-dependent particle widths and propagators on gauge and Higgs bosons and the top quark within the Standard Model (SM) and its SMEFT extensions near thresholds. By incorporating self-energy corrections via Dyson resummation, we quantify deviations from the fixed-width approximation and assess their implications for collider observables. While effects on the Higgs boson are negligible and the $W$ boson shows percent-level deviations in reconstructed transverse mass distributions, the top quark exhibits significant sensitivity near its mass threshold. Future lepton colliders, e.g., electron-positron machines or muon colliders, can offer sensitivity to these effects, enabling constraints on SMEFT Wilson coefficients. We perform a representative case study for the precision frontier available with a staged future muon collider. Our results highlight that momentum dependencies can provide additional sensitivity at precision-era experiments, enhancing the potential for discovering new physics there.