  Building on our recent derivation of the Ward-Schwinger-Dyson equations for
the cubic interaction model, we present here the first steps of their resurgent
analysis. In our derivation of the WSD equations, we made sure that they had
the properties of compatibility with the renormalisation group equations and
independence from a regularisation procedure which was known to allow for the
comparable studies in the Wess-Zumino model. The interactions between the
transseries terms for the anomalous dimensions of the field and the vertex is
at the origin of unexpected features, for which the effect of higher order
corrections is not precisely known at this stage: we are only at the beginning
of the journey to use resurgent methods to decipher non-perturbative effects in
quantum field theory.
