XY Factorization Bias in Luminosity Measurements
For most high-precision experiments in particle physics, it is essential to know the luminosity at highest accuracy. The luminosity is determined by the convolution of particle densities of the colliding beams. In special van der Meer transverse beam separation scans, the convolution function is sampled along the horizontal and vertical axes with the purpose of determining the beam convolution and getting an absolute luminosity calibration. For this purpose, the van der Meer data of luminometer rates are separately fitted in the two directions with analytic functions giving the best description. With the assumption that the 2D convolution shape is factorizable, one can calculate it from the two 1D fits. The task of XY factorization analyses is to check this assumption and give a quantitative measure of the effect of nonfactorizability on the calibration constant to improve the accuracy of luminosity measurements. \newline We perform a dedicated analysis to study XY non-factorization on proton-proton data collected in 2022 at $\sqrt{s} = 13.6$~TeV by the CMS experiment. A detailed examination of the shape of the bunch convolution function is presented, studying various biases, and choosing the best-fit analytic 2D functions to finally obtain the correction and its uncertainty.