### Speaker

### Description

Effective Field Theories (EFTs) organized as derivative expansions are controllable 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.

This is exemplified by ChPT: though nominally the EFT could be extended to a sizeable value below 4 pi F (about 1.2 GeV) the p-wave expansion stops converging little above threshold because of the presence of the strong rho(770) resonance.

Unitarized chiral perturbation theory extends the EFT reach to regimes where partial waves saturate unitarity, but its systematic uncertainty is unknown.

We address this shortcoming for the Inverse Amplitude Method (IAM), and carefully following its dispersive 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 a priori be expected to be reasonably successful.

A prerequisite is to provide a check for zeroes of the partial-wave amplitude before applying the method and, if any appear near the resonance region, we show how to adequately modify the IAM to take them into account.

Thus, if the LHC experiments were to measure a separation from the SM of WLWL or hh scattering encoded in HEFT coefficients, the IAM could be used to extrapolate to higher energies with a measure of theoretical control.