  We revisit a nearly ten-year old controversy on the diphoton decay of the
Higgs particle. To a large extent, the controversy turned around the respective
merits of the regularization techniques employed. The novel aspect of our
approach is that no regularization techniques are brought to bear: we work
within the Bogoliubov--Epstein--Glaser scheme of renormalization by extension
of distributions. Solving the problem actually required an expansion of this
method's toolkit, furnished in the paper.
