Calibration of electromagnetic shower features in the CMS calorimeter with machine-learning techniques

Monte Carlo simulations are used extensively in high-energy particle physics analyses. However, an incomplete description of the underlying physics can lead to significant discrepancies between observables measured in simulated and collision data. To mitigate potential biases arising from such mismodelling, it is essential to calibrate simulations to data. This paper presents two novel calibration methods based on machine-learning techniques: a reweighting approach, which employs a classifier to learn the ratio of probability density functions between simulation and data; and a normalising-flow approach, which learns a high-dimensional transformation to map simulation to data. Compared to traditional calibration methods, both approaches offer continuous, unbinned corrections across high-dimensional feature spaces, enabling improved global agreement with data. The techniques are demonstrated in the context of correcting the features of simulated electromagnetic showers in the CMS calorimeters, using proton-proton collision data collected during 2022 at $\sqrt{s}$ = 13.6 TeV, corresponding to an integrated luminosity of 26.7 fb$^{-1}$. The strengths and limitations of the two methods are compared.