Nonfactorization in Van der Meer scans in Run 2

The luminosity measurement of the CMS experiment is calibrated with Van der Meer (VdM) scans in special LHC fills. From two such scans in orthogonal directions (along the $x$ and $y$ axis of the CMS coordinate system), the overlap area of the proton density of the two beams is measured. This method neglects possible correlations between the $x$ and $y$ dependence of the beam proton densities, leading to a bias of the VdM measurement. In Run~2, the CMS experiment employed four different methods to assess the size of this nonfactorization bias and to derive a correction on the VdM result: The beam imaging method, the offset scan analysis, the diagonal scan analysis, and the beamspot evolution analysis. This note presents performance results of all four methods.