  We present a dispersion relation formalism to calculate a massive scalar
two-loop vertex function. Such calculation is of direct relevance in the
evaluation of the hadronic light-by-light contribution to the muon's anomalous
magnetic moment due to meson poles. The discontinuity of the two-loop diagram
is obtained by a sum of two- and three-particle cut contributions, which
involve a phase space integration over the physical intermediate states. The
real part of the vertex function is subsequently reconstructed through
evaluation of a dispersion integral. We explicitly demonstrate that the
dispersive formalism yields exactly the same result as the direct two-loop
calculation.
