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Effective Field Theories (EFTs) constructed as derivative expansions inpowers of momentum, in the spirit of Chiral Perturbation Theory (ChPT), are acontrollable approximation to strong dynamics as long as the energy of theinteracting particles remains small, as they do not respect exact elasticunitarity. This limits their predictive power towards new physics at a higherscale if small separations from the Standard Model are found at the LHC orelsewhere. Unitarized chiral perturbation theory techniques have been devisedto extend the reach of the EFT to regimes where partial waves are saturatingunitarity, but their uncertainties have hitherto not been addressed thoroughly.Here we take one of the best known of them, the Inverse Amplitude Method (IAM),and carefully following its derivation, we quantify the uncertainty introducedat each step. We compare its hadron ChPT and its electroweak sector Higgs EFTapplications. We find that the relative theoretical uncertainty of the IAM atthe mass of the first resonance encountered in a partial-wave is of the sameorder in the counting as the starting uncertainty of the EFT at near-thresholdenergies, so that its unitarized extension should \textit{a priori} be expectedto be reasonably successful. This is so provided a check for zeroes of thepartial wave amplitude is carried out and, if they appear near the resonanceregion, we show how to modify adequately the IAM to take them into account.

Systematizing and addressing theory uncertainties of unitarization with the Inverse Amplitude Method