Virtual Compton scattering off spin-zero particles at low energies

We discuss the low-energy behaviour of the virtual Compton scattering amplitude off a spin-zero target. We first compare various methods of obtaining a low-energy expression based either on the soft-photon approximation or the use of Ward-Takahashi identities. We point out that structure-dependent terms are defined with respect to a low-energy approximation of the pole terms, which commonly is separated from the full amplitude. We derive a general expression for the structure-dependent terms in an expansion in terms of the momenta k(1) and k(2) of the initial and final virtual photon, respectively, up to and including terms of order O(k(4)). At order O(k(2)) two terms appear that are related to the usual electric and magnetic polarizabilities of real Compton scattering. At order O(k(4)) we find nine new structures of which five can only be determined using virtual photons.