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 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.
Highlights
Inverse Amplitude Method (IAM), their values are taken from Next to Leading Order (NLO) Chiral Perturbation Theory (ChPT), a valid approximation because they are taken with s around zero, where the Effective Field Theories (EFTs) is valid
We will try to quantify the uncertainty in the position of a resonance following Eq (18); and we will exemplify with the vector-isovector resonance in hadron physics except in subsections 4.2 and 4.3 where the mass versus masslessness of the pions/Goldstone bosons in ChPT/Higgs Effective Field Theory (HEFT) respectively, do make a difference due to phase space
It is looking increasingly likely that the LHC will not find new resonances, but it may still have a chance of revealing non-resonant [77] separations from Standard Model cross-sections, in the Electroweak Symmetry Breaking Sector formed by the Higgs scalar boson h and longitudinal electroweak bosons ω
Summary
The LHC is preparing for its High-Luminosity Run (HL-LHC). It is possible that any new physics scale is beyond the reach of the collider and no new particles are found. These are well known to appear in the resonant J = 0,1 ππ phase shifts [1, 2], with the low-energy scalar resonance f0(500) around 500 MeV (the threshold being nearby at 280 MeV); in η → 3π decays [3]; in γγ → π0π0 [4], etc Unitarization techniques such as the Inverse Amplitude Method (IAM) reviewed in this article allow computation of amplitudes at higher energies, at least up to and including the first resonance in each channel, ( often more resonances can be generated like the f0(500) and f0(980) in the isoscalar scalar mesonic sector [5,6,7].) The same method has been deployed for Higgs Effective Field Theory (HEFT) in much recent work. The most powerful unitarization methods are based on dispersion relations, incorporating known analyticity properties of scattering amplitudes These methods solidly extrapolate the low-energy theory to the resonance region; a noteworthy approach among them, which has been broadly used, is the Inverse Amplitude Method 1 (IAM) [15,16,17,18]. A few more details and derivations are left for an appendix
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
