SciPost Physics

SciPost Phys. 11, 020 (2021) · published 3 August 2021

• doi: 10.21468/SciPostPhys.11.2.020
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

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.

• Shastry et al., Higgs–Higgs scattering and the (non-)existence of the Higgsonium
  Eur. Phys. J. C 83, 713 (2023) [Crossref]
• Fariborz et al., Chiral nonet mixing in $$\pi \eta $$ scattering
  Eur. Phys. J. C 82, 1133 (2022) [Crossref]
• Asiáin et al., Introducing tools to test Higgs boson interactions via WW scattering: One-loop calculations and renormalization in the Higgs effective field theory
  Phys. Rev. D 105, 015009 (2022) [Crossref]
• Delgado et al., Production of two, three, and four Higgs bosons: where SMEFT and HEFT depart
  J. High Energ. Phys. 2024, 37 (2024) [Crossref]
• Gómez-Ambrosio et al., Distinguishing electroweak EFTs with WLWL→n×h
  Phys. Rev. D 106, 053004 (2022) [Crossref]
• Cao et al., Roy equation analyses of ππ scatterings at unphysical pion masses
  Phys. Rev. D 108, 034009 (2023) [Crossref]
• Di Luzio et al., Axion-pion thermalization rate in unitarized NLO chiral perturbation theory
  Phys. Rev. D 108, 035025 (2023) [Crossref]
• Wang et al., Analysis on the composite nature of the light scalar mesons f0(980) and a0(980)
  Phys. Rev. D 105, 074016 (2022) [Crossref]
• Rothkopf et al., Unitarizing infinite-range forces: Graviton-graviton scattering, the graviball, and Coulomb scattering
  EPJ Web Conf. 274, 08011 (2022) [Crossref]
• Blas et al., Unitarization of infinite-range forces: graviton-graviton scattering
  J. High Energ. Phys. 2022, 266 (2022) [Crossref]
• Asiáin et al., Introducing tools to test Higgs boson interactions via WW scattering. II. The coupled-channel formalism and scalar resonances
  Phys. Rev. D 107, 115005 (2023) [Crossref]