At the one loop level, we make use of the renormalizable Abelian quantum field theory model of Kroll, Lee, and Zumino (KLZ) in order to compute the vertex corrections to the tree‐level, Vector Meson Dominance (VMD) electromagnetic pion form factor. This result, together with the one‐loop vacuum polarization contribution, implies an electromagnetic pion form factor which is in outstanding agreement with data in the whole range of accessible momentum transfers in the space‐like region. The time‐like form factor, which reproduces the Gounaris‐Sakurai formula at and near the rho‐meson peak, remains unaffected by the vertex correction at order O(g2). We also use the KLZ model to compute the pion scalar radius at the one loop level, finding 〈rπ2〉S = 0.40 fm2. From this value we find for the low energy constant of chiral perturbation theory l4 = 3.4.