Positivity Constraints in Flat-Space QFT

Abstract

Low energy effective field theories (EFTs) find applications in several areas of physics. Using basic and well-accepted principles of quantum field theory---unitarity, causality, locality, etc., it is possible to constrain the space of unknown Wilson coefficients appearing in the EFTs. We try to study the positivity constraints on the Wilson coefficients in the Euler--Heisenberg theory in the presence of a light fermion by using unitarity of the $S$-matrix and analyticity of the scattering amplitudes. Naïvely, the procedure fails and the previously obtained constraints no longer hold true. However, this is just an artefact of the analysis and the constraints are not affected. Then we try to use the same techniques to find constraints in an effective field theory containing only gluons. We find that since the one-loop amplitude diverges in the forward limit, the previously obtained constrained no longer seem to be true. The problem this time is different from the one in the theory containing photons, and it is unclear if it can be resolved somehow.