  In this paper we prove global well-posedness and modified scattering for the
massive Maxwell-Klein-Gordon equation in the Coulomb gauge on
$\mathbb{R}^{1+d}$ $(d \geq 4)$ for data with small critical Sobolev norm. This
extends to the general case $ m^2 > 0 $ the results of Krieger-Sterbenz-Tataru
($d=4,5 $) and Rodnianski-Tao ($ d \geq 6 $), who considered the case $ m=0$.
  We proceed by generalizing the global parametrix construction for the
covariant wave operator and the functional framework from the massless case to
the Klein-Gordon setting. The equation exhibits a trilinear cancelation
structure identified by Machedon-Sterbenz. To treat it one needs sharp $ L^2 $
null form bounds, which we prove by estimating renormalized solutions in null
frames spaces similar to the ones considered by Bejenaru-Herr. To overcome
logarithmic divergences we rely on an embedding property of $ \Box^{-1} $ in
conjunction with endpoint Strichartz estimates in Lorentz spaces.
