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Effects of vacuum polarization by hadronic and heavy-fermion insertions werethe last unknown two-loop QED corrections to high-energy Bhabha scattering andhave been first announced in \cite{Actis:2007fs}. Here we describe thecorrections in detail and explore their numerical influence. The hadroniccontributions to the virtual O(alpha^2) QED corrections to theBhabha-scattering cross-section are evaluated using dispersion relations andcomputing the convolution of hadronic data with perturbatively calculatedkernel functions. The technique of dispersion integrals is also employed toderive the virtual O(alpha^2) corrections generated by muon-, tau- andtop-quark loops in the small electron-mass limit for arbitrary values of theinternal-fermion masses. At a meson factory with 1 GeV center-of-mass energythe complete effect of hadronic and heavy-fermion corrections amounts to lessthan 0.5 per mille and reaches, at 10 GeV, up to about 2 per mille. At the Zresonance it amounts to 2.3 per mille at 3 degrees; overall, hadroniccorrections are less than 4 per mille. For ILC energies (500 GeV or above), thecombined effect of hadrons and heavy-fermions becomes 6 per mille at 3 degrees;hadrons contribute less than 20 per mille in the whole angular region.

Virtual Hadronic and Heavy-Fermion O(alpha^2) Corrections to Bhabha Scattering