# A practical way to regularize unfolding of sharply varying spectra with low data statistics

## TL;DR

This paper presents an improved regularization method for unfolding sharply varying spectra with low data statistics, reducing artifacts and producing physically plausible results, applicable to various spectra with similar features.

## Contribution

The paper introduces a novel unfolding regularization technique that uses full Poisson likelihood to improve results for low-statistics, sharply falling spectra.

## Key findings

- Produces continuous, physically plausible unfolded spectra
- Reduces unphysical artifacts and spikes
- Broad applicability to similar spectral data

## Abstract

Unfolding is a well-established tool in particle physics. However, a naive application of the standard regularization techniques to unfold the momentum spectrum of protons ejected in the process of negative muon nuclear capture led to a result exhibiting unphysical artifacts. A finite data sample limited the range in which unfolding can be performed, thus introducing a cutoff. A sharply falling "true" distribution led to low data statistics near the cutoff, which exacerbated the regularization bias and produced an unphysical spike in the resulting spectrum. An improved approach has been developed to address these issues and is illustrated using a toy model. The approach uses full Poisson likelihood of data, and produces a continuous, physically plausible, unfolded distribution. The new technique has a broad applicability since spectra with similar features, such as sharply falling spectra, are common.