Heavy mass expansion, light-by-light scattering through pointlike quanta, and the anomalous magnetic moment of the muon

Contributions from light-by-light scattering to ${(g}_{\mu }-2)/2,$ the anomalous magnetic moment of the muon, are mediated by the exchange of charged fermions or scalar bosons. Assuming large masses M, pointlike couplings for the virtual particles and employing the technique of large mass expansion, analytical results are obtained for virtual fermions and scalars in the form of a series in ${(m}_{\mu }{/M)}^2.$ This series is well convergent even for the case ${M=m}_{\mu }.$ For pointlike virtual fermions, the expansion confirms published analytical formulas. For virtual scalars, the result can be used to evaluate the contribution from pointlike charged pions. In this case our result confirms already available numerical evaluations; however, it is significantly more precise.