Electroweak precision observables at NLL order in the SMEFT

Abstract

Electroweak precision observables (EWPO) remain among the most powerful indirect probes of physics beyond the Standard Model (BSM), and future $e^+ e^-$ colliders are expected to substantially enhance their sensitivity. Within the framework of the Standard Model Effective Field Theory (SMEFT), we show how EWPO predictions can be systematically improved to next-to-leading-logarithmic (NLL) accuracy by combining fixed-order tree-level and one-loop matching with two- and one-loop renormalization-group evolution. We derive NLL expressions that encode the full dependence on all 210 independent Wilson coefficients and illustrate their impact through fits to both current and projected collider measurements. This work provides a basis for global SMEFT analyses at NLL precision, thereby maximizing the indirect reach to BSM physics through EWPO measurements. The phenomenological relevance of this framework is illustrated explicitly in both the custodial Randall-Sundrum model and a custodial composite Higgs model.