Alexandre Salas-Bernárdez, Felipe J. Llanes-Estrada, Juan Escudero-Pedrosa, Jose Antonio Oller
SciPost Phys. 11, 020 (2021) ·
published 3 August 2021
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Effective Field Theories (EFTs) constructed as derivative expansions in
powers of momentum, in the spirit of Chiral Perturbation Theory (ChPT), are a
controllable approximation to strong dynamics as long as the energy of the
interacting particles remains small, as they do not respect exact elastic
unitarity. This limits their predictive power towards new physics at a higher
scale if small separations from the Standard Model are found at the LHC or
elsewhere. Unitarized chiral perturbation theory techniques have been devised
to extend the reach of the EFT to regimes where partial waves are saturating
unitarity, 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 introduced
at each step. We compare its hadron ChPT and its electroweak sector Higgs EFT
applications. We find that the relative theoretical uncertainty of the IAM at
the mass of the first resonance encountered in a partial-wave is of the same
order in the counting as the starting uncertainty of the EFT at near-threshold
energies, so that its unitarized extension should \textit{a priori} be expected
to be reasonably successful. This is so provided a check for zeroes of the
partial wave amplitude is carried out and, if they appear near the resonance
region, we show how to modify adequately the IAM to take them into account.
