What is the scale of new physics behind the muon <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:math>?
Lukas Allwicher, Luca Di Luzio, Marco Fedele, Federico Mescia, Marco Nardecchia
Abstract
We study the constraints imposed by perturbative unitarity on the new physics interpretation of the muon $g\ensuremath{-}2$ anomaly. Within a Standard Model effective field theory approach, we find that scattering amplitudes sourced by effective operators saturate perturbative unitarity at about 1 PeV. This corresponds to the highest energy scale that needs to be probed in order to resolve the new physics origin of the muon $g\ensuremath{-}2$ anomaly. On the other hand, simplified models (e.g., scalar-fermion Yukawa theories) in which renormalizable couplings are pushed to the boundary of perturbativity still imply new on-shell states below 200 TeV. We finally suggest that the highest new physics scale responsible for the anomalous effect can be reached in nonrenormalizable models at the PeV scale.