# A response-matrix-centred approach to presenting cross-section measurements

## TL;DR

This paper introduces a response-matrix-centered forward-folding method for presenting cross-section measurements, offering an alternative to unfolding that simplifies detector effects modeling and includes a new Python software framework, ReMU.

## Contribution

It presents a novel forward-folding approach using response matrices and introduces ReMU, a Python package for constructing and applying these matrices in cross-section analyses.

## Key findings

- Response matrices effectively model detector effects.
- ReMU simplifies the use of response matrices in data analysis.
- The approach allows direct comparison of model predictions with data.

## Abstract

The current canonical approach to publishing cross-section data is to unfold the reconstructed distributions. Detector effects like efficiency and smearing are undone mathematically, yielding distributions in true event properties. This is an ill-posed problem, as even small statistical variations in the reconstructed data can lead to large changes in the unfolded spectra. This work presents an alternative or complementary approach: the response-matrix-centred forward-folding approach. It offers a convenient way to forward-fold model expectations in truth space to reconstructed quantities. These can then be compared to the data directly, similar to what is usually done with full detector simulations within the experimental collaborations. For this, the detector response (efficiency and smearing) is parametrised as a matrix. The effects of the detector on the measurement of a given model is simulated by simply multiplying the binned truth expectation values by this response matrix. Systematic uncertainties in the detector response are handled by providing a set of matrices according to the prior distribution of the detector properties and marginalising over them. Background events can be included in the likelihood calculation by giving background events their own bins in truth space. To facilitate a straight-forward use of response matrices, a new software framework has been developed: the Response Matrix Utilities (ReMU). ReMU is a Python package distributed via the Python Package Index. It only uses widely available, standard scientific Python libraries and does not depend on any custom experiment-specific software. It offers all methods needed to build response matrices from Monte Carlo data sets, use the response matrix to forward-fold truth-level model predictions, and compare the predictions to real data using Bayesian or frequentist statistical inference.