  We provide an exact calculation of next-to-next-to-leading order (NNLO)
massive corrections to Bhabha scattering in QED, relevant for precision
luminosity monitoring at meson factories. Using realistic reference event
selections, exact numerical results for leptonic and hadronic corrections are
given and compared with the corresponding approximate predictions of the event
generator BabaYaga@NLO. It is shown that the NNLO massive corrections are
necessary for luminosity measurements with per mille precision. At the same
time they are found to be well accounted for in the generator at an accuracy
level below the one per mille. An update of the total theoretical precision of
BabaYaga@NLO is presented and possible directions for a further error reduction
are sketched.
