Vector leptoquark pair production in e+e− annihilation

For slowly varying fields on the scale of the lightest mass the logarithm of the vacuum functional of a massive quantum field theory can be expanded in terms of local functionals satisfying a form of the Schrödingerequation, the principal ingredient of which is a regulated functional Laplacian. We extend a previous work to construct the next to leading order terms of the Laplacian for the Schrödinger equation that acts on such local functionals. Like the leading order the next order is completely determined by imposing rotational invariance in the internal space together with closure of the Poincaré algebra.