In high-energy colliders, discoveries are made possible by improving precision and accuracy of the measured rare events. Precision is maximized by increasing the collider integrated luminosity, whereas accuracy is addressed by minimizing the systematic errors via ad-hoc luminosity calibrations of the detectors.

This thesis contributes to improving the present understanding of the role and the impact of non-factorizable beam distributions on the aforementioned precision and accuracy reach. Starting from a theoretical approach, the concept of the non-factorizable distribution is introduced, originally showing that even Gaussian profiles of distributions matched to linear uncoupled lattices can be non-factorizable. Starting from this observation, the consequences of the losses in a synchrotron and the luminosity in a collider are developed and presented.

A measurement protocol to quantify the non-factorization is devised and, furthermore, it is demonstrated, numerically and experimentally, how non-factorization can be introduced in factorizable distributions via x-y coupling resonances in the presence of space charge. It is then shown experimentally that non-factorization can be transported along the full CERN accelerator chain, confirming that this is an inherent property of the beam distribution and not of the machine lattice.

This work directly contributes to the efforts devoted to improve the quality of the luminosity calibration in the HL-LHC era.