Analytic renormalization of massless theories

It is shown that analytic renormalization in massless theories with dimensionless coupling constants eliminates not only the ultraviolet but also the infrared divergences. It is shown that the analytically renormalized amputated coefficient function of an arbitrary two-point diagram of a theory of this class can be represented in the form $G(q)=\displaystyle\sum_{r=0}^MP^r(q)\ln^r\frac{q^2+i0}{\mu^2}$, where $P^r(q)$ are homogeneous polynomials of second degree for the boson external lines and of the first degree for the fermion external lines.