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

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.

Revised version, 47 pages in SciPost format, with 13 captioned figures

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Cited by in corpus (13)

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• Introducing tools to test Higgs interactions via $WW$ scattering I: one-loop calculations and renormalization in the HEFT
• Analysis on the composite nature of the light scalar mesons $f_0(980)$ and $a_0(980)$
• The QCD Axion: Some Like It Hot
• Spinless mesons and glueballs mixing patterns in SU(3) flavor limit
• Chiral Nonet Mixing in $\pi \eta$ Scattering
• Introducing tools to test Higgs interactions via $WW$ scattering II: the coupled channel formalism and scalar resonances
• Unitarity and Unitarization
• Unitarizing infinite-range forces: Graviton-graviton scattering, the graviball, and Coulomb scattering
• $N_C$ evolution of the light meson resonances
• Precision dispersive approaches versus unitarized Chiral Perturbation Theory for the lightest scalar resonances $\sigma /f_0(500)$ and $\kappa /K_0^{\ast }(700)$
• Assessment of systematic theory uncertainties in IAM unitarization