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

TL;DR

This paper systematically analyzes the uncertainties in the Inverse Amplitude Method (IAM) used for unitarizing Effective Field Theories, comparing its applications in hadron and electroweak sectors, and proposes modifications to improve its reliability.

Contribution

It provides a detailed quantification of the uncertainties in the IAM and offers a method to modify it when zeroes in the partial wave amplitude are near resonances.

Findings

The relative uncertainty of IAM at the first resonance is comparable to the initial EFT uncertainty near threshold.

Proper checks for zeroes in partial wave amplitudes are essential for reliable IAM application.

Proposed modifications improve IAM's accuracy when zeroes are near resonance regions.

Abstract

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.