  Positronium annihilation amplitudes that are computed by assuming a
factorization approximation with on-shell intermediate leptons do not exhibit
good analytical behaviour. Using dispersion techniques, we find new
contributions that interfere with the known results to restore analytical
properties. Those new amplitudes which cannot be obtained using standard
factorized amplitude formalism, contribute at order alpha^2. Therefore they
have to be evaluated before any theoretical conclusion can be drawn upon the
orthopositronium lifetime puzzle.
