  We present a fully differential calculation of lepton pair production, taking
into account the dominant next-to-next-to-leading order QED corrections as well
as next-to-leading order electroweak and polarisation effects. We include all
lepton masses, hard photon emission, as well as non-perturbative hadronic
corrections. The corresponding matrix elements are implemented in the Monte
Carlo framework McMule. In order to obtain a numerically stable implementation,
we extend next-to-soft stabilisation, a universal technique based on a
next-to-leading-power expansion, to calculations with polarised leptons. As an
example, we show results tailored to the Belle II detector with the current
setup as well as a potential future configuration that includes polarised
beams.
