XY Factorization Bias in Luminosity Measurements

TL;DR

This paper investigates the XY factorization bias in luminosity measurements for high-energy proton-proton collisions, analyzing non-factorizability effects to improve the precision of luminosity calibration.

Contribution

It provides a detailed analysis of XY non-factorization effects in luminosity calibration using CMS data, quantifying biases and proposing corrections to enhance measurement accuracy.

Findings

Identified non-factorizability effects in the beam convolution shape.

Quantified the impact of XY bias on luminosity calibration.

Proposed correction methods with uncertainty estimates.

Abstract

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.