Local existence of the Borel transform in euclidean massless Φ 4 4

Abstract

We extend the methods of [1] to prove large order estimates on the renormalized Feynman amplitudes of massless Φ44 euclidean field theory, at non-exceptional momenta. The Borel transform of the perturbative series is analytic in a disk centered at the origin of the complex plane. This result is a step towards the rigorous investigation of the infra-red singularities in the Borel plane, for theories containing massless particles, like the gauge theories.