Infrared structure of the leading conformal contribution to the electromagnetic vertex function

Abstract

We treat the infrared problem directly related to the asymptotic behavior of the form factor of a particle belonging to the fermion-antifermion channel, with anomalous dimension $\overline{d}$. For $\overline{d}<2$ we relate it to the off-shell vertex function; for $\overline{d}>2$ we examine the triangle graph which is considered to be the most infrared divergent. We show that the leading ${\ensuremath{\gamma}}_{5}$-even conformal contribution to the wave function does not give rise to infrared divergences, provided the dimensions of the various fields satisfy the conformal bounds. Thus the ensuing contribution to the asymptotic form factor is ${(\ensuremath{-}{q}^{2})}^{1\ensuremath{-}\overline{d}}$.