An iterative, dynamically stabilized method of data unfolding

TL;DR

The paper addresses unfolding of experimental data distorted by detector effects, introducing an iterative framework that uses a regularization function to separate real deviations from statistical fluctuations and to control bin-to-bin correlations. It combines Monte Carlo normalization, dynamic transfer-matrix improvement, and background fluctuation estimation within a single coherent strategy, demonstrated through both a complex, realistic scenario and a simplified toy example with thorough parameter studies. The approach provides a robust, generalizable tool for high-energy physics data analysis, enabling reliable reconstruction of true spectra while enabling error estimation and systematic studies. Practical guidelines for parameter tuning, validation via toy simulations, and extensions to multi-dimensional problems are discussed, and the authors provide code upon request.

Abstract

We propose a new iterative unfolding method for experimental data, making use of a regularization function. The use of this function allows one to build an improved normalization procedure for Monte Carlo spectra, unbiased by the presence of possible new structures in data. We are able to unfold, in a dynamically stable way, data spectra which can be strongly affected by fluctuations in the background subtraction and simultaneously reconstruct structures which were not initially simulated. This method also allows one to control the amount of correlations introduced between the bins of the unfolded spectrum, when the transfers of events correcting the systematic detector effects are performed.

Figures (16)

• Figure 1: Behaviour of the functions $f_{1..8}$ with respect to ${\Delta x}/{(\lambda \sigma )}$.
• Figure 2: Model $\bar{A}$ of transfer matrix. Here, for display reasons, the bins are four times larger than the real ones (an average was computed inside squares of $4X4$ initial bins).
• Figure 3: Normalization relative improvement limits as a function of $\lambda_N$, without background or with the usual background value, obtained after, at most, from left to right, 30, 50 and respectively 200 steps.
• Figure 4: Normalization relative improvement limits as a function of $\lambda_N$, without background or with a background twice less (left), twice larger (middle) and four times larger (right) than usual. In the right figure, only the upper limit of the normalization improvement with background is visible. These improvement values were obtained after, at most, 50 steps.
• Figure 5: Distance between the unfolding result and the true spectrum plus background fluctuations (left column), distance between the final reconstructed MC and the data minus the events to be subtracted (middle column), and the optimal number of steps (right column). These plots were obtained for $\lambda_S = 3$ (top line), $\lambda_S = 5$ (middle line) and $\lambda_S = 7$ (bottom line).