Searching for heavy resonances via oblique parameters in non-linear effective frameworks

Within the framework of a general non-linear effective field theory describing the electroweak symmetry breaking, we perform a detailed analysis of the next-to-leading contributions to the electroweak oblique parameters $S$ and $T$ from hypothetical heavy resonance states strongly coupled to Standard Model fields. This work extends our previous results by including parity-odd operators in the effective Lagrangian, contributions from fermionic cuts, and up-to-date experimental constraints. We demonstrate that in strongly-coupled ultraviolet completions satisfying both Weinberg Sum Rules -as is the case in asymptotically free gauge theories- the vector and axial-vector resonance masses are constrained to lie above $10$TeV. Conversely, scenarios allowing for lighter resonances with masses between $2$and $10$TeV necessarily imply a violation of the second Weinberg Sum Rule.