  At the Large Hadron Collider (LHC), absolute luminosity calibrations obtained
by the van der Meer (vdM) method are affected by the mutual electromagnetic
interaction of the two beams. The colliding bunches experience relative orbit
shifts, as well as optical distortions akin to the dynamic-$\beta$ effect, that
both depend on the transverse beam separation and must therefore be corrected
for when deriving the absolute luminosity scale. In the vdM regime, the
beam-beam parameter is small enough that the orbit shift can be calculated
analytically. The dynamic-$\beta$ corrections to the luminometer calibrations,
however, had until the end of Run 2 been estimated in the linear approximation
only. In this report, the influence of beam-beam effects on the vdM-based
luminosity scale is quantified, together with the associated systematic
uncertainties, by means of simulations that fully take into account the
non-linearity of the beam-beam force, as well as the resulting non-Gaussian
distortions of the transverse beam distributions. Two independent multiparticle
simulations, one limited to the weak-strong approximation and one that models
strong-strong effects in a self-consistent manner, are found in excellent
agreement; both predict a percent-level shift of the absolute pp-luminosity
values with respect to those assumed until recently in the physics publications
of the LHC experiments. These results also provide guidance regarding further
studies aimed at reducing the beam-beam-related systematic uncertainty on
beam-beam corrections to absolute luminosity calibrations by the van der Meer
method.
