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 effective field theory (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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>W</a:mi></a:math> 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.